From MAILER-DAEMON Fri Oct 4 13:59:10 2002 Return-Path: Received: from acsu.buffalo.edu (deliverance.acsu.buffalo.edu [128.205.7.57]) by linux00.LinuxForce.net (8.12.3/8.12.3/Debian -4) with SMTP id g94Hx6md024645 for ; Fri, 4 Oct 2002 13:59:06 -0400 Message-Id: <200210041759.g94Hx6md024645@linux00.LinuxForce.net> Received: (qmail 27210 invoked from network); 4 Oct 2002 17:58:49 -0000 Received: from listserv.buffalo.edu (listserv@128.205.7.35) by deliverance.acsu.buffalo.edu with SMTP; 4 Oct 2002 17:58:49 -0000 Date: Fri, 4 Oct 2002 13:58:12 -0400 From: "L-Soft list server at University at Buffalo (1.8e)" Subject: File: "GEODESIC LOG9807" To: Chris Fearnley Status: O Content-Length: 805489 Lines: 18193 ========================================================================= Date: Wed, 1 Jul 1998 06:16:21 -0400 Reply-To: monkey@one.net Sender: List for the discussion of Buckminster Fuller's works From: David Anderson Organization: Flying Monkey Software Subject: Re: Design Science In the News MIME-Version: 1.0 Content-Type: text/plain; charset=us-ascii Content-Transfer-Encoding: 7bit How much actual ozone has been lost? Why can't "ozone balloons" be deployed into the upper atmosphere into the holes and burst to replenish what's being destroyed? A worldwide CFC tax might be imposed on those purchasing ozone-depleting chemicals to finance the operation... - Dave Anderson monkey@one.net http://w3.one.net/~monkey P. O. Box 2321 wrote: > [In my universe, the headline would read something like 'Earth Not Doomed > If Design Science Initiative Adopted.'] > > BBC News Online: World > > Monday, June 22, 1998 Published at 17:51 GMT 18:51 UK > > Ozone layer to recover by 2050 > > Ozone layer to recover by 2050 > The ozone layer, which protects the Earth from ultraviolet radiation, will > recover by the middle of the next century - if countries fully implement > an international convention on the use of destructive chemicals, according > to the World Meteorological Organisation. > > The organisation says the thinning of the ozone layer will worsen for the > next few years because of the high emissions of ozone-depleting chemicals > in the last few decades. > > But in its four-yearly report, published on Monday, it says that the trend > can be reversed if the Montreal Protocol regulating their use is fully > implemented. > > The report, compiled by 200 scientists worldwide, underscores the efforts > by countries over the past decade to reduce their emissions of > ozone-depleting chemicals. > > The Montreal Protocol - signed by 132 countries - includes the phasing out > of the production of CFC gases contained in refrigerators and aerosols. > > But the report's optimism that the ozone layer will recover to its level > of 30 years ago by the middle of the next century, is tempered with > caution. > > Firstly. the convention has yet to be fully implemented. The developing > countries will only begin their phase-out of ozone destructive materials > next year and secondly, the report's predictions are based on scientific > models which can change. > > The World Meteorological Organisation also points out that the ozone layer > is currently in its most vulnerable state due to a high concentration of > chemicals built up over the 1970's and 80's. > > The report's authors say it will take another five years before these > chemicals die out. > > The report also says it will not be possible to detect any recovery in the > ozone layer for another 20 years because of changing atmospheric > conditions. ========================================================================= Date: Wed, 1 Jul 1998 13:48:43 -0700 Reply-To: List for the discussion of Buckminster Fuller's works Sender: List for the discussion of Buckminster Fuller's works From: Brian Hutchings Subject: oopsie <> Brian Hutchings 01-JUL-1998 13:48 r001806@pen2.ci.santa-monica.ca.us Subject: the humble p-ions <> Brian Hutchings 30-JUN-1998 1:30 r001806@pen2.ci.santa-monica.ca.us should be able to get to it, later, but I am presntly "trapped in the PEN", with no ability to link to any thing. so, when you say that these p-1 D points can be used "like" a field, with any prime p, do you mean "like a field" -- like a *field*; like the field of complex numbers etc.e.g. ??... as you know, only quaternions & octaves are fieldlike, dysmissing commutativity & then associativity, respectively; there's no 16-ions, conventionally, and certainly no 6-ions, 10-ions or 12-ions! ========================================================================= Date: Wed, 1 Jul 1998 13:51:25 -0700 Reply-To: List for the discussion of Buckminster Fuller's works Sender: List for the discussion of Buckminster Fuller's works From: Brian Hutchings Subject: Consensus "Science" in the News (as all ways) <> Brian Hutchings 01-JUL-1998 13:51 r001806@pen2.ci.santa-monica.ca.us monkeyunit, didn't you read, what I typed?... the putative "hole" is the Wintertime Polar Vortex -- it's night, there, two! SUBJECT: Re: Design Science In the News MESSAGE from =monkey@one.net 01-JUL-19 13:38 How much actual ozone has been lost? Why can't "ozone balloons" be deployed into the upper atmosphere into the holes and burst to replenish what's being destroyed? A worldwide CFC tax might be imposed on those purchasing ozone-depleting chemicals to finance the operation... ========================================================================= Date: Wed, 1 Jul 1998 13:55:08 -0700 Reply-To: List for the discussion of Buckminster Fuller's works Sender: List for the discussion of Buckminster Fuller's works From: Brian Hutchings Subject: Re: El Synopticon <> Brian Hutchings 01-JUL-1998 13:55 r001806@pen2.ci.santa-monica.ca.us oops, little Freudiac Slip; that should read "SynTOPICon", being Huthcins' (no relation, I think) Hundred Fabulous Ideas.... on the wayside, I now know *two* people, who have read the entirety of the _EB_ in their kiddiehood (or as well-read as that might have been !-) ========================================================================= Date: Wed, 1 Jul 1998 18:55:54 GMT Reply-To: List for the discussion of Buckminster Fuller's works Sender: List for the discussion of Buckminster Fuller's works From: Kirby Urner Organization: 4D Solutions Subject: Re: What is Work? (was Re: Energy, Entropy) MIME-Version: 1.0 Content-Type: text/plain; charset=us-ascii Content-Transfer-Encoding: 7bit We all know that VR headgear and the like so far creates a rather low grade experience of reality, is still dependent on primary sensory equipment (e.g. eyes, ears) in any case, and so is not "another reality" in the same intimate sense as we're born into (aka experience). Only Hollywood (the movies) is up to sustaining the myth that VR is so far evolved as to suggest a substitute -- and Hollywood has this capability because film/video is actually further along as a facsimile in some dimensions (VR adds the interactivity and buck-swivel, making those "3D glasses plus lurching seats" the most convincing VR experiences to date). >From a literary point of view, however, it makes sense to follow Hollywood's lead and converge the terminologies of reality and virtual reality a little more, to where the everyday sensorium is indeed a "workstation" or "job site" where energy unscrolls and unfurls, involving us in various twisted plots and stories. This makes sense from a pure physics point of view: energy is a quantity built around the notion of matter in motion, and its expenditure is in "frames of action" (time/size "snapshots" of stuff happening). The primordial experience is of "work" (encompasses "play") with XYZ-CGS abstractions such as "seconds" and "grams" having only secondary (derivative) meanings, primally anchored in the more generic sense of "change" or "flux" (signified by the greek letter DELTA). Thinking of your everyday "sphere" or "mindset" as VR headgear and a setting for "work" (energy expenditure through time) with the rate of work getting done related to "power" (rate of energy expense), gets you closer to the motherboard metaphor. Electromagnetic energy derived from spinning twisted coils through fields, carries heavy duty momentum (as from a river flowing) to your workstation, where "gears" (chipsets) transform the pumped momentum into usable (switchable) channels. A computer motherboard is similar to a water wheel, taking a cascade of downhill-flowing momentum and making it turn something, which is in turn linked to various gizmos -- which gizmos are software-programmable in the case of a computer. What's important to communicate is that a solar gradient is turning the "big wheels" which keep the rivers flowing (evaporation, wind patterns, condensation), such that a workstation is "riding the grade" of solar energy "flowing out into space" from source (fusion) to sink (partial vacuum) or ground. The various individual motherboards, or workstations, integrate into a vast telecommunications system which is connected around circumferentially (a "spherical motherboard") -- this is "motherboard earth", a metaphor designed to take its place alongside "spaceship earth" as a conceptual tool (in this case designed to connote "fragile, delicate, sophisticated, programmable, switchable"). "Motherboard earth" is convergent with "ecosystem" in that the humanly contrived portions are just "more programming" (human architecture or electronics -- i.e. "architectronics" -- different than "architectonics"). So whether or not you are actually sitting at a keyboard and screen (cell-silicon interface devices in a bio-metalic hybrid circuitry), you can look around, take in your "sensorium" and say to yourself "this is my workstation, a place to get the job done" (whatever "job" might mean in your case). For further reading: http://www.teleport.com/~pdx4d/motherboard.html http://www.teleport.com/~pdx4d/gst1.html http://www.inetarena.com/~pdx4d/ocn/calculus2.html http://www.teleport.com/~pdx4d/gstuniv.html http://www.inetarena.com/~pdx4d/outline2.html --------------------------------------------------------- Kirby T. Urner http://www.teleport.com/~pdx4d/kirby.html 4D Solutions http://www.teleport.com/~pdx4d/ [PGP OK] --------------------------------------------------------- ========================================================================= Date: Fri, 3 Jul 1998 13:57:31 +1200 Reply-To: List for the discussion of Buckminster Fuller's works Sender: List for the discussion of Buckminster Fuller's works From: cath sheard Subject: Cookie recipe - free with good reason! Comments: To: Sandra Robinson Comments: cc: Stewart & Sharyn Crilley , Rob Lusher , Rowan Crawford , Patrick G Salsbury , chat MIME-Version: 1.0 Content-Type: text/plain; charset="iso-8859-1" Content-Transfer-Encoding: 7bit There is a Neiman-Marcus cookie recipe at the very bottom of this message. Enjoy! My daughter & I had just finished a salad at Neiman-Marcus Cafe in Dallas & decided to have a small dessert. Because both of us are such cookie lovers, we decided to try the "Neiman-Marcus>Cookie." {EDITORIAL COMMENT: Neiman's is a VERY EXPENSIVE department store in the States.} It was so excellent that I asked if they would give me the recipe and the waitress said with a small frown, "I'm afraid not." "Well, I said, would you let me buy the recipe?" With a cute smile, she said,"Yes." I asked how much, and she responded, "Only two fifty. It's a great deal!" I said with approval, just add it to my tab. Thirty days later, I received my VISA statement from Neiman-Marcus and it was $285.00. I looked again and I remembered I had only spent $9.95 for two salads and about $20.00 for a scarf. As I glanced at the bottom of the statement, it said,"Cookie Recipe - $250.00" That's outrageous!! I called Neiman's Accounting Dept. and told them the waitress said it was "two-fifty," which clearly does not mean "two hundred and fifty dollars by any *POSSIBLE* interpretation of the phrase. Neiman-Marcus refused to budge. They would not refund my money, because according to them, "What the waitress told you is not our problem. You have already seen the recipe - we absolutely will not refund your money." At this point." I explained to her the criminal statutes which govern fraud in Texas, I threatened to refer them to the Better Business Bureau and the State's Attorney General for engaging in fraud. I was basically told, "Do what you want, we don't give a crap, and we're not refunding your money." I waited, thinking of how I could get even, or even try and get any of my money back. I just said, "Okay, you folks got my $250, and now I'm going to have $250.00 worth of fun." I told her that I was going to see to it that every cookie lover in the United States with an e-mail account has a $250.00 cookie recipe from Neiman-Marcus...for free. She replied, "I wish you wouldn't do this." I said, "Well, you should have thought of that before you ripped me off," and slammed down the phone on her. So here it is!!! Please, please, please pass it on to everyone you can possibly think of. I paid $250 for this...I don't want Neiman-Marcus to ever get another penny off of this recipe.... (Recipe may be halved) 2 cups butter 4 cups flour 2 tsp. soda 2 cups sugar 5 cups blended oatmeal (Measure oatmeal and blend in a blender to a fine powder.) 24 oz. chocolate chips 2 cups brown sugar 1 tsp. salt 1- 8 oz. Hershey Bar (grated) 4 eggs 2 tsp. baking powder 2 tsp. vanilla 3 cups chopped nuts (your choice) Cream the butter and both sugars. Add eggs and vanilla; mix together with flour, oatmeal, salt, baking powder, and soda. Add chocolate chips, Hershey Bar and nuts. Roll into balls and place two inches apart on a cookie sheet. Bake for 10 minutes at 375 degrees. Makes 112 cookies. Have fun!!! This is not a joke --- this is a true story. Ride free citizens! ========================================================================= Date: Wed, 1 Jul 1998 22:18:57 -0700 Reply-To: mburr@halcyon.com Sender: List for the discussion of Buckminster Fuller's works From: Michael Burr Organization: The Renaissance Man Wanna-Be Club Subject: Re: Cookie recipe - free with good reason! MIME-Version: 1.0 Content-Type: text/plain; charset=us-ascii Content-Transfer-Encoding: 7bit cath sheard wrote: > > There is a Neiman-Marcus cookie recipe at the very bottom of this message. > Enjoy! Incredible!! This tired old gag has been circulating around the net for 10 years... and there are still people who will propagate it! Simply Incredible!! ----------------------------------------------------------------- Michael N. Burr Renaissance Man Wanna-Be, Issaquah, WA ========================================================================= Date: Thu, 2 Jul 1998 01:01:14 GMT Reply-To: List for the discussion of Buckminster Fuller's works Sender: List for the discussion of Buckminster Fuller's works From: Kirby Urner Organization: 4D Solutions Subject: Re: CubeWorld: addinng dimensions MIME-Version: 1.0 Content-Type: text/plain; charset=us-ascii Content-Transfer-Encoding: 7bit >You are quite right, any three non-coplanar lines can define all the >volume there is. But the unit volumes will be uh tetrahedrals (guess) >of some sort. Opposite angles wouldn't match. And unless things >distort about the point of rotation in such a space you could sense the >unequal angles. > Making the regular tetrahedron a unit of volume is not a bad move. Turns out the octahedron of same edge, complements when filling space, has a volume of precisely 4 (relative to tet unit), cube volume 3 (edge=face diagonal) and rhombic dodecahedron (a spacefiller) a volume of precisely 6. >Or maybe you couldn't. A orthogonal set of axis will make a more >usefull and accurate measure, though. > I have no problem with XYZ as a useful apparatus. However, the tetrahedron is symmetric about the origin in that its 4 vectors through vertices divide space into 4 equal regions (quadrants). You can define a coordinate system game with 4-tuples instead of 3-tuples, and avoid the need for "vector reversal" (multiplication by negatives) to span volume. See: http://www.teleport.com/~pdx4d/quadrays.html >As you point out, orthogonality is not a requirement, just 3 non >coplanar lines are enough. > > Nick Lindan PS: Re chirality of tetrahedron and zigzag forming with mirror image, that was with reference to the equiangular tet, not just any 720 degree system of 4 triangles. --------------------------------------------------------- Kirby T. Urner http://www.teleport.com/~pdx4d/kirby.html 4D Solutions http://www.teleport.com/~pdx4d/ [PGP OK] --------------------------------------------------------- ========================================================================= Date: Thu, 2 Jul 1998 21:52:06 +1200 Reply-To: List for the discussion of Buckminster Fuller's works Sender: List for the discussion of Buckminster Fuller's works From: MA & ALM Thompson Subject: Re: Cookie recipe - free with good reason! Comments: To: chat@massey.ac.nz, Sandra Robinson Comments: cc: Stewart & Sharyn Crilley , Rob Lusher , Rowan Crawford , Patrick G Salsbury In-Reply-To: <01bda625$f0e9d920$LocalHost@cathandtony> MIME-Version: 1.0 Content-Type: text/plain; charset="iso-8859-1" Content-Transfer-Encoding: 7bit Cath Many thanks. We'll be only too happy to give it a go. Michael & Ann Thompson ========================================================================= Date: Wed, 1 Jul 1998 22:56:10 -0800 Reply-To: List for the discussion of Buckminster Fuller's works Sender: List for the discussion of Buckminster Fuller's works From: "Clifford J. Nelson" Organization: gte.net Subject: RBF Mathematica Notebooks Mime-Version: 1.0 Content-Type: text/plain; charset=US-ASCII Content-Transfer-Encoding: 7bit Download MathReader 3.0 from mathsource and you can look at the Mathematica 3.0 notebooks which are about the "Synergetics coordinate system" that Bucky wrote about in Synergetics, Synergetics 2 . http://www.mathsource.com/cgi-bin/msitem?0209-450 MathReader 3.0 is somewhere on: http://www.mathsource.com Cliff Nelson ========================================================================= Date: Thu, 2 Jul 1998 11:11:19 -0700 Reply-To: List for the discussion of Buckminster Fuller's works Sender: List for the discussion of Buckminster Fuller's works From: Kirby Urner Subject: Re: RBF Mathematica Notebooks Comments: cc: synergetics-l@teleport.com In-Reply-To: <6nfbiu$diq$1@news-2.news.gte.net> Mime-Version: 1.0 Content-Type: text/plain; charset="us-ascii" At 10:56 PM 7/1/98 -0800, you wrote: >Download MathReader 3.0 from mathsource and you can look at the Mathematica >3.0 notebooks which are about the "Synergetics coordinate system" that >Bucky wrote about in Synergetics, Synergetics 2 . > The synergetics coordinate system consists of an isotropic vector matrix representing a nonexperiential equilibrious state which, perturbed, gives rise to energy ripples propagating omnidirectionally by means of a space-filling jitterbug disturbance.[1] Specific to any center in the IVM is a concentric hierarchy of progressively larger polyvertexial systems or networks (getting away from the "solid wall" polyhedral conventions), and one of Fuller's innovations was to recalibrate this hierarchy using the tetrahedron as a volumetric unit, and revectoring his "dimension" signifier accordingly (the tetrahedron is 4D in synergetics).[2] Central to synergetics is U=MP, meaning Universe isn't just its physicality (P), but records information or sense (much as magnetic media digitally encode software), i.e. has a "metaphysical" component (M). Our experiences entwine both M and P components and the "more with less" gradient (ephemeralization) has to do with ascending a learning curve vis-a-vis the generalized principles (M), such that we can do more work with less time/energy (P).[3] This central M vs. P distinction is reflected in the coordinate system in the angle vs. frequency distinction. Purely angularly defined systems have no specific scale and are conceptual independently of any energy involvement (the so-called Platonic polyhedra are patterns first and foremost, with any special case models, some of them pre-dating Plato, being physical and therefore frequenced (i.e. characterized by oscillation or disturbance within the IVM)). The angular-prefrequency pattern aspect (M) is identified as 4D in Synergetics. The frequenced instantiations of pattern in scaled, energy-involved, twisted scenarios are 4D+ (more than 4D) i.e. have the added aspect of time-size, persistence in spacetime. Energy turns generalizations to special case instantiations. Experience, information, is sensory and special case, but relates back to principles via a pyramid of generalizations.[4] Synergetics is a philosophical language and capturing all this meaning and nuance is difficult if not impossible using the highly crypto-compressed notations of the mathematicians. Fuller stayed with a more prose-style semantics for a reason: he was communicating the subject-matter of the humanities in addition to incorporating scientifically omnitriangulated information. In this sense, its "coordinate system" is self- contained -- a built-in feature of the language used to define synergetics and its concepts. 'Synergetics' as published in 2 volumes (now on the web) is not "incomplete" because largely devoid of crypto-compressed notations -- it is a work outside of that culture, and deliberately so. However, that shouldn't keeping explorers like Cliff Nelson from inventing new gizmos, especially those embedded in computer hardware, which will take off from Fuller's original work and give us new tools for coordinating our systems in Universe -- including building more bridges between the math-sciences and humanities. God knows we could use some more intelligent coordinating in this chaotic, fecund and pell-mell pattern integrity we call "humanity" aboard Spaceship Earth. ==== Notes: [1] the rigid-rod space-filling jitterbug is a mechanical model and actually pushes centers further apart during icosaphase. A more fluid model uses alternate IVMs with spheres (expanding) in voids between other (shrinking) spheres. [2] see http://www.teleport.com/~pdx4d/terms.html#4d [3] see http://www.teleport.com/~pdx4d/gst2.html [4] see http://members.xoom.com/Urner/working2.html see http://members.xoom.com/Urner/working4.html ========================================================================= Date: Fri, 3 Jul 1998 01:49:50 -0700 Reply-To: List for the discussion of Buckminster Fuller's works Sender: List for the discussion of Buckminster Fuller's works From: Brian Hutchings Subject: RBF Mathematica Notebooks MESSAGE from ="List 03-JUL-1998 1:20 Download MathReader 3.0 from mathsource and you can look at the Mathematica 3.0 notebooks which are about the "Synergetics coordinate system" that Bucky wrote about in Synergetics, Synergetics 2 . http://www.mathsource.com/cgi-bin/msitem?0209-450 MathReader 3.0 is somewhere on: http://www.mathsource.com Cliff Nelson - - - - - <> Brian Hutchings 03-JUL-1998 1:49 r001806@pen2.ci.santa-monica.ca.us y oh, come-on; go for the prose-poem! ========================================================================= Date: Fri, 3 Jul 1998 13:26:47 -0700 Reply-To: List for the discussion of Buckminster Fuller's works Sender: List for the discussion of Buckminster Fuller's works From: Brian Hutchings Subject: Science Friday on the Beach (day of the baskers ?-) <> Brian Hutchings 03-JUL-1998 13:26 r001806@pen2.ci.santa-monica.ca.us very fruitful beachtalk, folks; please, send that author's address, or forward this to him, as I may not be able to get to his site, www.topbeaches.com, soon. as was said about the numbers of people that live, at the coast, this is an implied bias on the supposed retreat or advance of continental glaciers; however, this was the first that I heard the pointing-out of *midlattitude* glaciers, and that is another important bias, in terms of *civilized* observations. if you use sources, such as satellites, you get a not-so-melting impression, although they *do* show some apparent equatorial "warming" -- minus the bias of "urban heat Islands" (UHI; most writing on this does not acknowledge the burning of "fossilized" fuels, either, which only increases, if the weather gets colder .-) there may, as yet, be found reasons for the slight, apparent changes in the level of sea re the beach, although such "consensus" groups as the IPCC simply do not seriously assess the data that is available, if sparsely, from prior centuries, and they rely profoundly upon computerized simulacra (these admissions are found, in their assembled reports, though not in the "executive summaries"; "95% confidence" is particularly poignant, giving a statistical gloss to a political committee, if you consider that the 95% figure that is so-often used, is perfectly arbitrary -- a "round figure" in the base of ten [recall, when the "second-hand smoke" EPA meta-study used 10%, or 90% "confidence-level", which was well-justified for assessing little-kids-who-cannot-choose, but some folks made a big deal over that]). for instance, there have been a few, good "mainstream" papers in *Science* and in *Nature*, using an underwater-volcanic hypothesis to account for El Nino, instead of putative relations to "global" warming, or the sloshing of winds and currents. to recapitulate, if "glass-house" gasses effect the tropical regions, more, as one would expect, then the resultant greater *differential* between poles & equator would bring larger extremes of weather; hotter summers, yes, but also colder winters -- except in the middle of cities, for the latter. also, you may get transient melting of coastal glaciers, like the Hubbard Glacier in Northwestern Alaska, as the weather-she-changes! -- Shakespeare'd dead -- long-live the spear-shaker! (June 15th issue of *NF*; call 800/453-4108) ========================================================================= Date: Fri, 3 Jul 1998 18:44:24 GMT Reply-To: List for the discussion of Buckminster Fuller's works Sender: List for the discussion of Buckminster Fuller's works From: Kirby Urner Organization: 4D Solutions Subject: Re: CubeWorld: addinng dimensions MIME-Version: 1.0 Content-Type: text/plain; charset=us-ascii Content-Transfer-Encoding: 7bit Sej Mac wrote: >It is very difficult, but possible, for a human to see, in his mind's eye, how four >dimensions connect after the fashion of 3 Ds. It is possible for a human to dream a >conceptual (not symbolic) picture of how 11 Ds connect (and curve around on themselves). I >have known a handful of people who have done this while sleeping. Very few physicists or >mathemeticians can do this kind of conceptualization; their understanding is physics-cultural >and mathematic; i.e., they can grasp the equations, but not the picture. > We agree that the "dimension" convention is cultural, but diverge otherwise. My point is I don't need to buy volume is "3D" in the first place. The "height, width, depth" discussion presumes we could have one without the other two, but all my experiences with shapes include my freedom to look from a different angles, at least in principle. Given the observer (camera, viewpoint) is different from the observed (even in "the mind's eye") we're in a volumetric space regardless -- but why do we call it 3D? The most primitive wireframe or signifier of containment is the tetra- hedron (simpler than cube). It has 4 axes protruding from its face centers -- that's four spokes versus the Cartesian 6 (3 plus/minus 180 degree pairs). How about I say volume is 4D? I can even show you a 4D coordinate system: http://www.teleport.com/~pdx4d/quadrays.html The hypercross dogmatists have this cult of "only the very inner circle can visualize..." and hold out their 4-D hypercross as a kind of religious icon, demanding our faith in those with the occult vision. They grip their "Flatland" by Edwin Abbott, not admitting to logical flaws in his notion that we can imagine 2D beings "from the inside" (i.e. with 2D viewpoints). Even a simple line segment implies a canvas (background) and distance from the observer (this line is being viewed) -- and that's volume already (so what is a 2D being seeing that's different?). Yet from this logical impossibility of "Flatland" we're propagandized to make the leap to yet another impossibility: four mutual perpendiculars, the hypercross. Hypercross dogmatics bears the marks of a religious cult, a belief system with an inner circle of occult visionaries (some able to see in "eleven dimensions" or more) and sychophantic brow-beaters dumbing themselves down in an effort to persuade themselves they too can "see" the nonsensical. As I've posted elsewhere, the math makes sense and we can do cave paintings (visuals) to help with 4-tuple (and more) networks, and people can develop their faculties for working the methods (computers make this easier for everyone) -- I don't dispute any of these claims. But even someone like me, who doesn't buy that "volume is XYZ three dimensional" as the only sensible lingo, can play these polytope games while avoiding bewitchment by the more dogmatic practitioners of same. I reserve my awe for the more deserving, sorry. The metaphors relating to polytope geometry are visual because of the analogous methods used. But a different metaphorics, centering around "compression" and "decompression" of shapes vis-a-vis n-tuple databases might be helpful in "deprogramming" cult members tired of being "sucked in" by the false gods of the dogmatists. Did you see 'Life by the Numbers' on PBS? Has this math head gazing at a tesseract for hours then wandering down the street and into a church, to bliss out looking at the stained glass windows (slanting light) and meditate on the transcendent hyperdimensionality of it all. This is what I mean by my claim that "dimension talk" is cultural -- the lay public is very used to going from n-tuple geometry to consideration of the mysterious, the mystical -- it's all so engrained. If a physicist wants to impress an audience (of fundraisers especially), just truck out that "physics is on the brink of discovering a new dimension" and you've got them, wallets open. Just pass the plate. If you study the early 1900s e.g. Linda Henderson's "The Fourth Dimension and Non-Euclidean Geometry in Modern Art" (she gets interviewed for this PBS episode), you see how spirituality started piggy-backing on higher dimensional math early on, with people like Ouspensky and Bragdon leading the charge. That's how hypercubes and tesseracts became the comic book "doors into the unknown" that science fiction writers need (our mathematician in the church was hooked by comix). I have nothing against spirituality or using math lingo to channel humanities content, but get pissed when the hypercross dogmatists refuse to see their practice doing just this i.e. using culturally embedded memes to win market share, whereas those who practice a different (and I'd say in some cases more honest) art are prejudicially adjudged to be "soft" or "unversed" or "self-indulgent" (when it's really their humanities metaphorics that's doing at least half the work -- such hypocrisy!). To be more specific, Bucky Fuller's 'Synergetics' started diverging, terminology-wise, from the evolving "dimension" patter early in the game (he started with "4D Timelock" sending first copy to Bragdon). He paid attention to Einstein and the rest but was crafting a language consistent with other intuitions as well, and came up with consistent usage patterns centering around a tetrahedron as 4D (as well as a unit of volume). But synergetics gets: (a) dismissed as hocus-pocus humanities or (b) twisted into some brand of hypercross dogmatism because the academic mainstream is just too culturally mired/invested to acknowledge another thread, internally consistent, might have branched away from the post-Victorian intellectual chatter in those early 1900s parlors and salons and come up somewhere else much later in the 20th century, germinating a whole alternative outlook and vision not all that beholden to the curriculum gods now arrogantly piloting their juggernaut into the shallows, while ignoring a design science agenda because it appears too steeped in a philosophical language they: (a) do not understand (b) write off as "crazy" (or "close to crazy") because they don't have time to study it (vicious circle: it can't be relevant, because if it were, I would have learned of it by now, but none of my peers know much about it, ergo, it must be of low grade significance and/or quality) -- so welcome to the world overspecialized, every thinker neatly compartmented in a cubicle, trusting somewhere there's a "big picture" or an "invisible hand" which compensates for all this deliberate narrow-mindedness. Obviously I've had it up to here with the self-righteous know-it-alls and vent some of my wrath in 'Synergetics versus Hypercross Dogmatics' at http://www.teleport.com/~pdx4d/hypercross.html Sure, it's easy to paint me as the fanatic, big name curriculum gods as paragons of rationality, and that's how come I get to stay bottled up and marginalized, even though I've done my homework. Unfortunately for the dogmatists, this bottle leaks and alternative memes are seeping through the culture. Sooner or later, 'Synergetics' will no longer be taboo, even in the Ivory Tower, and then maybe we'll get around to doing some real work for a change, instead of twiddling our thumbs and wasting golden opportunities left and right to start providing more comprehensively and anticipatorily for a sustainable future. Kirby --------------------------------------------------------- Kirby T. Urner http://www.teleport.com/~pdx4d/kirby.html 4D Solutions http://www.teleport.com/~pdx4d/ [PGP OK] --------------------------------------------------------- ========================================================================= Date: Fri, 3 Jul 1998 15:09:13 -0700 Reply-To: List for the discussion of Buckminster Fuller's works Sender: List for the discussion of Buckminster Fuller's works From: Kirby Urner Subject: Re: RBF Mathematica Notebooks In-Reply-To: <199807030849.BAA08829@pen2.ci.santa-monica.ca.us> Mime-Version: 1.0 Content-Type: text/plain; charset="us-ascii" > oh, come-on; > go for the prose-poem! > All prose, odd-ball or strait-laced, is decompressed from a core cultural lattice, or poetics if you will, just some is more self-aware about that (as Shakespeare could have told you). Kirby ========================================================================= Date: Fri, 3 Jul 1998 16:33:17 -0700 Reply-To: List for the discussion of Buckminster Fuller's works Sender: List for the discussion of Buckminster Fuller's works From: Brian Hutchings Subject: spooks in geometry <> Brian Hutchings 03-JUL-1998 16:33 r001806@pen2.ci.santa-monica.ca.us yeah; I prefer to read the wordproblemma, before being immersed in the headbucket! as for "tetrahedreality", or tetragonality, Bucky has done a wonderful job of evoking many, many experiments o'thought, using nothing more than "construtable" algegbra, that is, "up" to secondroots, or trigonal ones. you're correct, also right, that we have to relatively decry the tesseriacs, like Heinlein, or the typico-sacrilgious fold-out of Dali (like, if you're going to unfold the hexahedron, Why into a flat cross?... there is a more-symmetrical form, or essentially assymetrical, like the flame-form of Tenen et al.) the Flatlanders and hyperspacers were all, mostly, promoted by the good-to-be-bad folks of the British Psychical Research Society, such as Lord Rayleigh (when the Curies caught them, under the tablecloth, they were quite indignant, about the sensitivity of the medium -- and that was BMcL, Before MacLuhan !-)... you have only to listen to such latter-day, Empire-inflected gurus, like Deepak "continuum mouth" Chopra, to get the flavor of Science as Double-speak, or the "two cultures" paradigmatic, Aristotelian, Descartesian dualism between sceince & art. in spite of his influence by the Dialers and Transcendentalists, and other proponents of the "Enlightenment", Bucky represents a breaking-away from that, I think (therefore, I eat !-) I have to draw the line at "4D as volumetric containment", except that that's what I think; it *defines* volume, which is usefully 3D (although it is *worked* with 4 parameters in homogenous coordinates etc.), as well as "contains" it, in the sense, energetically, of those 4th-power *power* equations in mechanics; as far as I know, Bucky was unaware of the latter, although he *might* have looked them "up", later, Apres MacL. ========================================================================= Date: Fri, 3 Jul 1998 16:48:05 -0700 Reply-To: List for the discussion of Buckminster Fuller's works Sender: List for the discussion of Buckminster Fuller's works From: Brian Hutchings Subject: **** on a roofshingle (ADMburger meets modular carbos) <> Brian Hutchings 03-JUL-1998 16:48 r001806@pen2.ci.santa-monica.ca.us we have til the 7th (at the earliest), when Congress goes back to DC, to lobby them at home, on the subject of the bureaucratic "career" police-state apparatus in the DoJ, and its racist FBI (from its days of establishment, under Charles Bonaparte; see the Freemasonic Lodge in DC, with its Gen.Albert Pike collections, and its lovingly-preserved replica of "Gay" Edgar Hoover's office); see http://www.larouchepub.com/mcdade-murtha_2526.html -- that's on HR#3396, which already has almost 190 sponsors, very bipartisan, which is nice to see, for some thing that is not just another populist, goment-bashing shill. if you want a Geodesic connection, read the article on hte "machine-tool principle" -- thank you! -- > Shakespeare is dead -- long-live Shakespeare! (in *NF* of June 15th; > New Benjamin Franklin Publishing House, 800/453-4108) > > http://www.meru.org > http://www.tarpley.org > http://www.inet.uni-c.dk/~sch-inst/radio.html ========================================================================= Date: Fri, 3 Jul 1998 18:42:32 -0700 Reply-To: List for the discussion of Buckminster Fuller's works Sender: List for the discussion of Buckminster Fuller's works From: Kirby Urner Subject: Re: spooks in geometry Comments: cc: synergetics-l@teleport.com In-Reply-To: <199807032333.QAA12338@pen2.ci.santa-monica.ca.us> Mime-Version: 1.0 Content-Type: text/plain; charset="us-ascii" > I have to draw the line at "4D as volumetric containment", > except that that's what I think; > it *defines* volume, which is usefully 3D (although > it is *worked* with 4 parameters in homogenous coordinates etc.), > as well as "contains" it, in the sense, energetically, > of those 4th-power *power* equations in mechanics; > as far as I know, Bucky was unaware of the latter, although > he *might* have looked them "up", later, Apres MacL. > Volume is usefully navigated using XYZ maybe, but you can buy the XYZ apparatus and leave "D talk" in the dust (don't even bother to read the manual) -- just like Fractals make perfect sense minus the hype re "fractional dimensions" (take it or leave it). The 4D meme in Buckyite poetics is prior to any (x,x,x) typographical claptrap, or even axes (of spin) -- just an observation about inherent fourness of symmetry about the origin when enclosing it minimally. The tetrahedron is the "straight edge sphere" -- the primordial blob with "cutting" edges. The "perfect sphere" meanwhile, violates the "permeability of all surfaces" law, forcing "continua" where mental gymnasts perpetually want it to be, but where experimentalists fail to observe any such. Taking only the positive XYZ rays, the thing sits on a table top, like a tripod, with a 90-90-90 origin-apex (1/8th octa). A single additional axis ("straight up") would do (for mapping the rest of space by tip-to-tail scaling of these four "basis vectors), but symmetry dictates the 180 degree polarization of the initial three into a "negative mirror" three for a total of six (with the mirrors not considered "as basic" because for some reason left is more basic than right -- or vice versa). But that same primitive sixness can be found in the tetrahedron as well -- any open triangle zigzag defines the degrees of freedom you need for volume navigation, be the angles "right" or no. By stretching these 3 you can "snake" to any point. But this 3-vector zigzag is connecting 4 noncoplanar points, and the complementary 3-vectors are inevitably defined -- giving the tetrahedron. So the "3D" of the Cartesians is just a half-quantum (a 3-vector zigzag), one side of a coin (3+3=6). So "3D" I can probably live with (as 1/2 of "6D" -- an edge-focused view vs. the facial/vertexial "4D"). It's just the 0D, 1D, 2D that I don't need. Hand me a flat surface and I can flip it over. Once down to primitive conceptual volume (aka the tetrahedron) you can taketh no further dimensions away, only degrees of freedom (by adding constraints). Synergetics begins with 4D (not building up starting with 0D -- although the "zerovolume tetrahedron" has meaning) and then adds frequency of bringing energy into the picture. People will generally admit that the "ghostly abstract Cartesian frame" is not "energetic" i.e. is "weightless/imaginary" but leave it to Bucky to actually formalize this distinction in his language -- what makes it "philosophical" (because potentially glib about the metaphysical versus physical, whereas "hard science" steers clear -- to its own perpetual befuddlement, as we can't get away from our own experience as humans in Universe). Kirby ========================================================================= Date: Fri, 3 Jul 1998 20:35:41 -0700 Reply-To: nolindan@ix.netcom.com Sender: List for the discussion of Buckminster Fuller's works From: "Nicholas O. Lindan" Organization: ICGNetcom Subject: Re: CubeWorld: addinng dimensions Mime-Version: 1.0 Content-Type: text/plain; charset=us-ascii Content-Transfer-Encoding: 7bit Kirby Urner wrote: > > My point is I don't need to buy volume is "3D" in the first place. > > The most primitive wireframe or signifier of containment is the tetra- > hedron (simpler than cube). It has 4 axes protruding from its face > centers -- that's four spokes versus the Cartesian six Cartesian has 3 orthogonal axis. A tetrahedron has 4 non-orthogonal axis. Tetrahedron loses: too many axis, and axis are of poor quality. In 99.99% of the cases do things the way we do because it is the best way to do them - even when we can't figure out why that is. To come up with a really new approach to something fundamental you have to be a one in a billion. 'Course everybody is a "one in a billion", we just all differ on which one we and other folks are. Nick Lindan ========================================================================= Date: Sat, 4 Jul 1998 00:08:26 -0700 Reply-To: List for the discussion of Buckminster Fuller's works Sender: List for the discussion of Buckminster Fuller's works From: Brian Hutchings Subject: Re: CubeWorld: addinng dimensions MESSAGE from =nolindan@ix.netcom.com 03-JUL-1998 23:48 Kirby Urner wrote: > > My point is I don't need to buy volume is "3D" in the first place. > > The most primitive wireframe or signifier of containment is the tetra- > hedron (simpler than cube). It has 4 axes protruding from its face > centers -- that's four spokes versus the Cartesian six Cartesian has 3 orthogonal axis. A tetrahedron has 4 non-orthogonal axis. Tetrahedron loses: too many axis, and axis are of poor quality. In 99.99% of the cases do things the way we do because it is the best way to do them - even when we can't figure out why that is. To come up with a really new approach to something fundamental you have to be a one in a billion. 'Course everybody is a "one in a billion", we just all differ on which one we and other folks are. Nick Lindan - - - - - <> Brian Hutchings 04-JUL-1998 0:08 r001806@pen2.ci.santa-monica.ca.us I Kant believe, you typed that stuff, Kafka! ========================================================================= Date: Sat, 4 Jul 1998 00:40:27 -0700 Reply-To: List for the discussion of Buckminster Fuller's works Sender: List for the discussion of Buckminster Fuller's works From: Brian Hutchings Subject: knock on clear (D-mention it) <> Brian Hutchings 04-JUL-1998 0:40 r001806@pen2.ci.santa-monica.ca.us well, the "3-vector" open trigonal "trajectory" is also descartesian; he used that, instead of the 3 axes going through a single crossing; the shape thus engnedered is the quadrirectangular tetrahedron, like the A-module or the Mite (I think). the "edge-focus" is tres apropos, if you are thinking of an "atomic" polyhedron, as opposed to a lattice of them; the duals are edge-precessed (with vertices & facets, interchanging). in the lattice, the edges & facets are dual (and vertices dualize with cells). per fractals, let us not take from M.Mandelbrot his big deal.... as for the "straight-edge sphere", Bucky equally enthused for the round-edged tetrahedron. the "perfect sphere" dates to Nicholas de Cusa's "the Game of Spheres" and "on the Quadrature of the Circle" (15th CCE .-)... ther permeability of all spherics (?) is immaterial to the *conception* of the sphere, as the embodiment of "circular action", and of "construtability" -- to maintain the neologism, for a while, which was a mystaque. that is where modern, post-Grecian science has its origins, as perpetuated by Cusa's students, Leonardo and Pacioli, and the Italian Renaissance (Cusa was German; see ?-) thus quoth: to read the manual) -- just like Fractals make perfect sense minus the hype re "fractional dimensions" (take it or leave it). The 4D meme in Buckyite poetics is prior to any (x,x,x) typographical claptrap, or even axes (of spin) -- just an observation about inherent fourness of symmetry about the origin when enclosing it minimally. The tetrahedron is the "straight edge sphere" -- the primordial blob with "cutting" edges. The "perfect sphere" meanwhile, violates the "permeability of all surfaces" law, forcing "continua" where mental gymnasts perpetually want it to be, but where experimentalists fail -- "the end of history" is "up" here: http://www.tarpley.net ========================================================================= Date: Sat, 4 Jul 1998 15:08:19 -0400 Reply-To: skring@banet.net Sender: List for the discussion of Buckminster Fuller's works From: Sej Mac Organization: IBM.NET Subject: Re: CubeWorld: addinng dimensions MIME-Version: 1.0 Content-Type: text/plain; charset=us-ascii Content-Transfer-Encoding: 7bit OOps; pressed the wrong button! Sorry. More later Kirby Urner wrote: > Sej Mac wrote: > ========================================================================= Date: Sat, 4 Jul 1998 02:33:19 GMT Reply-To: List for the discussion of Buckminster Fuller's works Sender: List for the discussion of Buckminster Fuller's works From: Kirby Urner Organization: 4D Solutions Subject: Re: CubeWorld: addinng dimensions MIME-Version: 1.0 Content-Type: text/plain; charset=us-ascii Content-Transfer-Encoding: 7bit "Nicholas O. Lindan" wrote: >Kirby Urner wrote: >> >> My point is I don't need to buy volume is "3D" in the first place. >> >> The most primitive wireframe or signifier of containment is the tetra- >> hedron (simpler than cube). It has 4 axes protruding from its face >> centers -- that's four spokes versus the Cartesian six > >Cartesian has 3 orthogonal axis. A tetrahedron has 4 non-orthogonal >axis. > The Cartesian apparatus has 6 rays spoking out from the origin, the tetrahedron only 4. The 3 positive XYZ rays are helpless to reach all of space without their negative reflections (but these aren't considered as "basic" because left is not equal to right for some silly reason (a cultural convention)). The 3 positive XYZ axes sit on a table-top like a tripod. One more axis sticking up would give us all we need to span volume, but instead we multiply all the tripod vectors by -1 to get three more. We say space is 3D because any 3 noncoplanar vectors in a tip-to- tail open triangle will "snake" between any two points, given unlimited stretching. But these 3 vectors interconnect four vertices, and inevitably define a complementary 3-vector zig-zag to make a tetrahedron. So "3D" refers to a half-tetrahedron set, but the other half is always present. I relate "3D" the tetrahedron's primitive sixness (3+3=6). On that basis, I'll continue speaking about the "3Dness" of conceptual volume ("4D" refers to the 4 faces/vertices, instead of the 3+3 edges). >Tetrahedron loses: too many axis, and axis are of poor quality. > The tetrahedron is simpler than the cube, no question about it. The four axes carve space into 4 equal quadrants, spherically symmetric about the origin. The Cartesian apparatus is over-built by contrast, wasting axes by opposing itself at 180 degrees. Picture a spaceship with 4 rockets aimed towards the vertices of a tetrahedron. A computer to apportion thrust in such a way as to move in any direction (from any A to any B). The Cartesian spaceship has 6 rockets, with pairs redundantly arranged to push against each other. If you add pairs of v-rays (spokes through the tetrahedron's vertices) you get e-rays (spokes through it's mid-edges) and these latter correspond to XYZ. In other words, start with the primitive tetrahedron and its 4 spokes, add all the pairs, and get the 6 spokes of XYZ -- which you may now paint with positive/negative labeling and use as per usual (but without forgetting the tetrahedral genesis i.e. XYZ = e-rays = rays through tetrahedron's mid-edges). >In 99.99% of the cases do things the way we do because it is the best >way to do them - even when we can't figure out why that is. > I have no problem using XYZ and the centuries-worth of games evolved to go with it -- but the "dimension talk" that goes with XYZ is dispensible. You don't need to buy that space is "3D" in order to use Cartesian coordinates (we found a hole in the fence and get to go on all the rides without paying that high price of admission). For a long time humans were biased to think of a rectilinear universe because they're tiny vis-a-vis the giant planetary sphere. Only high seas cultures and inner circle religious never forgot the earth's roundness. As a greek doing post and lintel architecture, you tend to think two columns side-by-side are parallel. But as a New Yorker, you know the World Trade Center towers are slightly further apart at the top. As an astrophysicist, you know that trajectories accelerate inward (convergent), outward (divergent) or around (spiro-orbital). This whole idea of an infinite non-convergent, everywhere parallel frame is metaphysics inherited from flatlanders. A lot of cultures never bought it, never will. >To come up with a really new approach to something fundamental you have >to be a one in a billion. 'Course everybody is a "one in a billion", we >just all differ on which one we and other folks are. > I'm not coming up with anything new. Triangulation, 60 degree coordination, tetrahedral structuring, is ancient, billions of years old, built in to the fabric of nature. Squares are weak, cubes are wobbly. Triangles are strong, tetrahedra stable. Kirby --------------------------------------------------------- Kirby T. Urner http://www.teleport.com/~pdx4d/kirby.html 4D Solutions http://www.teleport.com/~pdx4d/ [PGP OK] --------------------------------------------------------- ========================================================================= Date: Sat, 4 Jul 1998 04:19:30 GMT Reply-To: List for the discussion of Buckminster Fuller's works Sender: List for the discussion of Buckminster Fuller's works From: Kirby Urner Organization: 4D Solutions Subject: Re: CubeWorld: addinng dimensions MIME-Version: 1.0 Content-Type: text/plain; charset=us-ascii Content-Transfer-Encoding: 7bit "Clifford J. Nelson" wrote: >Buckminster Fuller's success makes him "one in a billion". According to his >books Synergetics and Synergetcs 2, all of the polyhedra with atomic >vertices in nature have only rational integer Synergetics coordinates. Citation please. I don't recall anything about "rational integers" which is redundant in any case. Whole number volumes for more shapes, yes (not all of course, and incommensurability ala root-of-2 not swept under the rug). A more Persian approach to mathematics I'd say, by which I mean symbols are terminal (e.g. floating point) or algorithmic -- by which means synergetics gets away from "infinite precision" fictions (so-called "reals") like PI (as if natural phenomena had the time to fully expand it). >Synergetics coordinates are based on the tetrahedron. They can be >transformed into four perpendicular coordinates, but then they won't be >rational integers. > Cliff and I don't agree here as "four perpendicular coordinates" is nonsense to my ears. "Rational integers" also grates, as all integers are rational by definition -- makes it sound like Bucky (author of 'Synergetics') was some kind of dunderhead, which he was not. Kirby --------------------------------------------------------- Kirby T. Urner http://www.teleport.com/~pdx4d/kirby.html 4D Solutions http://www.teleport.com/~pdx4d/ [PGP OK] --------------------------------------------------------- ========================================================================= Date: Sat, 4 Jul 1998 16:12:28 GMT Reply-To: List for the discussion of Buckminster Fuller's works Sender: List for the discussion of Buckminster Fuller's works From: Kirby Urner Organization: 4D Solutions Subject: Re: CubeWorld: addinng dimensions MIME-Version: 1.0 Content-Type: text/plain; charset=us-ascii Content-Transfer-Encoding: 7bit >--------------------------- >Synergetics section 201.03 page 23 : > >Synergetics makes possible a rational, whole number, low-order quantation >of all important geometries of expirience because the tetrahedron, the >octahedron, the rhombic dodecahedron, the cube, and the vector equilibrium >embrace and comprise all of the lattices of all the atoms. >---------------------------- Right, lattices. But when you get to 5-fold symmetry (non-lattice) then you don't have the whole numbers for polys (e.g. icosa = ~18.51). > >A rational integer as opposed to a guassian integer or an algebraic number >integer. Many books use the term rational integer. > You should do more work to define then -- seems to reel in a lot of irrelevancies only to obscure the topic at hand. To me, an integer is zero, any positive whole, or its negative mirror. Simple. > I don't have a section number for this, but, if you are intertested you >can find it yourself. Bucky wrote that Synergetcis coordinates can be >transformed to perpendicular coordinates and vice-versa. > >To me that means that 4 dimensions in one system is 4 dimensions in the >other. > Right, to you -- one of your misunderstandings of the text (I've already supplied the citations). Kirby --------------------------------------------------------- Kirby T. Urner http://www.teleport.com/~pdx4d/kirby.html 4D Solutions http://www.teleport.com/~pdx4d/ [PGP OK] --------------------------------------------------------- ========================================================================= Date: Sat, 4 Jul 1998 16:15:01 GMT Reply-To: List for the discussion of Buckminster Fuller's works Sender: List for the discussion of Buckminster Fuller's works From: Kirby Urner Organization: 4D Solutions Subject: Re: CubeWorld: addinng dimensions MIME-Version: 1.0 Content-Type: text/plain; charset=us-ascii Content-Transfer-Encoding: 7bit Paul Birke wrote: >Hi All > >I have been a big fan of Bucky for years. His discovery of the >coordinates of the Universe I have believed to be a fundamental insight >into nature. But, I had not the impression that he proved a 4D universe >was the one in whihc we live in-but I would like to know if he did. For >my motivation here, I am thinking about a possible 4D universe re Electo >Magnetics. We have to find a place in which to place Electro-Magnetic >Momentum for one! >BTW,I have Synergetics but not Synergetics 2. >Paul Victoria Birke, Electrical Engineer You should read the section entitled "Remoteness of Synergetics Vocabulary". Big barrier to appreciating this work is people come to it after years of schooling in conventional nomenclature and think when Fuller writes "four dimensional" he means "three-D + time" or "four Euclidean dimensions". He does not, and his alternative use, like the standard one, is more definitional -- proved by its ability to get work done in the real world and to integrate seamlessly with the rest of the work. Kirby --------------------------------------------------------- Kirby T. Urner http://www.teleport.com/~pdx4d/kirby.html 4D Solutions http://www.teleport.com/~pdx4d/ [PGP OK] --------------------------------------------------------- ========================================================================= Date: Fri, 3 Jul 1998 19:23:32 -0800 Reply-To: List for the discussion of Buckminster Fuller's works Sender: List for the discussion of Buckminster Fuller's works From: "Clifford J. Nelson" Organization: gte.net Subject: Re: CubeWorld: addinng dimensions Mime-Version: 1.0 Content-Type: text/plain; charset=US-ASCII Content-Transfer-Encoding: 7bit On Fri, Jul 3, 1998 7:35 PM, Nicholas O. Lindan wrote: > >Cartesian has 3 orthogonal axis. A tetrahedron has 4 non-orthogonal >axis. > >Tetrahedron loses: too many axis, and axis are of poor quality. > >In 99.99% of the cases do things the way we do because it is the best >way to do them - even when we can't figure out why that is. > >To come up with a really new approach to something fundamental you >have >to be a one in a billion. 'Course everybody is a "one in a billion", we >just all differ on which one we and other folks are. > > Nick Lindan > Buckminster Fuller's success makes him "one in a billion". According to his books Synergetics and Synergetcs 2, all of the polyhedra with atomic vertices in nature have only rational integer Synergetics coordinates. Synergetics coordinates are based on the tetrahedron. They can be transformed into four perpendicular coordinates, but then they won't be rational integers. Download MathReader 3.0 from mathsource (if you do not already have Mathematica 3.0) and you can look at the Mathematica 3.0 notebooks which are about the "Synergetics coordinate system" that Bucky Fuller wrote about in Synergetics, Synergetics 2 . http://www.mathsource.com/cgi-bin/msitem?0209-450 MathReader 3.0 is somewhere on: http://www.mathsource.com/ What is this version of the "Synergetics coordinate system" called by mathematicians ? Cliff Nelson ========================================================================= Date: Sat, 4 Jul 1998 12:16:08 GMT Reply-To: List for the discussion of Buckminster Fuller's works Sender: List for the discussion of Buckminster Fuller's works From: Paul Birke Organization: @Home Network Subject: Re: CubeWorld: addinng dimensions MIME-Version: 1.0 Content-Type: text/plain; charset=us-ascii Content-Transfer-Encoding: 7bit Hi All I have been a big fan of Bucky for years. His discovery of the coordinates of the Universe I have believed to be a fundamental insight into nature. But, I had not the impression that he proved a 4D universe was the one in whihc we live in-but I would like to know if he did. For my motivation here, I am thinking about a possible 4D universe re Electo Magnetics. We have to find a place in which to place Electro-Magnetic Momentum for one! BTW,I have Synergetics but not Synergetics 2. Paul Victoria Birke, Electrical Engineer ========================================================================= Date: Fri, 3 Jul 1998 23:43:10 -0800 Reply-To: List for the discussion of Buckminster Fuller's works Sender: List for the discussion of Buckminster Fuller's works From: "Clifford J. Nelson" Organization: gte.net Subject: Re: CubeWorld: addinng dimensions Mime-Version: 1.0 Content-Type: text/plain; charset=US-ASCII Content-Transfer-Encoding: 7bit On Fri, Jul 3, 1998 8:19 PM, Kirby Urner wrote: >"Clifford J. Nelson" wrote: > >>Buckminster Fuller's success makes him "one in a billion". According to his >>books Synergetics and Synergetcs 2, all of the polyhedra with atomic >>vertices in nature have only rational integer Synergetics coordinates. > >Citation please. I don't recall anything about "rational integers" >which is redundant in any case. Whole number volumes for more shapes, >yes (not all of course, and incommensurability ala root-of-2 not >swept under the rug). > --------------------------- Synergetics section 201.03 page 23 : Synergetics makes possible a rational, whole number, low-order quantation of all important geometries of expirience because the tetrahedron, the octahedron, the rhombic dodecahedron, the cube, and the vector equilibrium embrace and comprise all of the lattices of all the atoms. ---------------------------- > >>Synergetics coordinates are based on the tetrahedron. They can be >>transformed into four perpendicular coordinates, but then they won't be >>rational integers. >> > >Cliff and I don't agree here as "four perpendicular coordinates" is >nonsense to my ears. "Rational integers" also grates, as all integers >are rational by definition -- makes it sound like Bucky (author of >'Synergetics') was some kind of dunderhead, which he was not. > >Kirby > A rational integer as opposed to a guassian integer or an algebraic number integer. Many books use the term rational integer. I don't have a section number for this, but, if you are intertested you can find it yourself. Bucky wrote that Synergetcis coordinates can be transformed to perpendicular coordinates and vice-versa. To me that means that 4 dimensions in one system is 4 dimensions in the other. Cliff Nelson ========================================================================= Date: Sat, 4 Jul 1998 15:06:54 -0400 Reply-To: skring@banet.net Sender: List for the discussion of Buckminster Fuller's works From: Sej Mac Organization: IBM.NET Subject: Re: CubeWorld: addinng dimensions Comments: To: GEODESIC@LISTSERV.ACSU.BUFFALO.EDU#!rnews0#!rnews0#!rnews0#!rnews0#!rnews9510 MIME-Version: 1.0 Content-Type: text/plain; charset=us-ascii Content-Transfer-Encoding: 7bit Wow! You have extemporaneously packed so much ideation into such a small "volume," that I can scarcely separate out the distinct threads. Also, you are much more up todate on the literature in this particular area, while I almost never read math or topology. But I will do the best I can to respond to your very interesting post---(and maybe that will inspire Kirby Urner wrote: > Sej Mac wrote: > > >It is very difficult, but possible, for a human to see, in his mind's eye, how four > >dimensions connect after the fashion of 3 Ds. It is possible for a human to dream a > >conceptual (not symbolic) picture of how 11 Ds connect (and curve around on themselves). I > >have known a handful of people who have done this while sleeping. Very few physicists or > >mathemeticians can do this kind of conceptualization; their understanding is physics-cultural > >and mathematic; i.e., they can grasp the equations, but not the picture. > > > > We agree that the "dimension" convention is cultural, but diverge > otherwise. > > My point is I don't need to buy volume is "3D" in the first place. The > "height, width, depth" discussion presumes we could have one without the > other two, but all my experiences with shapes include my freedom to look > from a different angles, at least in principle. Given the observer > (camera, viewpoint) is different from the observed (even in "the mind's > eye") we're in a volumetric space regardless -- but why do we call it 3D? > The most primitive wireframe or signifier of containment is the tetra- > hedron (simpler than cube). It has 4 axes protruding from its face > centers -- that's four spokes versus the Cartesian 6 (3 plus/minus > 180 degree pairs). How about I say volume is 4D? I can even show you > a 4D coordinate system: http://www.teleport.com/~pdx4d/quadrays.html > > The hypercross dogmatists have this cult of "only the very inner circle > can visualize..." and hold out their 4-D hypercross as a kind of religious > icon, demanding our faith in those with the occult vision. They grip their > "Flatland" by Edwin Abbott, not admitting to logical flaws in his notion > that we can imagine 2D beings "from the inside" (i.e. with 2D viewpoints). > Even a simple line segment implies a canvas (background) and distance from > the observer (this line is being viewed) -- and that's volume already (so > what is a 2D being seeing that's different?). Yet from this logical > impossibility of "Flatland" we're propagandized to make the leap to yet > another impossibility: four mutual perpendiculars, the hypercross. > > Hypercross dogmatics bears the marks of a religious cult, a belief system > with an inner circle of occult visionaries (some able to see in "eleven > dimensions" or more) and sychophantic brow-beaters dumbing themselves > down in an effort to persuade themselves they too can "see" the nonsensical. > > As I've posted elsewhere, the math makes sense and we can do cave paintings > (visuals) to help with 4-tuple (and more) networks, and people can develop > their faculties for working the methods (computers make this easier for > everyone) -- I don't dispute any of these claims. But even someone like > me, who doesn't buy that "volume is XYZ three dimensional" as the only > sensible lingo, can play these polytope games while avoiding bewitchment > by the more dogmatic practitioners of same. I reserve my awe for the > more deserving, sorry. > > The metaphors relating to polytope geometry are visual because of the > analogous methods used. But a different metaphorics, centering around > "compression" and "decompression" of shapes vis-a-vis n-tuple databases > might be helpful in "deprogramming" cult members tired of being "sucked > in" by the false gods of the dogmatists. > > Did you see 'Life by the Numbers' on PBS? Has this math head gazing > at a tesseract for hours then wandering down the street and into a church, > to bliss out looking at the stained glass windows (slanting light) and > meditate on the transcendent hyperdimensionality of it all. This is > what I mean by my claim that "dimension talk" is cultural -- the lay > public is very used to going from n-tuple geometry to consideration of > the mysterious, the mystical -- it's all so engrained. If a physicist > wants to impress an audience (of fundraisers especially), just truck > out that "physics is on the brink of discovering a new dimension" and > you've got them, wallets open. Just pass the plate. > > If you study the early 1900s e.g. Linda Henderson's "The Fourth > Dimension and Non-Euclidean Geometry in Modern Art" (she gets interviewed > for this PBS episode), you see how spirituality started piggy-backing on > higher dimensional math early on, with people like Ouspensky and Bragdon > leading the charge. That's how hypercubes and tesseracts became the comic > book "doors into the unknown" that science fiction writers need (our > mathematician in the church was hooked by comix). > > I have nothing against spirituality or using math lingo to channel > humanities content, but get pissed when the hypercross dogmatists refuse > to see their practice doing just this i.e. using culturally embedded > memes to win market share, whereas those who practice a different (and > I'd say in some cases more honest) art are prejudicially adjudged to > be "soft" or "unversed" or "self-indulgent" (when it's really their > humanities metaphorics that's doing at least half the work -- such > hypocrisy!). > > To be more specific, Bucky Fuller's 'Synergetics' started diverging, > terminology-wise, from the evolving "dimension" patter early in the game > (he started with "4D Timelock" sending first copy to Bragdon). He paid > attention to Einstein and the rest but was crafting a language consistent > with other intuitions as well, and came up with consistent usage patterns > centering around a tetrahedron as 4D (as well as a unit of volume). > > But synergetics gets: > (a) dismissed as hocus-pocus humanities or > (b) twisted into some brand of hypercross dogmatism > > because the academic mainstream is just too culturally mired/invested > to acknowledge another thread, internally consistent, might have branched > away from the post-Victorian intellectual chatter in those early 1900s > parlors and salons and come up somewhere else much later in the 20th > century, germinating a whole alternative outlook and vision not all > that beholden to the curriculum gods now arrogantly piloting their > juggernaut into the shallows, while ignoring a design science agenda > because it appears too steeped in a philosophical language they: > (a) do not understand > (b) write off as "crazy" (or "close to crazy") because they don't > have time to study it (vicious circle: it can't be relevant, because > if it were, I would have learned of it by now, but none of my peers > know much about it, ergo, it must be of low grade significance and/or > quality) -- so welcome to the world overspecialized, every thinker > neatly compartmented in a cubicle, trusting somewhere there's a "big > picture" or an "invisible hand" which compensates for all this > deliberate narrow-mindedness. > > Obviously I've had it up to here with the self-righteous know-it-alls > and vent some of my wrath in 'Synergetics versus Hypercross Dogmatics' > at http://www.teleport.com/~pdx4d/hypercross.html > > Sure, it's easy to paint me as the fanatic, big name curriculum gods as > paragons of rationality, and that's how come I get to stay bottled up > and marginalized, even though I've done my homework. Unfortunately > for the dogmatists, this bottle leaks and alternative memes are seeping > through the culture. Sooner or later, 'Synergetics' will no longer be > taboo, even in the Ivory Tower, and then maybe we'll get around to > doing some real work for a change, instead of twiddling our thumbs > and wasting golden opportunities left and right to start providing > more comprehensively and anticipatorily for a sustainable future. > > Kirby > > --------------------------------------------------------- > Kirby T. Urner http://www.teleport.com/~pdx4d/kirby.html > 4D Solutions http://www.teleport.com/~pdx4d/ [PGP OK] > --------------------------------------------------------- ========================================================================= Date: Sat, 4 Jul 1998 17:32:42 GMT Reply-To: Rob Johnson Sender: List for the discussion of Buckminster Fuller's works From: Rob Johnson Organization: is in the eye of the beholder Subject: Re: CubeWorld: addinng dimensions In-Reply-To: pdx4d@teleport.com (Kirby Urner) In article <35a1abab.113644956@news.teleport.com>, pdx4d@teleport.com (Kirby Urner) wrote: >Cliff and I don't agree here as "four perpendicular coordinates" is >nonsense to my ears. "Rational integers" also grates, as all integers >are rational by definition -- makes it sound like Bucky (author of >'Synergetics') was some kind of dunderhead, which he was not. I am not defending the article you criticize, but the terms you seem to have trouble with are perfectly sensible. First, four perpendicular coordinates makes perfect sense in any space of four or more dimensions. Of course, in a space of three or fewer dimensions, there are at most three perpendicular coordinates. There are numbers called algebraic integers, which are roots of monic polynomials (those with integer coefficients where the highest order term has coefficient 1). The Golden Ratio, (1+sqrt(5))/2 is an algebraic integer because it is a root of x^2-x-1. It turns out that the sum, difference, and product of any two algebraic integers is also an algebraic integer. One interesting fact is that the only rational algebraic integers are standard integers, thus the term rational integers to differentiate them from the algebraic integers. This is fairly standard terminology. Theorem: all rational algebraic integers are integers. Proof: Suppose p/q, with gcd(p,q) = 1, is a root of the monic polynomial n-1 n --- k x + > c x [1] --- k k=0 Since gcd(p,q) = 1, we can find a and b so that ap + bq = 1. Write p/q as (1-bq)/aq and substitute into [1]: n-1 n --- k 0 = ((1-bq)/aq) + > c ((1-bq)/aq) [2] --- k k=0 Multiply [2] by a^n q^{n-1} to get n n-1 (1-bq) --- k n-k n-k-1 0 = ------ + > c (1-bq) a q [3] q --- k k=0 Since the right summand of [3] is sums of products of integers, it is obviously an integer. That means that the left summand of [3] must also be an integer. Using the binomial expansion on the left summand of [3] we get n n (1-bq) 1 --- n-k k-1 ------ = - + > C(n,k) (-bq) q [4] q q --- k=1 Once again, the right summand of [4] is sums of products of integers, so it is easily seen to be an integer. This means that 1/q is an integer. Since q and 1/q both are integers, q must be 1 or -1, and therefore, p/q is an integer. QED Rob Johnson robjohn9@idt.net ========================================================================= Date: Sat, 4 Jul 1998 17:54:22 GMT Reply-To: List for the discussion of Buckminster Fuller's works Sender: List for the discussion of Buckminster Fuller's works From: Paul Birke Organization: @Home Network Subject: Re: CubeWorld: addinng dimensions MIME-Version: 1.0 Content-Type: text/plain; charset=us-ascii Content-Transfer-Encoding: 7bit Hi All Are there any examples of the use of Fuller's Vector Equilibrium coordinate system in practical application. He basically said here there were 12 preferred directions in the Universe. Maybe 6 "in" and 6 "out". (Bucky always talked about nature being only "in" or "out" and not "up" , "down' or "sideways".) For instance, has someone made a multiple gyroscope based on this system--sort of s Super-gyrosope. Say 6 spinning disks at + rotation and other intervening 6 at - rotation. I have often wondered if this would produce a rather immovable object! Furthermore, could you vector the individual disk rotational speeds to overcome local gravity is the next question I have asked myself! Paul Victor Birke, Electrical Engineer ========================================================================= Date: Sat, 4 Jul 1998 19:06:28 -0400 Reply-To: monkey@one.net Sender: List for the discussion of Buckminster Fuller's works From: David Anderson Organization: Flying Monkey Software Subject: Externally Octet-Trussed Geodesic Patches MIME-Version: 1.0 Content-Type: text/plain; charset=us-ascii Content-Transfer-Encoding: 7bit An extension of the tetra- octa- and icosahedral geodesic octet truss bracing previously explored is presented: the truss is moved to the outside of the geodesic shell. Html tables and vrml worlds are included. http://w3.one.net/~monkey/geodesics/outside -- - Dave Anderson monkey@one.net http://w3.one.net/~monkey ========================================================================= Date: Sun, 5 Jul 1998 14:38:18 -0700 Reply-To: List for the discussion of Buckminster Fuller's works Sender: List for the discussion of Buckminster Fuller's works From: Brian Hutchings Subject: spooks in mapland <> Brian Hutchings 05-JUL-1998 14:38 r001806@pen2.ci.santa-monica.ca.us pi is just a ratio, the "half-parameter" of Gaussian orbital conics; we can equally say that the circumference of an ellipse is unit, and the diameter is pith (1/pi), or that the surface of a sphere is unit, and the diameter, again, pith. the "incommeasurability" and "transcendentali thus be shoved into the other tabular column!... these are merely algebraic or algorithmic ones, if you prefer. as for the quadrants o'space, they require 6 partial planes (planar rays?) to divide them, whereas the 4 planes of the IVM (or "zero-tet") divide space into 14 chunky rays (with trigonal and tetragonal origins), or 7 if considered as if akin to double-cones (if the "zerotet" origin is mad the 4 planes divide space into 15; see, How ?-) as I have previously suggested, Bucky's work is *entirely* euclidean, or UberEuclidean, or what ever, althoug we can argue all night, as to whether he had the right, to assign 3+1 dimensions to space, "primitively" or "pre-time-size"; I think, he does, and this is his essential dysjuncture from Minkowskian phase-hype, and the ultimate tripe of "lightcones" etc.ad vomitorium (viz, a cone is just a quadric, a surface of second-degree .-) as for "real mathematicians", it's more associated with what Loeb reviews as "bcc", body-centered cubical crystals, which is just a convention de l'hexahedron, again. mathematically, you have to go to homogenous co-ordinates, or descartesian+1 parameters in "homogenous" projective space. as well, fourth-degree equations are associated with certain mechanics, which can be intinately portrayed with tetrahedra, some how -- or, perhaps, promiscuously !?! as for the "rational integers", I like the mention of the distinction from the "gaussian" or complex integers, which was really the first attempt to show that number is inherently nonlinear, as in the study of gaussian primes, or the "phi-field" quadratic field, based upon the second root of minus five, I think. in that, "rational integers" are those with no "imaginary" componen n + 0i.... I'm going to save that proof, and attempt it, later; it's over most of our head, I think, and it took me a minute to dyscern your "Epsilon" from pink noise; I should say, not "over our head", but "not our wad o'chew", dear boy! thus quoth: Theorem: all rational algebraic integers are integers. Proof: Suppose p/q, with gcd(p,q) = 1, is a root of the monic polynomial n-1 n --- k x + > c x [1] --- k k=0 Since gcd(p,q) = 1, we can find a and b so that ap + bq = 1. Write p/q as (1-bq)/aq and substitute into [1]: n-1 n --- k 0 = ((1-bq)/aq) + > c ((1-bq)/aq) [2] --- k k=0 Multiply [2] by a^n q^{n-1} to get n n-1 (1-bq) --- k n-k n-k-1 0 = ------ + > c (1-bq) a q [3] q --- k k=0 Since the right summand of [3] is sums of products of integers, it is obviously an integer. That means that the left summand of [3] must also be an integer. Using the binomial expansion on the left summand of [3] we get n n (1-bq) 1 --- n-k k-1 ------ = - + > C(n,k) (-bq) q [4] q q --- k=1 Once again, the right summand of [4] is sums of products of integers, so it is easily seen to be an integer. This means that 1/q is an integer. Since q and 1/q both are integers, q must be 1 or -1, and therefore, p/q is an integer. QED Rob Johnson robjohn9@idt.net -- if politics sucks, Sir George is a White'Hoe [*]; see http://www.tarpley.net * the other, spewing end of a Black Hole, turned inside-out; a 1000 Motes o'L ========================================================================= Date: Sun, 5 Jul 1998 14:48:51 -0700 Reply-To: List for the discussion of Buckminster Fuller's works Sender: List for the discussion of Buckminster Fuller's works From: Brian Hutchings Subject: gyrobrains <> Brian Hutchings 05-JUL-1998 14:48 r001806@pen2.ci.santa-monica.ca.us in 2 words, Hell, no!... take that **** to Art Bell, if you don't mind blodying your digits i'the Touchtone (tm) Syndrome; I mean, I got through, once, and that looks like My Last Chance (well, I did get in a nice, rhetorical dig, which plainly PO'd him --he really does not screen calls; I asked him, If you were the Head Druid, how wouul You, your Lordspaceship, go about employing your minions (on the breeteesh dole, or whatever sort of free lunch is available for the aristocracy) to create a "cropcircle" in the bucolic fields o'corn (no need to do it at night, of course, unless the Moon is full) -- agricCULTurally? thus quoth: For instance, has someone made a multiple gyroscope based on this system--sort of s Super-gyrosope. Say 6 spinning disks at + rotation and other intervening 6 at - rotation. I have often wondered if this would produce a rather immovable object! Furthermore, could you vector the individual disk rotational speeds to overcome local gravity is the next question I have asked myself! Paul Victor Birke, Electrical Engineer ========================================================================= Date: Sun, 5 Jul 1998 14:55:58 -0700 Reply-To: List for the discussion of Buckminster Fuller's works Sender: List for the discussion of Buckminster Fuller's works From: Brian Hutchings Subject: gyrobrains <> Brian Hutchings 05-JUL-1998 14:55 r001806@pen2.ci.santa-monica.ca.us ah, PVB, EE, let me flesh that nasty reposte, "out". in the headmonted victual sidereality, AKA the Rectal Display Unit, *acceleration* cannot be simulated, no-matter how-many axes are employed in the spincycle; so, the usual instruction is, Skip lunch or clean-up after yourself! (or, don't "ask yourself" with an exclamation-point .-) -- dungeons & dragons and Sir George: http://www.tarpley.net ========================================================================= Date: Sun, 5 Jul 1998 15:38:25 -0700 Reply-To: List for the discussion of Buckminster Fuller's works Sender: List for the discussion of Buckminster Fuller's works From: Brian Hutchings Subject: Windowless'00 (MS-Kubikle (tm)) <> Brian Hutchings 05-JUL-1998 15:38 r001806@pen2.ci.santa-monica.ca.us re the sphere, I guess, we don't want to mix the dimensionally-incommeasurable surface, and the diameter. to get pi; eh?... so, naturally, we ratio thte surface to the equatorial plane, through which the "pole" pierces, getting 4; consequently, the 4 "bowtie" planes of the "vector equilibrium, AKA the cuboctahedron of the Greeks, or the semiregular dodecagon of Bucky's "posthumous" useage. I don't know, if there is any "spheric" that has that whole-ratio aspect, but I really doubt it, unless it's the decagonal section of either the dodecahedron (icosag.) or the icosah. (dodecag.). any legislature want to go for "pi=4" ?? ========================================================================= Date: Sun, 5 Jul 1998 20:17:30 -0700 Reply-To: List for the discussion of Buckminster Fuller's works Sender: List for the discussion of Buckminster Fuller's works From: Brian Hutchings Subject: geodesics in *that* space <> Brian Hutchings 05-JUL-1998 20:17 r001806@pen2.ci.santa-monica.ca.us just ignore the "metrical" stuff, if you wish; we already have a proof, *in ignorantia* for "post-pythagorean trigona", in *Quantum*, of all silly, virtual places. Subject: Explicit Embedding of Hyperbolic Plane in 4D Euclidean Space? From: ksbrown@seanet.com (Kevin Brown) Date: Sun, Jul 5, 1998 13:50 EDT Message-id: <359fbc81.7043141@news.seanet.com> Hilbert proved there is no complete embedding of the 2D hyperbolic plane (i.e., surface of constant negative curvature) in 3D Euclidean space. On the other hand, I've seen references that say it IS possible to embed the complete hyperbolic plane in 4D Euclidean space. Unfortunately none of those references gave an explicit embedding. Does anyone know of such an embedding? I've been trying to construct one in the 4D orthogonal coordinate system W,X,Y,Z in E^4 by expressing those coordinates as functions of arbitrary 2D surface coordinates u,v. For example, using subscripts to denote partial derivatives, with W = W(u,v) we can write the total derivative as dW = W_u du + W_v dv and similarly for the other E^4 coordinates, so the incremental distance ds along any path is related to the incremental coordinate changes by (ds)^2 = (dW)^2 + (dX)^2 + (dY)^2 + (dZ)^2 = g[uu] (du)^2 + 2 g[uv] (du)(dv) + g[vv] (dv)^2 where the components of the metric tensor are g[uu] = (W_u)^2 + (X_u)^2 + (Y_u)^2 + (Z_u)^2 g[uv] = g[vu] = (W_u)(W_v) + (X_u)(X_v) + (Y_u)(Y_v) + (Z_u)(Z_v) g[vv] = (W_v)^2 + (X_v)^2 + (Y_v)^2 + (Z_v)^2 and the determinant of this metric is g = (W_u W_v - X_u X_v)^2 + (W_u W_v - Y_u Y_v)^2 + (W_u W_v - Z_u Z_v)^2 + (X_u X_v - Y_u Y_v)^2 + (X_u X_v - Z_u Z_v)^2 + (Y_u Y_v - Z_u Z_v)^2 We could proceed to compute the curvature as a function of these metric components and their first and second derivatives, and then try to infer what functions W,X,Y,Z would cause that curvature to come out as a constant negative value, but this doesn't seem like a very efficient approach. Is there some more direct way of determining a 2D surface of constant negative curvature in E^4? ========================================================================= Date: Sun, 5 Jul 1998 21:55:42 -0700 Reply-To: List for the discussion of Buckminster Fuller's works Sender: List for the discussion of Buckminster Fuller's works From: Kirby Urner Subject: Re: spooks in mapland In-Reply-To: <199807052138.OAA23102@pen2.ci.santa-monica.ca.us> Mime-Version: 1.0 Content-Type: text/plain; charset="us-ascii" > as I have previously suggested, > Bucky's work is *entirely* euclidean, or UberEuclidean, or what ever, althoug > we can argue all night, as to whether he had the right, > to assign 3+1 dimensions to space, "primitively" or "pre-time-size"; I think, > he does, and this is his essential dysjuncture from Minkowskian phase-hype, > and the ultimate tripe of "lightcones" etc.ad vomitorium (viz, > a cone is just a quadric, a surface of second-degree .-) I don't buy that you've ever comprehended the extremely simple definitions in Synergetics, which are "lower level" than 1+1=2 (in the direction of Whitehead-Russell's 'Principia' -- and don't let mention of Russell trigger any ideological knee-jerks, as my point is one of "direction"). Ergo, your analysis that it's "entirely Euclidean" or whatever, carries no weight with me -- until I have a sense that you have even a glimmer of the obvious, unarguable, pristine 4Dness of prefrequency volume. Like, are you even capable of "taking Bucky's side" for the sake of proving you know his argument? Not one to not practice what I preach, I'll try it again: lets assume we've agreed to begin with Volume as primitive. You can tie me up in various ways, but mentally I'm "free as a bird" (meaning "soaring" -- if you're thinking seagull, that's your problem). So if this is the "stage" then what's so "3" about it? You immediately reach for some cube-corner orthonormal gizmo. Why on earth? Reach for the tetrahedron as your toy box "explainer of volume" and say "yes child, 3ness is here, in an open triangle zigzag" -- trace with finger -- "but so is 4ness, in the windows and vertices, so don't get overhooked on the 3ness (balance is all), and beware the hypercrossers, who will ensnare you in infinite rectilinear pomp and circumstance before you're allowed to 'graduate' to any of their bully pulpits (after which point you'll likely be ruined for comprehending Synergetics, if the case of Hutchings is any guide)". > as for "real mathematicians", > it's more associated with what Loeb reviews as "bcc", > body-centered cubical crystals, > which is just a convention de l'hexahedron, again. IVM = fcc not bcc, you realize yes? You can get bcc from 4 IVMs interpenetrating (same as two cube nets, as far as vertices go, with one's corners the other's centers). >mathematically, > you have to go to homogenous co-ordinates, or descartesian+1 parameters > in "homogenous" projective space. And quadrays, don't forget. Not homogenous, not barycentric, not trilinear. Cartesian XYZ is handed (usually left) and helpless to reach all points circa (0,0,0) unless aided and abetted by vector reversal aka multiplication by negative scalar. Quadrays (not planes, vectors) divide space into 4 quadrants (just four, not more). No permuting of signage (+++ ++- +-+ +--...) required. All points are (a,b,c,d) and non-redundantly labeled, stipulating no negatives need apply. The apparatus is so Cartesian as to be a variant of same -- just 4 positive spokes guiding vector clone 'n add instead of 6 positive/negative. So easy to share with kids! So unnecessary to give airs of high brow sophistication to know the ins and outs! At which point we get another meandering, off-topic empty "show of learning" from our technogeek-in-residence. But if you understand all that you've cited below (and above) as well as you appear to understand Bucky (very little), then I say "a mile wide, an inch deep is that clown Hutchings" (a Shakespearean clown perhaps, but still anything but "Bottomless"). Kirby ========================================================================= Date: Mon, 6 Jul 1998 04:33:36 GMT Reply-To: List for the discussion of Buckminster Fuller's works Sender: List for the discussion of Buckminster Fuller's works From: Kirby Urner Organization: 4D Solutions Subject: Re: CubeWorld: addinng dimensions MIME-Version: 1.0 Content-Type: text/plain; charset=us-ascii Content-Transfer-Encoding: 7bit Sej Mac wrote: >pdx4d@teleport.com (Kirby Urner) wrote: > >> The hypercross dogmatists have this cult of "only the very inner circle >> can visualize...". . . > >Knowing nothing about hypercross, I have found independently, and from a >clinical orientation and setting, that very few people can visualize more >than the 3 Ds of conventional experience. This is a way of talking about the experimental data, I agree. Some people are better at mental arithmetic too. As to whether what goes on is "visualizing more than 3Ds" I'd have to say that depends on whether you buy hypercross lingo -- which I don't, for the most part. >This does not mean that those who appear to be able to do so comprise some >secret cult (the ones I know of didn't even know one another), or are "chosen" >by any criteria of superiority, such as God, genes, special intelligence, or >adherence to any group or cult. With practice, a good teacher, you can develop mental tricks, short cuts, abbreviations, which let you do what computers do: sketch what "projections" of these n-tuple polytopes look like (ala that too-well- known tesseract aka hypercube cave painting). Whether this means being able to visualize a perfectly nonsensical thing: 4 pencils all stuck perpendicular to the other 3 through some common point, I'd prefer to say NOT!. A grammatical preference I guess -- color me Wittgensteinian. Not sure it boils down to an empirical difference between us, in other words -- just different ways of talking (different rule books, operating manuals). >This may be true to one extent or another, but another possibility is that >you are just "belolding" them this way. I know nothing about their philosophy, >their metaphysic, their world view, but I can pose a developmental hypothesis: >these people have separately arrived at this "developmental readiness," become >very curious about cosmic dimension, and bumped into some others who also have >these interests. Our culture is wired up so that "dimension" does triple over-time duty as math term, science fiction device, and quasi-religious icon into varieties of religious experience. I hesitate to meddle, as I'll just get in trouble with the inner circle hypercrossers, but lets just say that my school of thought doesn't preach any awe of "dimension" or "hyperdimensional" anything, tends to view those that do as somewhat superstitious, all too often hoodwinked as well since many of those well-versed in dimension talk don't "believe" in it any more than I do, but do nothing to quell the religious fervor surrounding said usages, because, hey, it helps to give one's work an aura of authority and, dare I say it, religious other-worldliness (I tred with caution, as many hard-nosed anti- religious "hard sciences" types get all soft and mushy in the "dimensions" department and don't want that aspect of their "faith" too closely scrutinized). >I would estimate you need a broader perspective by which to evaluate these >hypercrossers. > I think we already have a culture bowled over, awed by, in the thrall of hypercrossers, and having a nay-sayer like me in the mix is healthy. Most don't even think about raising skeptical inquirer type flags in this "home territory". Hell, I'm right in Martin Gardner's back yard fer gosh sakes! >It has been a long time since I read _Flatland_, but the book provided a >significant service to mankind in that it expanded human minds to a position >"out of the box" of prevailing experience with regard to how we see the world. This is part of the standard curriculum what you're saying. For the sake of argument, lets just say I see it as a sorry-assed religious tract, full of misleading "logic" that has mired generations in trying to visualize the impossible. Dark ages scholasticism with its pin-head angels had nothing on this age. Abbott got nothing right. There's no "2D" point of view. If you see a segment, that's against a background, and the fact that you're seeing it means there's a distance separating you from it. Volume! Another anomoly in this culture is the "god's eye view" of course -- or forget there's even an observer at all (but what "scientific" maxim do you subtract the only empirical datum connecting us to one another, our experience as humans in Universe?). We think nothing of "omniscient cameras" in the movies, flying through space, watching people in their most intimate private moments. This is tantamount to a belief in angels (as "Wings of Desire" explores -- stars Columbo). > >> Even a simple line segment implies a canvas (background) and distance from >> the observer (this line is being viewed) -- > >Analytically, and for the purposes of understanding, this is not necessarily >true. What is true is that we do live and experience (a matter of our common >cognitive heritage) in a 3-D world, You've lost me. What's so "three" about it. Oh yeah, 3 orthogonals (as if 90 degrees were more special than 89 degrees -- and I'm sure it is, for some applications -- but so is 60 degrees very special. I see "3 D" referring to a zigzag (the angles don't really matter, so long as not all 3 segments lie on the same plane). 4 noncoplanar points describe two 3-segment zigzags and the "three dee" people are obsessing about one of those pair. Volume is "three dee" because a tetrahedron is defined by two complementary zigzags. See http://members.xoom.com/Urner/images/genesis3d.gif But if you decide to focus on the faces or vertices of the tetrahedron (most primitive wireframe, cage, enclosure, containment) instead of its 3+3 edges, then you might as well say volume is 4D (because the 4 spokes through the vertices from an origin are just as irreducible as the 6 edges and the 6 spokes protruding through their midpoints, aka XYZ). >It is only when our minds escape the "box" that it can investigate objectively >and renewedly. > I would agree that only when we have escaped from the cube as our reflex- conditioned image of a primitive "box" have we made some headway against ensnarement by the GrecoAngloRoman cultural matrix. >What happened in the case of _Flatlands_ (among many other developments >at about that time), is that it let humanity escape from the box, and as >an indirect result, topology and physics have advanced considerably. > That's the appropriate posture of religious awe, I concur. The hyper- crossers are nodding their heads. I, in contrast, am a trouble-maker, like that refusenik Bucky and his infernal 4D tetrahedron (and now quadrays too!). http://www.teleport.com/~pdx4d/quadrays.html >we can understand that in a proposed 1-D universe, You can limit my degrees of freedom to a left/right motion, make me walk the plank or whatever. But I don't buy "1-D universe" as a thinkable concept. Call me a heretic I guess. >of line extension to infinity in both directions Have no empirical need for "infinity" either -- consider it more GrecoAngloRoman ghostly metaphysics, spoonfed to kids while helpless to defend critically, thereby perpetuated from one generation to the next. Fortunately, the world is bigger than this one culture's sphere, and lots of students aren't buying (no imperial masters to force them to any more), even as they learn the ins and outs of XYZ, n-tuple mathematics, Relativity, quantum physics, you name it -- none of which depends on worshipping at the hypercrosser sanctum. >more D, but the premis is wrong when considering 1-D, so the Canvas >conclusion is wrong. But I don't consider 1-D. I see a string looping around in volume. So what? Sorry to sound so polemical here, but you seem so arms-out zombie-like in possession by this cult. Everywhere I look... >I have no background info by which to evaluate the hypercross. I have >clinical background for evaluating 11 dimensions which curve round back >on themselves. Clinical background as an in-patient perhaps? :-) >This alone supports (hardly proves!) the possibillity that the universe >actually does have 10-12 dimensions which curve round on themselves. It's a way of talking. You can bend and twist "dimension" like putty these days and peer review won't squawk, so long as you play by the basic hypercrosser rule-book (Rule 12A: Synergetics is taboo, Bucky was "close to crazy", but Coxeter a curriculum god because he can "visualize in higher dimensions" -- ever since he was a kid of 14). > As I am sure you will agree, in science (and in all walks of life, IMO), >it is very important not to jump to conclusions too rapidly even when >the most powerful evidence seems overwhelming. From where I sit, this >is powerful evidence, but hardly overwhelming, and certainly not convincing. >We'll wait and see. This William James approach to higher dimensions, with rows and columns of visionary-patients lying in their hospital beds, one or another occasionally sitting bolt upright and shouting "Eureka! I can see in Higher D" -- all has a spooky X-Files quality to it. Proves what I'm saying about our culture, about where "dimension talk" fits in (somewhere between the Twilight Zone and Bill Nye the Science Guy). > >Well, that is the objective, no? to maintain your cognitive and intellectual >equilibrium rather than being "pro" or "con" until you have more evidence? Why look at this as a matter of experiential "evidence" (clinical or otherwise)? Mathematicians make up games, define terms, keep things fairly tight, with family resemblance from one game to the next, recognizable recycling of concepts. "Fractional dimension" (aka fractals) seems to plug a semantic hole (and a visual one -- line snaking so densely as to be "almost but not quite 2D") and so a new terminology enters the common currency. It's not a matter of taking testimony from psychics, just agreeing that this is a sensible-enough extension of the nomenclature. Think of the game of chess. It comes with certain rules. You don't have to "wait for the jury to come in" whether the knight can move this funny way or not -- just look it up. So in math, this dimension talk is glued together. I've been a math teacher and know how to pass on the memes. But I think in the interests of being "broad minded" we should teach the Synergetics view as "math from mars" or something suitably extraterrestrial -- just to keep our minds limber, our disciplines honest. When games become dogmas and refusing to play by the rules is just cause for banishment (as Synergetics as been, to the point of going out of print, despite the author meeting so many criteria for deserving an academic readership in the philosophy department), then I think all the more reason to suggest healthy degree of Skepticism might be just what the doctor ordered. Kirby --------------------------------------------------------- Kirby T. Urner http://www.teleport.com/~pdx4d/kirby.html 4D Solutions http://www.teleport.com/~pdx4d/ [PGP OK] --------------------------------------------------------- ========================================================================= Date: Mon, 6 Jul 1998 03:28:47 GMT Reply-To: List for the discussion of Buckminster Fuller's works Sender: List for the discussion of Buckminster Fuller's works From: Kirby Urner Organization: 4D Solutions Subject: Re: CubeWorld: addinng dimensions MIME-Version: 1.0 Content-Type: text/plain; charset=us-ascii Content-Transfer-Encoding: 7bit robjohn9@idt.net (Rob Johnson) wrote: >I am not defending the article you criticize, but the terms you seem to >have trouble with are perfectly sensible. First, four perpendicular >coordinates makes perfect sense in any space of four or more dimensions. >Of course, in a space of three or fewer dimensions, there are at most >three perpendicular coordinates. > I'd say 4 mutual orthogonals makes no sense, and so I come up with alternative metaphorics to talk about 4-tuple or n-tuple polytopes (earlier: compress/decompress instead of "project"). This is humanities stuff -- rewiring some figures of speech to less overtax the channel with noise-to-signal. Takes work, but often worth the energy expenditure (more syntropic curriculum for next generation, with "hypercross dogmatics" gathering dust -- but lots of the math staying just as useful). >There are numbers called algebraic integers, which are roots of >monic polynomials (those with integer coefficients where the highest >order term has coefficient 1). The Golden Ratio, (1+sqrt(5))/2 is an >algebraic integer because it is a root of x^2-x-1. It turns out that >the sum, difference, and product of any two algebraic integers is also >an algebraic integer. > I buy there's this taxonomy, but don't think Cliff needed to haul it into his presentation of Synergetics, unless he's trying to show off -- pointless displays of learning ala Hutchings (who quotes all the rest of this proof in another post). Kirby --------------------------------------------------------- Kirby T. Urner http://www.teleport.com/~pdx4d/kirby.html 4D Solutions http://www.teleport.com/~pdx4d/ [PGP OK] --------------------------------------------------------- ========================================================================= Date: Mon, 6 Jul 1998 03:32:32 GMT Reply-To: List for the discussion of Buckminster Fuller's works Sender: List for the discussion of Buckminster Fuller's works From: Kirby Urner Organization: 4D Solutions Subject: Re: CubeWorld: addinng dimensions MIME-Version: 1.0 Content-Type: text/plain; charset=us-ascii Content-Transfer-Encoding: 7bit Paul Birke wrote: >(Bucky always talked about nature being only "in" or "out" and not "up" >, "down' or "sideways".) > In, out or around. Like if you're a comet, you're convergently on a collision course with a body, getting spit out of one (kachoo), or are in spiro-orbital path around and around (like a strand in a rope -- solar system is chaotic, not Newtonian they say). >For instance, has someone made a multiple gyroscope based on this >system--sort of s Super-gyrosope. Say 6 spinning disks at + rotation >and other intervening 6 at - rotation. I have often wondered if this >would produce a rather immovable object! Furthermore, could you vector >the individual disk rotational speeds to overcome local gravity is the >next question I have asked myself! > You can do the 8 triangles of the cuboctahedron in a rotor that spins, even stick them together magnetically (circle-magnets). Ken Snelson did one of these, sent it to me in the mail (the tensegrity guru, ya know, also author of a whole other way of visualizing the atom -- a practice that went out of style when the uncertainty people gave up on find "the one that is literally true" (like, we'll never know). So why not have several? So long as they fit the facts as we know them, more or less. Kirby --------------------------------------------------------- Kirby T. Urner http://www.teleport.com/~pdx4d/kirby.html 4D Solutions http://www.teleport.com/~pdx4d/ [PGP OK] --------------------------------------------------------- ========================================================================= Date: Mon, 6 Jul 1998 10:59:58 EDT Reply-To: List for the discussion of Buckminster Fuller's works Sender: List for the discussion of Buckminster Fuller's works From: Zac Elston Subject: Re: spooks in mapland Mime-Version: 1.0 Content-type: text/plain; charset=US-ASCII Content-transfer-encoding: 7bit In a message dated 98-07-06 00:56:32 EDT, you write: > earth? Reach for the tetrahedron as your toy box "explainer of > volume" and say "yes child, 3ness is here, in an open triangle > zigzag" -- trace with finger -- "but so is 4ness, in the windows > and vertices, so don't get overhooked on the 3ness (balance is > all), and beware the hypercrossers, who will ensnare you in > infinite rectilinear pomp and circumstance before you're allowed I can not wait to have a child of my own to do this to. :) Just think of how little Zac jr. will cause a riot in pre school, building domes and octahedral truses.... can anyone think of name that includes a reference to three? troika sounds cool, but really isn't what I want to call a kid... -zac ========================================================================= Date: Mon, 6 Jul 1998 11:50:41 -0700 Reply-To: List for the discussion of Buckminster Fuller's works Sender: List for the discussion of Buckminster Fuller's works From: Kirby Urner Subject: Syn-l: Curriculum notes (AFSC) Comments: cc: raysimon@javanet.com, tops@canby.com Mime-Version: 1.0 Content-Type: text/plain; charset="us-ascii" Notes for upcoming meeting with youth coordinators, American Friends Service Committee, in Seattle -- presenting re the 1998 Math Makeover Campaign (sponsored, in part, by the Philosophers' Network) Primary references: http://www.inetarena.com/~pdx4d/ocn/ http://www.inetarena.com/~pdx4d/ocn/calculus2.html http://www.teleport.com/~pdx4d/makeover1.html -------------- Philosophy for young people (curriculum notes): The focus here is getting "beyond flatland" early, meaning returning to those "scribing in sand" demonstrations by coming to "Euclid's world" from space [1], i.e. from spatial geometry, wherein surfaces are clearly aspects of volumetric topologies. Classes focus on Sun->Earth economy with energy transfer from fusion to "big cycle" weather/climate and biomass formation (e.g. agriculture, wilderness). The geometry of electromagnetic waves linked to Archimedes screw (irrigation) as precursor to latter phase-in of cross-product (curl). Field trip to local alternator farm (e.g. Bonneville dam) if feasible. Use Earth as link to spherical geometry, projecting polyhedra from inside as "shadow-castings" e.g. spherical tetrahedron gives 4 equal regions on the surface, each of area equal to spherical cross-section.[2] Projecting icosahedron gives 20 spherical triangles setting stage for world map projection and overview of resources (emphasize sufficiency, if intelligence in the wings).[3] Zoom in on a beach in Greece and show ancient greek philosophers with ruler and compass using 'Elements'-style postulates and constructing theorems (do some). Relate "points" to grains of sand, "plane" to sandy beach. Emphasize locally flat aspect of Earth, given relatively tiny dimensions of humans, and Greek propensity to use post-and-lintel (e.g. Parthenon) as precursor of western civ fixation on "orthogonal" as "normal" even though it isn't, outside human designs.[4] De-emphasize points as "zero dimensional" or planes as "infinitely expansive" (important for historical context and backward compatibility, but not for drilling).[5] Zoom in further on beach sand and idealize as close-packed spheres. Explore packing 12 around 1 (2 ways) one way giving cuboctahedron. Use to set stage for concentric hierarchy w/ tetrahedral and octahedral voids in 2:1 ratio (population) and 1:4 volume. Cuboctahedron = 8 tetrahedra + 6 1/2 octahedra for volume 20. Jitterbug as bridge to 5-fold (e.g. icosahedron, rhombic triacontahedron). Do volumes again with cube as unit and compare. Discuss cube as model of 3rd powering. Do again with tetrahedron as 3rd powering model. Emphasize philosophy of math as self-consistent games, some tightly coupled, some relatively isolated.[6] Regarding axioms, note their definitional nature without dwelling too much on "self-evidence" (not really a necessary stipulation). Look at "real numbers" as "rationals" plus "irrationals" then revisit through eyes of another culture, e.g. a so-called "Persian math" with different categories: symbols as "terminal" versus "algorithmic" (bears a family resemblance to "rational" and "irrational", certainly).[7] Discuss definitions as cultural artifacts, not "cast in stone for all time" (perhaps concluding with Ozymandius poem).[8] NOTES: [1] picturing from Al Gore's L1 webcam for example [2] Exercise: 8000 miles diameter w/ pi r^2 gives approx 16,000,000 x 3 = 48,000,000. Earth surface area roughly 48,000,000 x 4 = 192,000,000 square miles. [3] computer algorithm by Robert Gray, global data from WorldSat http://www.teleport.com/~pdx4d/dymax.html [4] sections of virus, buckyballs (C60), stickyballs (C36) relevant (good intro to 5-fold symmetry segment) [5] genesis of '3D' might be retold using the tetrahedron: show 3-edge zigzag "snake" defines complement, and therefore concept of volume. http://members.xoom.com/Urner/images/genesis3d.gif [6] [Aldous Huxley quote in Stuart Kaufmann book goes here] [7] http://members.xoom.com/Urner/images/persian.gif [8] http://www.lgmicro.com/ozymandius.htm ========================================================================= Date: Mon, 6 Jul 1998 14:45:27 -0700 Reply-To: List for the discussion of Buckminster Fuller's works Sender: List for the discussion of Buckminster Fuller's works From: Brian Hutchings Subject: void + void = void <> Brian Hutchings 06-JUL-1998 14:45 r001806@pen2.ci.santa-monica.ca.us ah, well, it's like waking from a dream, trying to recall some or *any* haunting particular, left only with a glimmer, and this stupid Don Juan Goes Tripping with Carlos, Again book, on the Dymaxion Bedstand. thanks, Kirby, for clearing-up that question of crystallography -- that might save me on the Tripos, if I fail the Newtonian Catechisms; someday, I *will* graduate from the School of Bully-Clown Pulpitdom. seriously, re the EuberUclideanness of Bucky's space-think, I don't see how you can show, otherwise, and certainly not by citing Bertrand "let's US and SU fight to the death" Russell [*]; his entire programme was cinched to death by a Goedle (ha-ha). I really have not been enthused with quadrays, since they are just 3D with a 4-way signpost, as opposed to 3 2-way signposts; is this supposed to be parsimonious?... well, I'll have to get a dictionary. on the other hand, I have not seen any of the *applications* of quadrays; perhaps, they are the next-best thing to sliced-bread on the catering line! to paraphrase MLK, "I have a glimmer!" -- * see the article, "How Bertrand Russell Became an Evil Man", in *21st C.Science and Technolgy*; also online, http://www.larouchepub.com -- dragons & dungeons and Sir George: http://www.tarpley.net ========================================================================= Date: Mon, 6 Jul 1998 14:58:00 -0700 Reply-To: List for the discussion of Buckminster Fuller's works Sender: List for the discussion of Buckminster Fuller's works From: Kirby Urner Subject: Re: void + void = void In-Reply-To: <199807062145.OAA29717@pen2.ci.santa-monica.ca.us> Mime-Version: 1.0 Content-Type: text/plain; charset="us-ascii" > seriously, re the EuberUclideanness of Bucky's space-think, > I don't see how you can show, otherwise, and certainly not > by citing Bertrand "let's US and SU fight to the death" Russell [*]; You've done nothing to define "Euclidean" -- if it means buying "three dee" then clearly not, if buying continuous surfaces then not, if "planes to infinity" then not. As far as scribing on sand with a stick to demonstrate/prove that criss-cross in a parallelogram defines mutual bisectors and the like, then sure, Synergetics is sharing the wealth with Greek civ -- nothing to sneeze at, a fine culture, great thinkers and all that. Prefrequency realm is Platonic -- OK with me. Euclidean beach head established -- not conceding that territory to hypercrossers' that's for shore. > I really have not been enthused with quadrays, since > they are just 3D with a 4-way signpost, as opposed > to 3 2-way signposts; is this supposed to be parsimonious?... You keep saying they're 3D even though they're clearly 4D -- all 4 basis vectors same as one another (not 3+1). >well, > I'll have to get a dictionary. on the other hand, > I have not seen any of the *applications* of quadrays; perhaps, > they are the next-best thing to sliced-bread on the catering line! > The *application* is what I've done with them at my website, buried in a Wittgenstein-style investigation of where do we get this "D-talk" and how could it have evolved differently on a planet with more 60-degree informed views... But I get the impression you're "flying blind on instruments" i.e. web is for people who pay per view. > to paraphrase MLK, "I have a glimmer!" > Still not convinced. But show isn't waiting for you to get it either -- take all the time you need, or settle for never. Kirby ========================================================================= Date: Mon, 6 Jul 1998 14:59:02 -0700 Reply-To: List for the discussion of Buckminster Fuller's works Sender: List for the discussion of Buckminster Fuller's works From: Brian Hutchings Subject: Survivalist Workshop! <> Brian Hutchings 06-JUL-1998 14:59 r001806@pen2.ci.santa-monica.ca.us on that outline, you forgot the transcendentally reals (no-algebraical; I think, that includes takingroots). ========================================================================= Date: Mon, 6 Jul 1998 09:47:51 GMT Reply-To: List for the discussion of Buckminster Fuller's works Sender: List for the discussion of Buckminster Fuller's works From: "R.J.Chapman" Organization: University of Exeter, UK Subject: Re: CubeWorld: addinng dimensions pdx4d@teleport.com writes: > > hypercross lingo > hypercrossers (3 times) > sorry-assed > 4D (twice) > XYZ (twice) > GrecoAngloRoman (twice) > quadrays > hypercrosser sanctum > hypercrosser rule-book > Synergetics (3 times) > -- Robin Chapman + "They did not have proper Department of Mathematics - palms at home in Exeter." University of Exeter, EX4 4QE, UK + rjc@maths.exeter.ac.uk - Peter Carey, http://www.maths.ex.ac.uk/~rjc/rjc.html + Oscar and Lucinda ========================================================================= Date: Mon, 6 Jul 1998 01:40:48 -0800 Reply-To: List for the discussion of Buckminster Fuller's works Sender: List for the discussion of Buckminster Fuller's works From: "Clifford J. Nelson" Organization: gte.net Subject: Re: CubeWorld: addinng dimensions Mime-Version: 1.0 Content-Type: text/plain; charset=US-ASCII Content-Transfer-Encoding: 7bit On Sun, Jul 5, 1998 7:28 PM, Kirby Urner wrote: >robjohn9@idt.net (Rob Johnson) wrote: [snip] > >>There are numbers called algebraic integers, which are roots of >>monic polynomials (those with integer coefficients where the highest >>order term has coefficient 1). The Golden Ratio, (1+sqrt(5))/2 is an >>algebraic integer because it is a root of x^2-x-1. It turns out that >>the sum, difference, and product of any two algebraic integers is also >>an algebraic integer. >> > >I buy there's this taxonomy, but don't think Cliff needed to haul >it into his presentation of Synergetics, unless he's trying to >show off -- pointless displays of learning ala Hutchings (who >quotes all the rest of this proof in another post). > >Kirby > You have wrongly concluded that an average vocabulary doesn't have to be increased to understand Bucky Fuller's writing. When I first read Synergetics 1&2 and didn't know the terms or wasn't sure of the meaning of the words, and didn't look up the words in the dictionary (circa 1960 dictionary, when the books were commissioned), I tried to guess the meaning of the words from the context. I wrongly concluded that Bucky was being metaphorical just when he was being most precise sometimes. That is a frequent mistake in your interpretations of Synergetics. Read this again. --------------------------- Synergetics section 201.03 page 23 : Synergetics makes possible a rational, whole number, low-order quantation of all important geometries of expirience because the tetrahedron, the octahedron, the rhombic dodecahedron, the cube, and the vector equilibrium embrace and comprise all of the lattices of all the atoms. ---------------------------- You are saying Bucky Fuller was just showing off because he used the phrase "rational, whole number, low-order quantation", instead of just "whole number, low- order quantation". And you have written that it makes him seem like a dunderhead, before you found out that it is common terminology in books about algebraic number fields. But, some of the words and terms Bucky used are recherche. Literlly: sought out with care, hence of high quality; choice, rare. He couldn't write books about his thinking, using only well known terms and words. Cliff Nelson ========================================================================= Date: Mon, 6 Jul 1998 16:57:36 GMT Reply-To: List for the discussion of Buckminster Fuller's works Sender: List for the discussion of Buckminster Fuller's works From: Kirby Urner Organization: 4D Solutions Subject: Re: CubeWorld: addinng dimensions MIME-Version: 1.0 Content-Type: text/plain; charset=us-ascii Content-Transfer-Encoding: 7bit "Clifford J. Nelson" wrote: >the meaning of the words from the context. I wrongly concluded that Bucky >was being metaphorical just when he was being most precise sometimes. That >is a frequent mistake in your interpretations of Synergetics. > I wouldn't equate "being metaphorical" with "imprecise". Sometimes metaphors fit the experience hand-in-glove. >You are saying Bucky Fuller was just showing off because he used the phrase >"rational, whole number, low-order quantation", instead of just "whole >number, low- order quantation". And you have written that it makes him seem >like a dunderhead, before you found out that it is common terminology in >books about algebraic number fields. > No, you misrepresent what I said. The "rational integer" thing was yours, not his. I think he includes "rational" for its double-meaning as "sensible, sane" and "whole" for its "wholesome and complete" and "quantation" for its link to "quantum" and his identification of the tetrahedron with same root. Plus we have the straight the math book meanings. We also want "rational" hanging around because we DO have fractions in Synergetics (e.g. modules, MITEs) and decimals carried out to several places. He even uses PI, albiet very sparingly (because to approach sphericity takes more work than just doing it on paper -- nature is energetic). The precision in the above quote comes in with the qualifier "lattice". 5-fold shapes are aperiodic, don't tile or make a lattice (lattice = skeleton you can pick up and translate and juxtapose as self-identical). He says the lattice shapes (provides a list) come out whole number. The low-order quantation also refers to 2pff + 2 as a sphere-packing or quantation device vis-a-vis simple systems, which always have even numbers of vertices. A bipyramid of two face-bonded tetrahedra (5 vertices) is a "complex system" of simple systems glommed on to one another (alligators also complex). >But, some of the words and terms Bucky used are recherche. Literlly: sought >out with care, hence of high quality; choice, rare. He couldn't write books >about his thinking, using only well known terms and words. > I would agree. But in your post you were (a) advertising yourself as interpreting Synergetics i.e. proffering a coordinate system that you hope people will identify as Buckyesque, as well as Cliff Nelson's and (b) talking about your coordinate system using terminology that presumes background reading in the arcana of a math syllabus which is not specifically roped in by Bucky -- nor does he ever say "rational integer" in the way you mean. More relevant to read Koestler (e.g. 'Act of Creation') than some paper on "algebraic integers" if you want to access Synergetics (a work in the humanities, precise without needing to piggy-back on Mathematica to get the job done). Kirby --------------------------------------------------------- Kirby T. Urner http://www.teleport.com/~pdx4d/kirby.html 4D Solutions http://www.teleport.com/~pdx4d/ [PGP OK] --------------------------------------------------------- ========================================================================= Date: Mon, 6 Jul 1998 18:22:43 GMT Reply-To: List for the discussion of Buckminster Fuller's works Sender: List for the discussion of Buckminster Fuller's works From: Kirby Urner Organization: 4D Solutions Subject: More USA history, Critical Path style MIME-Version: 1.0 Content-Type: text/plain; charset=us-ascii Content-Transfer-Encoding: 7bit "korling" wrote: >I will also remind you that just because you fight on the side of someone in >one war, in no way makes them your ally after that war is over. The Soviets >knew this just as well as the U.S. did. We "allied" with the Soviets out of >necessity only and didn't try to hide the fact that we were not at all >pleased with their form of politics. > >Korling > You are very quick with this "we" -- as if you speak for everyone doing the fighting pre/post 1946 (I wasn't even born yet myself). A lot of USA-based banks and businesses were very anxious to roll back FDR-style "New Deal" thinking, which was too close to "socialism" for their everlasting comfort. Vast government holdings were privatized and a lot of Depression-Era safety-net programs killed -- which the public accepted because post-war USA was boom-times, given the intact physical plant, spanking new from the war effort. The GI Bill staffed a huge boom in academia, got the space program off the ground, always with strong allegience to WWII era military ethics (which was minus much grasp of the behind-the-scenes business politics, which were submerged in a pseudo-technical Economics with built-in hostility to "command economies" but not to "command and control" of taxpayer-funded defense contracting). Plus we have to remember the racism was more intact, institutionally, with much of Anglo culture not yet thinking twice about equity for historically disenfranchised (still the province of "radicals" to think along those lines -- and soon all radicals would be "commies" -- very convenient, given all the 3rd world freedom and independence movements that need suppressing so United Fruit et al could get on with it). >From the Soviet point of view, post WWII you had a lot of Nazi intelligence infiltrating post-War USA, finding like-minded Anglos (lots of Anglo banks sympathetic to eugenics movement pre-WWII (backed Adolph early) -- not that anti-semitism wasn't endemic in USSR as well (obviously)). But in any case what you got was a sea-change after FDR, with a more Nazi- style approach to world affairs minus the idealism and hopefulness of Marx-Lenin style utopianism for all, not just some "chosen people" (Aryan, white, Christian, whatever). Back to a social darwinist "capitalism" of a new legal template variety (LAWCAP), a divestiture of USA power under neo-capitalist management (Keynes-modulated), and a puppeting of said USA through a costly era of prime contractors irrigated Cold War economics. To say that "we" (meaning all USAers) bought into this post New Deal deal is inaccurate. A lot of homo pinkos and their nigger druggie long-haired friends continued to keep a political left alive, despite McCarthyite-style witch hunts and Nixon-style psychosis. It's also inaccurate to think the bonds against Nazis forged with Russians during WWII were all snapped at the highest levels when LAWCAP started running the USA's affairs.[1] Politicians who bought this caricature have since been out-maneuvered on a lot of fronts, and may have to start breaking the news that WWIII (aka the Cold War) really is over (peace dividend intact) -- with the "bad guys" losing yet again. LAWCAP: lost the Cold War to the Russians, and losing the design science revolution to the USA. Kirby [1] the "shoot down" of the Gary Powers U2 -- if you read the fine print, looked more like a "confidance building measure". --------------------------------------------------------- Kirby T. Urner http://www.teleport.com/~pdx4d/kirby.html 4D Solutions http://www.teleport.com/~pdx4d/ [PGP OK] --------------------------------------------------------- ========================================================================= Date: Mon, 6 Jul 1998 19:47:08 GMT Reply-To: List for the discussion of Buckminster Fuller's works Sender: List for the discussion of Buckminster Fuller's works From: Kirby Urner Organization: 4D Solutions Subject: Re: CubeWorld: addinng dimensions MIME-Version: 1.0 Content-Type: text/plain; charset=us-ascii Content-Transfer-Encoding: 7bit scott@math.csuohio.edu (Brian M. Scott) wrote: >Your 'school of thought' appears to be a school of jargon that does >little *but* preach. > Easy for you to say. Do you have a viewpoint or is your practice to coast along sniping and carping? -- dime a dozen on the internet. >Your confusion of mathematical and physical space is at least a >century and a half out of date. > I'm not in the least confused. That you call the math world a "space" is metaphoric of course (I use it too -- "semantic space" even cooler), is projected a posteriori from the energized space of everyday affairs. In my lingo (what you call a "jargon", as if you didn't speak one), the difference between purely conceptual space and energized space is accommodated by the "Frequency" difference. Most math jargons, on the other hand, don't formalize the distinction, leaving "the physical world" to physicists and exulting in the "purity" of prefrequency their visualizations (or algebraic ones -- visualization is only slowly making a come-back, after disillusionment around earlier visual modeling, which was stigmatized as "naive"). Anyone who tries to talk about the difference between mathematical space and physical space tends to fall through the cracks as a philosopher (a kind of "no man's land" between self-satisfied fields). >>Hell, I'm right in Martin Gardner's back yard >>fer gosh sakes! > >An intellectual garden dwarf? Or is that where he keeps his >collection of faddists? > I've planted a "this site under investigation" (thinkers at work) skeptical inquirer flag smack in the middle of the hypercrossers' hyperdimensional headquarters. Whatcha gonna do about it guy, besides make wisecracks ala yer typical garden variety crypto-mystic caught in the spotlight? Kirby --------------------------------------------------------- Kirby T. Urner http://www.teleport.com/~pdx4d/kirby.html 4D Solutions http://www.teleport.com/~pdx4d/ [PGP OK] --------------------------------------------------------- ========================================================================= Date: Mon, 6 Jul 1998 18:30:09 GMT Reply-To: List for the discussion of Buckminster Fuller's works Sender: List for the discussion of Buckminster Fuller's works From: "Brian M. Scott" Organization: Cleveland State University Subject: Re: CubeWorld: addinng dimensions On Mon, 06 Jul 1998 04:33:36 GMT, pdx4d@teleport.com (Kirby Urner) wrote: >I hesitate to meddle, as I'll just get in trouble with the inner >circle hypercrossers, but lets just say that my school of thought >doesn't preach any awe of "dimension" or "hyperdimensional" anything, Your 'school of thought' appears to be a school of jargon that does little *but* preach. >tends to view those that do as somewhat superstitious, all too often >hoodwinked as well since many of those well-versed in dimension talk >don't "believe" in it any more than I do, Your confusion of mathematical and physical space is at least a century and a half out of date. >Hell, I'm right in Martin Gardner's back yard >fer gosh sakes! An intellectual garden dwarf? Or is that where he keeps his collection of faddists? Brian M. Scott ========================================================================= Date: Mon, 6 Jul 1998 15:50:13 -0700 Reply-To: List for the discussion of Buckminster Fuller's works Sender: List for the discussion of Buckminster Fuller's works From: Kirby Urner Subject: Re: CubeWorld: addinng dimensions Comments: cc: rjc@noether.ex.ac.uk In-Reply-To: Mime-Version: 1.0 Content-Type: text/plain; charset="us-ascii" At 09:47 AM 7/6/98 GMT, R.J.Chapman wrote: >pdx4d@teleport.com writes: >> >> hypercross lingo >> hypercrossers (3 times) >> sorry-assed >> 4D (twice) >> XYZ (twice) >> GrecoAngloRoman (twice) >> quadrays >> hypercrosser sanctum >> hypercrosser rule-book >> Synergetics (3 times) >> Your point being.... that you can count? Kirby ========================================================================= Date: Mon, 6 Jul 1998 18:54:52 EDT Reply-To: List for the discussion of Buckminster Fuller's works Sender: List for the discussion of Buckminster Fuller's works From: Zac Elston Subject: Re: void + void = void Mime-Version: 1.0 Content-type: text/plain; charset=US-ASCII Content-transfer-encoding: 7bit In a message dated 98-07-06 18:03:20 EDT, you write: > > I have not seen any of the *applications* of quadrays; perhaps, HA! I have captured the elusive fallacy known as Argumentum ad ignorantiam A.K.A (appeal to ignorance) Defined as : Using the absence of proof for a proposition as evidence for the truth of the opposing proposition Ahh...remember the days of ignorance......:) For anyone currently perplexed enough to wonder just what the hell to do with triangles, remember that progress is made (in every conceivable field) not by seeing the obvious but by seeing something new that leads one to an obvious answer. (at least that's what my professors told me...LOL) Nature is very tricky with this. My specialty, sociology, is not an exact science in any dimension and not even the greatest philosophers ever would argue that it was. Sociology is about understanding different perspectives and seeing the world through the eyes of another. Understanding what makes a person react to stimuli and how to predict such reactions through historical analysis of similar reactions and similar stimuli. Now what does this have to do with triangles? Nothing :). But if you ignore the fact that triangles provide a unique and cohesive way of looking at geometry and physics, you soon see that there might be something that was missed by all those squares. Perception is the key. The sociology of squares is as pervasive as ever and affects the thinking of human kind to such a degree that non-linear topics are taboo. If it doesn't fit in a square world, then it must be wrong. Problem is that the world is round. *****This is not a supporting argument for Bucky-Thought**** But it does illustrate the absurdity of arguing 3 sides or 4. What if 5 were the correct answer? Would that make the world a better place? Not if nobody noticed, it wouldn't. (follow the negatives?) If YOU can't find an application that can not be covered by squares, that by no means disproves that synergetic concepts have merit, it just means you aren't seeing anything new. And that's not very interesting ..in fact many millions of people see nothing new everyday . (look in my mail box as evidence) -zac ========================================================================= Date: Mon, 6 Jul 1998 23:01:14 GMT Reply-To: List for the discussion of Buckminster Fuller's works Sender: List for the discussion of Buckminster Fuller's works From: Kirby Urner Organization: 4D Solutions Subject: Re: CubeWorld: addinng dimensions MIME-Version: 1.0 Content-Type: text/plain; charset=us-ascii Content-Transfer-Encoding: 7bit rjchapma@exeter.ac.uk (R.J.Chapman) wrote: >pdx4d@teleport.com writes: >> >> hypercross lingo >> hypercrossers (3 times) >> sorry-assed >> 4D (twice) >> XYZ (twice) >> GrecoAngloRoman (twice) >> quadrays >> hypercrosser sanctum >> hypercrosser rule-book >> Synergetics (3 times) >> The man can count! Go Exeter! Kirby --------------------------------------------------------- Kirby T. Urner http://www.teleport.com/~pdx4d/kirby.html 4D Solutions http://www.teleport.com/~pdx4d/ [PGP OK] --------------------------------------------------------- ========================================================================= Date: Mon, 6 Jul 1998 22:02:12 -0700 Reply-To: List for the discussion of Buckminster Fuller's works Sender: List for the discussion of Buckminster Fuller's works From: Brian Hutchings Subject: fantasy island(s) <> Brian Hutchings 06-JUL-1998 22:02 r001806@pen2.ci.santa-monica.ca.us Zac, it's "argumentarium ad vomitorium gigantum"; you are drowning in your own hurlfest! > > I have not seen any of the *applications* of quadrays; perhaps, HA! I have captured the elusive fallacy known as Argumentum ad ignorantiam A.K.A (appeal to ignorance) the apps that I vaguely recall from Syn-l, were mildly amusing, if not fully developed, in terms of the raison d'etre of quadrays. now, as for the technique of using a quadruple of numbers, there is certainly no requirement, that one of them always be zero; should that be the standard, though, then I'd have to say, It's got 4 one-way signposts! -- dragons, dungeons, daquiris and Sir George ("Hey, this is not bad for a jailcell, Barbara!") http://www.tarpley.net ========================================================================= Date: Mon, 6 Jul 1998 22:25:06 -0700 Reply-To: List for the discussion of Buckminster Fuller's works Sender: List for the discussion of Buckminster Fuller's works From: Kirby Urner Subject: Re: fantasy island(s) In-Reply-To: <199807070502.WAA32011@pen2.ci.santa-monica.ca.us> Mime-Version: 1.0 Content-Type: text/plain; charset="us-ascii" > the apps that I vaguely recall from Syn-l, > were mildly amusing, if not fully developed, > in terms of the raison d'etre of quadrays. now, You were always a shallow on Syn-L too, a dabbler, a dilettente, looking for an excuse to say "vomit" in some new, cutesy way, or a chance to stick a wad of already-been-chewed LaRouchie gum under someone's chair. > as for the technique of using a quadruple of numbers, > there is certainly no requirement, that one of them always be zero; In quadrays one coordinate must be zero, as at least one of the 4 quadrays is not needed per any given point (in XYZ, you don't need at least 3 of the 6 per point -- but permuted signage, in place of 0's position, clues which of eight -- instead of 4 -- regions we're in). > should that be the standard, though, then > I'd have to say, It's got 4 one-way signposts! > Yes, 4 one-way signposts. Got a problem with that? Prefer 6? The 4 taken two-at-a-time give the 6, so you're welcome to both 4D systems (V-Cartesian or E-Cartesian -- thru Vertices or Edges -- I can play either way). Kirby ========================================================================= Date: Mon, 6 Jul 1998 22:29:09 -0700 Reply-To: List for the discussion of Buckminster Fuller's works Sender: List for the discussion of Buckminster Fuller's works From: Brian Hutchings Subject: Mo'Better History (get rid of the Chicago School Fabian Socialist <> Brian Hutchings 06-JUL-1998 22:29 r001806@pen2.ci.santa-monica.ca.us "boomtimes", not exactly; Truman brought-on a recession, after 2 terms, along with his (Averill Harriman's) policy, of getting rid of Roosevelt's policy to roll-back the British, Dutch and French Empires, the other reason for Bretton Woods etc. the resultant "independence revolts" were promoted by these groups, with little republican support, if any. there were not "a lot" of "Anglo" banks that backed the Nazis; there was just Brown Brothers-Harriman, and Sir George's daddy -- "Poppy". as for Nixon, he was set-up by the WAND (sik) Corp., prior to Watergating; if you really want to *know* him intimately, as it were, see the Stone trilogy, inclusive of "JFK" -- that's what I've heard, at any rate. I frankly did not grok your last paragraph, Kirby, unless it was akin to Bucky's say-so that'78 (?) was the Year of Living Undangerously (or what ever .-) thus quoth: It's also inaccurate to think the bonds against Nazis forged with Russians during WWII were all snapped at the highest levels when LAWCAP started running the USA's affairs.[1] Politicians who bought this caricature have since been out-maneuvered on a lot of fronts, and may have to start breaking the news that WWIII (aka the Cold War) really is over (peace dividend intact) -- with the "bad guys" losing yet again. LAWCAP: lost the Cold War to the Russians, and losing the design science revolution to the USA. now *that* was a giant, oozing nonsequiter; there ought t'be a law! -- dragons, dungeons, daquiris, the Dalai Lama [*], Sir George, and a cast of thousands of spooks! http://www.tarpley.net * "Seven weeks in South America, filming this **** !!" ========================================================================= Date: Mon, 6 Jul 1998 22:44:51 -0700 Reply-To: List for the discussion of Buckminster Fuller's works Sender: List for the discussion of Buckminster Fuller's works From: Kirby Urner Subject: Re: Mo'Better History In-Reply-To: <199807070529.WAA32200@pen2.ci.santa-monica.ca.us> Mime-Version: 1.0 Content-Type: text/plain; charset="us-ascii" At 10:29 PM 7/6/98 -0700, you wrote: ><> Brian Hutchings 06-JUL-1998 22:29 > r001806@pen2.ci.santa-monica.ca.us > > "boomtimes", not exactly; Compared to Great Depression... 1950s brought us suburban TV dinner culture w/ lots of cool appliances (not knocking this early design science push to free Rosey the Riveter from homemaker drudgery, now that the guys were back from the front and had the major breadwinner jobs again). > there were not "a lot" of "Anglo" banks that backed the Nazis; > there was just Brown Brothers-Harriman, and Sir George's daddy -- > "Poppy". Yes, we've both read Tarpley's book at least. Have you done any other independent research to "follow the pound"? > as for Nixon, he was set-up by the WAND (sik) Corp., > prior to Watergating; if you really want to *know* him intimately, > as it were, see the Stone trilogy, inclusive of "JFK" -- > that's what I've heard, at any rate. I've seen 'JFK' and 'Nixon' and take both with plenty of salt, thanks. Which ain't to say Stone is without talent. > I frankly did not grok your last paragraph, Kirby, > unless it was akin to Bucky's say-so that'78 (?) was the Year > of Living Undangerously (or what ever .-) > Whatever. Thanks for sharing, Bri. Kirby ========================================================================= Date: Tue, 7 Jul 1998 06:00:18 GMT Reply-To: List for the discussion of Buckminster Fuller's works Sender: List for the discussion of Buckminster Fuller's works From: Kirby Urner Organization: 4D Solutions Subject: Re: CubeWorld: addinng dimensions MIME-Version: 1.0 Content-Type: text/plain; charset=us-ascii Content-Transfer-Encoding: 7bit dodecagona@aol.com (Dodecagona) wrote: > >A*L sucketh >(I don't want'em t'sew me .-) Note: twas Brian Hutchings' (aka Dodecagona's) doing, not mine, that this thread burst into sci.math in the middle (been here, done this already). Lots of posts missing from this NG's version, with Dodecagona's noise detracting from what little remains of the signal. I vote we give up discussing any Synergetics on sci.math, permanently -- mathematicians have already voted with their feet on this one (had plenty of time to take ownership of the concentric hierarchy with its A and B mods etc. but didn't take advantage, as the record clearly shows). We're doing this stuff in the philosophy department now. If you want to study Synergetics, please change channels. Or sit here and hang out with Dodecagona some more -- he's about as ignorant of Synergetics as they come (Cliff is a veritable synergetics Ph.D. by comparison). Fun chatting. Tuning out. Urner. --------------------------------------------------------- Kirby T. Urner http://www.teleport.com/~pdx4d/kirby.html 4D Solutions http://www.teleport.com/~pdx4d/ [PGP OK] --------------------------------------------------------- ========================================================================= Date: Tue, 7 Jul 1998 04:03:46 -0700 Reply-To: List for the discussion of Buckminster Fuller's works Sender: List for the discussion of Buckminster Fuller's works From: Brian Hutchings Subject: "the story, behind the story" <> Brian Hutchings 07-JUL-1998 4:03 r001806@pen2.ci.santa-monica.ca.us "JFK" had a screenplay that was written by Mark Lane, the lawyer whoe proved (on appeal in a libel case) that E.Howard Hunt was in Dallas, one funny day; not ha-ha funny. one of the primary consultants, portrayed as Mr.X, Proutty, was almost on that scene, reprising his role in the security of Eisenhower in Mexico City, except that he was given a vacation, to be the military attache for a group of statesmen visiting MacMurdo Station (a-hem; fun-nee). unfortunately, Lane took his name off of the script, after it was re-written, after the script leaked & pressure was applied for certain changes (I know not which); however, not having seen any of these movies, I know that the gist of it is quite true, as far as it goes & accounting for artistic licenses taken, and paid-for! beyond his first-hand knowledge on the Board of Economic War (?), Bucky is in no guise of a historian, however accurate his speculations as metaphor, as far as I recall (there is only a 2 or 3 years overlap, between my study of Bucky and Lyn .-) as it may be, there was no shocking dyscontinuity; it's just that Bucky's political economy is a cartoon, maybe a cartouche, not a serious program; possibly, it was not ever intended to be, but you can ask Ed about that; eh? JFK was a very flawed President, but not for *any* of the reasons that were alleged in Vanity Fair by Timothy Leary (e.g.) or, say, Michael Parenti -- who I'm hearing on KPFK, at the moment-being. a book that shows what he was doing, or trying to do, _Battling Wall Street_, does not get into the murder. -- get'im! http://www.tarpley.net ========================================================================= Date: Tue, 7 Jul 1998 09:55:19 GMT Reply-To: List for the discussion of Buckminster Fuller's works Sender: List for the discussion of Buckminster Fuller's works From: "R.J.Chapman" Organization: University of Exeter, UK Subject: Re: CubeWorld: addinng dimensions pdx4d@teleport.com writes: > I hesitate to meddle oh no you don't! -- Robin Chapman + "They did not have proper Department of Mathematics - palms at home in Exeter." University of Exeter, EX4 4QE, UK + rjc@maths.exeter.ac.uk - Peter Carey, http://www.maths.ex.ac.uk/~rjc/rjc.html + Oscar and Lucinda ========================================================================= Date: Tue, 7 Jul 1998 08:46:01 -0700 Reply-To: List for the discussion of Buckminster Fuller's works Sender: List for the discussion of Buckminster Fuller's works From: Kirby Urner Subject: Re: CubeWorld: addinng dimensions Comments: cc: rjc@noether.ex.ac.uk In-Reply-To: Mime-Version: 1.0 Content-Type: text/plain; charset="us-ascii" At 09:55 AM 7/7/98 GMT, R.J.Chapman wrote: >pdx4d@teleport.com writes: >> I hesitate to meddle > >oh no you don't! > Well, maybe for a second or two... Kirby ========================================================================= Date: Tue, 7 Jul 1998 12:26:30 EDT Reply-To: List for the discussion of Buckminster Fuller's works Sender: List for the discussion of Buckminster Fuller's works From: Zac Elston Subject: Re: CubeWorld: addinng dimensions Mime-Version: 1.0 Content-type: text/plain; charset=US-ASCII Content-transfer-encoding: 7bit In a message dated 98-07-07 06:46:28 EDT, you write: > I vote we give up discussing any Synergetics on sci.math, > permanently -- mathematicians have already voted with their > feet on this one (had plenty of time to take ownership of > the concentric hierarchy with its A and B mods etc. but > didn't take advantage, as the record clearly shows). So am I to understand that 'bit.listserv.geodesic' (List for the discussion of Buckminster Fuller's works) is no longer being used as an open forum for it's stated purpose? Or is it rather that bit.listserv.geodesic will be a philosophical conversation pit? Either would be sad as I don't need to discuss philosophy, I need help with the math. > Fun chatting. Tuning out. Urner. cool...gimme some ========================================================================= Date: Tue, 7 Jul 1998 12:17:46 -0700 Reply-To: List for the discussion of Buckminster Fuller's works Sender: List for the discussion of Buckminster Fuller's works From: Kirby Urner Subject: Re: CubeWorld: addinng dimensions Comments: cc: rjc@noether.ex.ac.uk In-Reply-To: <7cd2a646.35a24c38@aol.com> Mime-Version: 1.0 Content-Type: text/plain; charset="us-ascii" >So am I to understand that 'bit.listserv.geodesic' (List for the discussion of >Buckminster Fuller's works) is no longer being used as an open forum for it's >stated purpose? Or is it rather that bit.listserv.geodesic will be a >philosophical conversation pit? Either would be sad as I don't need to discuss >philosophy, I need help with the math. > Not to worry -- I'm absconding with all the math we need to do a revamped kind of philosophy (includes engineering). Just a matter of boosting the stock of an undervalued discipline, somewhat at the expense of windbags who think Synergetics is theirs to make fun of. Kirby PS: Can you believe this Chapman guy fancies himself a fuddy dud (aka PhD, doctor of philosophy) but didn't know A and B modules stuff (aka "baby math")? Unbelievable! ========================================================================= Date: Tue, 7 Jul 1998 18:36:07 -0400 Reply-To: monkey@one.net Sender: List for the discussion of Buckminster Fuller's works From: David Anderson Organization: Flying Monkey Software Subject: Re: CubeWorld: adding dimensions MIME-Version: 1.0 Content-Type: text/plain; charset=us-ascii Content-Transfer-Encoding: 7bit Hear, hear! I'm in it for the math as well. (I'm an engineer, after all.) BTW: if you want Zac Jr. to have a name that includes a "sense of three", just go for calling him Zac III (Zac the third) and skip the Jr. generation completely. There are no rules, only conventions - you can up the rules as you go along, as long as you don't weird-out the grandparents too often. :o) - Dave Anderson monkey@one.net http://w3.one.net/~monkey Zac Elston wrote: > In a message dated 98-07-07 06:46:28 EDT, you write: > > > I vote we give up discussing any Synergetics on sci.math, > > permanently -- mathematicians have already voted with their > > feet on this one (had plenty of time to take ownership of > > the concentric hierarchy with its A and B mods etc. but > > didn't take advantage, as the record clearly shows). > > So am I to understand that 'bit.listserv.geodesic' (List for the discussion of > Buckminster Fuller's works) is no longer being used as an open forum for it's > stated purpose? Or is it rather that bit.listserv.geodesic will be a > philosophical conversation pit? Either would be sad as I don't need to discuss > philosophy, I need help with the math. > > > Fun chatting. Tuning out. Urner. > > cool...gimme some ========================================================================= Date: Tue, 7 Jul 1998 13:35:41 -0700 Reply-To: List for the discussion of Buckminster Fuller's works Sender: List for the discussion of Buckminster Fuller's works From: PAC Organization: gte.net Subject: Re: CubeWorld: addinng dimensions Kirby Urner wrote in message <35a526cb.61516065@news.teleport.com>... >scott@math.csuohio.edu (Brian M. Scott) wrote: >I'm not in the least confused. That you call the math world >a "space" is metaphoric of course (I use it too -- "semantic >space" even cooler), is projected a posteriori from the >energized space of everyday affairs. In my lingo (what >you call a "jargon", as if you didn't speak one), the >difference between purely conceptual space and energized >space is accommodated by the "Frequency" difference. Wouldn't energized space also be conceptual? > >Most math jargons, on the other hand, don't formalize the >distinction, leaving "the physical world" to physicists >and exulting in the "purity" of prefrequency their >visualizations (or algebraic ones -- visualization is >only slowly making a come-back, after disillusionment >around earlier visual modeling, which was stigmatized as >"naive"). Anyone who tries to talk about the difference >between mathematical space and physical space tends to >fall through the cracks as a philosopher (a kind of >"no man's land" between self-satisfied fields). Hey, I'm in "no man's land", but I'm always self-satisfied by my complete ignorance of technical matters (>: but here s a problem I m having in conceptualized 3D volume space because I think it s wrong specifying that an object _located_in a 3D volume has only three degrees of freedom because an infinite number of other relations exist that are not adequately defined by any XYZ coordinate system given that XYZ systems seem to adhere to an up/down/right/left syndrome. And this also applies to transitions due to diagonals and curved relations. Saying that an object can be _located_ at a precise point with three or four mathematical dimensions is totally different from saying that it exists, moves, and relates in only three or four (degrees of freedom) dimensions. For instance, adding a time dimension still does not solve the problem that objects just do not move up/down/right/left (or even _set_ diagonal positions drawn by specific giga-tuple geometric figures needed to fill the void of improper non-linear or diagonal movement) as would be defined by a 3D coordinate system. I think we re putting ourselves in an artificial cage here. I think that any entity only exists as defined by an infinite amount of relations, not the coordinates of any n-dimensional system artificially used for location purposes. For instance, if two objects in a physical 3D volume can be connected and _located_ by a line drawn between them, that does not mean that they exist in 2D. Then having two objects being _located_ by XYZ coordinates in 3D does not mean they exist in three degrees of freedom either, but rather that this is just a mathematical XYZ graph for locating an object rather than a specific physical attribute of the erroneously called 3D space itself. Locating an object with XYZ coordinates is different from the relations (or freedom) of that object in 3D space. Saying that we exist in a type of 4D "Flatland" also appears wrong. We probably exist in a multitude of dimensions, and for any of them to be non-functional might change radically our viewpoint of reality that is just assumed to be a 4D Flatland but very well might need to contain the multiplicity of all dimensions to be comprehensible even in what we consider 4D. The overview of a higher dimension is not as important as to how all dimensions relate together. Could be, Phil C. ========================================================================= Date: Wed, 8 Jul 1998 00:00:13 GMT Reply-To: List for the discussion of Buckminster Fuller's works Sender: List for the discussion of Buckminster Fuller's works From: Kirby Urner Organization: 4D Solutions Subject: Re: CubeWorld: addinng dimensions MIME-Version: 1.0 Content-Type: text/plain; charset=us-ascii Content-Transfer-Encoding: 7bit "PAC" wrote: > Wouldn't energized space also be conceptual? > You might be thinking about something else when it smacks you though -- wouldn't want to leave the driving to someone who thinks "it's all in my head". >giga-tuple geometric figures needed to fill the void of improper non-linear >or diagonal movement) as would be defined by a 3D coordinate system. My approach is more pragmatic. Use it if it works, upgrade to something better if you get the opportunity and it really matters to you (so far, I'm sticking with Windows 95). XYZ does a lot of real work in the real world -- whether we call it 4D or 3D. When working with kids, a sense of the fcc lattice (aka IVM) and how polys fit in with simple whole number volumes (as per Cliff's post) -- that's healthy stuff that deserved more airplay decades ago. Maybe it's not mathematics though, given the cool reception by those self-advertising as educators in this department. I've been boosting it as "polymath" elsewhere ("afterschool polymath for underserved youth" is a newsgroup header out there somewhere). > The overview of a higher dimension is not as important as to how all >dimensions relate together. > > Could be, > > Phil C. > Yeah, well... I'm not really in the market for idle musings at this point re "dimension". I've got a "jargon" that serves, and bridges to the standard "jargon" (bi-directional) which work. Mostly I'm just serving known quantities, already spelled out, checked, verified (not to discourage idle speculation or anything, just that's not what they pay me for). Kirby --------------------------------------------------------- Kirby T. Urner http://www.teleport.com/~pdx4d/kirby.html 4D Solutions http://www.teleport.com/~pdx4d/ [PGP OK] --------------------------------------------------------- ========================================================================= Date: Tue, 7 Jul 1998 22:00:19 -0400 Reply-To: monkey@one.net Sender: List for the discussion of Buckminster Fuller's works From: David Anderson Organization: Flying Monkey Software Subject: Visualizing the Bulge in Geodesic Projections MIME-Version: 1.0 Content-Type: text/plain; charset=us-ascii Content-Transfer-Encoding: 7bit ...since a few of you asked. A set of VRML worlds which represent the projection of a equilateral triangular side onto the geodesic at different frequencies for different primitive solids. A metric for the bulge is also discussed. http://w3.one.net/~monkey/geodesics/ballpatch -- - Dave Anderson monkey@one.net http://w3.one.net/~monkey ========================================================================= Date: Tue, 7 Jul 1998 23:00:13 -0700 Reply-To: List for the discussion of Buckminster Fuller's works Sender: List for the discussion of Buckminster Fuller's works From: Kirby Urner Subject: Re: Visualizing the Bulge in Geodesic Projections Comments: To: monkey@one.net In-Reply-To: <35A2D2B3.6AFB5000@one.net> Mime-Version: 1.0 Content-Type: text/plain; charset="us-ascii" At 10:00 PM 7/7/98 -0400, you wrote: >...since a few of you asked. A set of VRML worlds which represent the >projection of a equilateral triangular side onto the geodesic at >different frequencies for different primitive solids. A metric for the >bulge is also discussed. > > http://w3.one.net/~monkey/geodesics/ballpatch David -- This is interesting stuff, and classy VRML to boot -- enjoyed viewing some just now. Looking at your higher frequency icosa triangle, I'm imagining that it is itself just one of a large number of triangles -- thinking of this as a generic view of the "difference" between a spherical and chordal triangle, with spheres comprising the "surfaces" (at whatever frequency). Bob Gray has devised an algorithm for going from these spherical triangles to flat ones: involves doing 3 lines parallel to the edges, intersecting at a coordinate, on the spherical, then flattening the triangle and finding those 3 lines now define a triangle, not a point -- so take the center of that triangle as the corresponding "mapped" locus. http://www.teleport.com/~pdx4d/dymax.html is my page on the Fuller Projection and links to Bob Gray's site. His work was used on WorldSat data to derive the gym-sized photo-mosaiced version, a prized posession of the World Game Institute's. I like the work you do, sense I'm lagging. Hope to pick up some slack soon. I'm getting tired of bickering with those know-it-alls who know nothing of Synergetics and would rather collaborate than waste time with numbskulls. But I think it's good from time to time to remind newsgroupies that design science is alive and kicking, thanks to the hard work of so many (not all of whom are even aware of one another yet). Kirby ========================================================================= Date: Tue, 7 Jul 1998 21:41:58 -0700 Reply-To: List for the discussion of Buckminster Fuller's works Sender: List for the discussion of Buckminster Fuller's works From: PAC Organization: gte.net Subject: Re: CubeWorld: addinng dimensions Kirby Urner wrote in message <35a2b479.163337653@news.teleport.com>... >"PAC" wrote: > >> Wouldn't energized space also be conceptual? >> > >You might be thinking about something else when it smacks >you though -- wouldn't want to leave the driving to someone >who thinks "it's all in my head". I don't know. Maybe energized quantum weird stuff and expanding space is the only way to understand beyond inherent geometric 3D pratfalls. > >>giga-tuple geometric figures needed to fill the void of improper non-linear >>or diagonal movement) as would be defined by a 3D coordinate system. > >My approach is more pragmatic. Use it if it works, upgrade to something >better if you get the opportunity and it really matters to you (so far, >I'm sticking with Windows 95). XYZ does a lot of real work in the real >world -- whether we call it 4D or 3D. > >When working with kids, a sense of the fcc lattice (aka IVM) and how >polys fit in with simple whole number volumes (as per Cliff's post) >-- that's healthy stuff that deserved more airplay decades ago. >Maybe it's not mathematics though, given the cool reception by those >self-advertising as educators in this department. I've been boosting >it as "polymath" elsewhere ("afterschool polymath for underserved youth" >is a newsgroup header out there somewhere). Well, if you give a class on the subject, I'd happily drop in - as long as nobody throws spit-wads at the back of my head or leaves gum under my desk (>; That is if I can sit in one spot for a short period of time w/o fidgeting. > >> The overview of a higher dimension is not as important as to how all >>dimensions relate together. >> > >Yeah, well... I'm not really in the market for idle musings at this >point re "dimension". I've got a "jargon" that serves, and bridges >to the standard "jargon" (bi-directional) which work. Mostly I'm >just serving known quantities, already spelled out, checked, verified >(not to discourage idle speculation or anything, just that's not what >they pay me for). It's cool dude. But how dimensions relate together might explain more on how they can be best conceptualized as physical realties: Are they layered and acting congruently from a single controlling source? Do they just intersect at specific "focal spots"? Or maybe totally sublimated the one to the other which in this case would create problems as to how to differentiate them out w/o artificially implying a hierarchical order that might not exist in a sublimated context - specially if one specific identity in the universe is a reflection of the rest (with all dimensions included to boot) of the cosmos. Phil C. ========================================================================= Date: Wed, 8 Jul 1998 05:25:03 GMT Reply-To: List for the discussion of Buckminster Fuller's works Sender: List for the discussion of Buckminster Fuller's works From: Kirby Urner Organization: 4D Solutions Subject: Re: CubeWorld: addinng dimensions MIME-Version: 1.0 Content-Type: text/plain; charset=us-ascii Content-Transfer-Encoding: 7bit "PAC" wrote: > > I don't know. Maybe energized quantum weird stuff and expanding space >is the only way to understand beyond inherent geometric 3D pratfalls. > 4D = angles = pre-time/size (before any energy gets into the picture) 4D+ = angles + frequency = action/adventure in a real time scenario http://members.xoom.com/Urner/images/persian.gif > > Well, if you give a class on the subject, I'd happily drop in - as long >as nobody throws spit-wads at the back of my head or leaves gum under my >desk (>; Brian might -- ABC gum is a specialty of his. > It's cool dude. But how dimensions relate together might explain more >on how they can be best conceptualized as physical realties: Are they >layered and acting congruently from a single controlling source?... Humans invent clever language games for getting real work done in the real world (language phases over into tools with no clear cut line between, and on onward/outward from there). They also invent clever language games for getting no real work done in the real world (no limit to our cleverness it seems). "Dimension" has a long and twisted history and has gotten caught up in both kinds of game -- not a big surprise that it hooks cosmic fish (space cases) so easily. What I want to see is a space age community of die-hards willing to "test pilot" 21st century technology today (e.g. Fly's Eye and Pillow domes). To really get how this community fits into a plan (a big picture informs the ethos, provides a sense of mission), some up front polymath training will be required. I'm driving up to Seattle tomorrow to meet with youth coordinators and start wheels turning for some mo betta programming (including Web TV) to percolate outwards from our regional network. http://www.inetarena.com/~pdx4d/ocn/calculus2.html for more details if interested. Kirby --------------------------------------------------------- Kirby T. Urner http://www.teleport.com/~pdx4d/kirby.html 4D Solutions http://www.teleport.com/~pdx4d/ [PGP OK] --------------------------------------------------------- ========================================================================= Date: Wed, 8 Jul 1998 15:20:41 -0400 Reply-To: List for the discussion of Buckminster Fuller's works Sender: List for the discussion of Buckminster Fuller's works From: Michael Stutz Subject: Tetrahedral kites MIME-Version: 1.0 Content-Type: TEXT/PLAIN; charset=US-ASCII Instructions for making a four-panel tetrahedral kite: http://www.sct.gu.edu.au/~anthony/kites/tetra/plan/ ========================================================================= Date: Wed, 8 Jul 1998 17:26:31 -0700 Reply-To: List for the discussion of Buckminster Fuller's works Sender: List for the discussion of Buckminster Fuller's works From: PAC Organization: gte.net Subject: Re: CubeWorld: addinng dimensions Kirby Urner wrote in message <35a3ff6e.182529497@news.teleport.com>... >"PAC" wrote: >> >> I don't know. Maybe energized quantum weird stuff and expanding space >>is the only way to understand beyond inherent geometric 3D pratfalls. >> > >4D = angles = pre-time/size (before any energy gets into the picture) >4D+ = angles + frequency = action/adventure in a real time scenario Well, this would have to be explained to me more, and I think you're getting tired of this stuff right now considering the responses (>; but I certainly could understand that thinking of space as energy states would alter geometric spacial dimensions. I guess continuums and QM stuff would do the same. > >> It's cool dude. But how dimensions relate together might explain more >>on how they can be best conceptualized as physical realties: Are they >>layered and acting congruently from a single controlling source?... > >Humans invent clever language games for getting real work done in >the real world (language phases over into tools with no clear cut >line between, and on onward/outward from there). They also invent >clever language games for getting no real work done in the real >world (no limit to our cleverness it seems). "Dimension" has a >long and twisted history and has gotten caught up in both kinds >of game -- not a big surprise that it hooks cosmic fish (space >cases) so easily. It is rather comic book in dealing with dimensions like this, but // universes and other such would follow along these lines more than dimensions as entities being differentiated by varying degrees . If dimensions are totally sublimated (seemingly the typical model) into each other then we really are just dealing with a difference of degrees between them and regardless of the strange curvatures involved from tacking one dimension to another, if we are dealing with any type of dimensional continuum, which I think is assumed, then any lower dimension is pretty much rendered non-existent compared to a higher one, the lower one being totally subsumed, and certainly more problematical for any sentient creatures to have access to a lower one but not a higher one as often stated As far as I see it, we re basically dealing with one final combined dimension and regarding any other as separated from the continuum would be false except for artificial evaluations. So then the issue becomes why are we giving dimensions special status beyond saying that, for instance, the number eight is one greater than the number 9? Why would it then be assumed that reality consists of 11 dimensions as opposed to an infinite number of them combined into a final expanse? Unless, perhaps, everything combines to one totality in reverse order as the dimensions increased. Alternatively, some kind of special purpose fandangled multi-twisting hyper-crossed shape of some superior relevance. This basically boils down to the rather simple idea that in a 3d graph, given any type of continuum, which is usually assumed, 2d does not exist except as artificially extracted, and cannot be applied as a separate existent in space as is somewhat assumed when dealing with the 11 dimensions that exist as "separate" physical realities. Phil C. ========================================================================= Date: Thu, 9 Jul 1998 16:49:50 GMT Reply-To: List for the discussion of Buckminster Fuller's works Sender: List for the discussion of Buckminster Fuller's works From: Kirby Urner Organization: 4D Solutions Subject: An Overview of the Quadray Coordinate System MIME-Version: 1.0 Content-Type: text/plain; charset=us-ascii Content-Transfer-Encoding: 7bit AN OVERVIEW OF THE QUADRAY COORDINATE SYSTEM by Kirby Urner 4D Solutions July 9, 1998 NeoCartesian Coordinates Quadrays comprise a NeoCartesian coordinate system with four positive basis rays (1,0,0,0) (0,1,0,0) (0,0,1,0) (0,0,0,1) from an origin (0,0,0,0). Whereas the conventional XYZ apparatus uses 3-tuples and permuted signage to map volume, quadrays assign a unique address to each point using only positive scalars or zero. This is made possible by the fact that positive vectors point symmetrically in four directions from the origin, meaning we can approach the origin (0,0,0,0) from any direction by means of a positive basis vector sum. Put another way: a vector pointing 180 degrees from a positive vector is likewise a positive vector e.g. -(1,0,0,0) = (-1,0,0,0) = (0,1,1,1) Because (1,1,1,1) is a sum of four vectors pulling equally and symmetrically away from they origin (e.g. is (1,0,0,0) + (0,1,0,0) + (0,0,1,0) + (0,0,0,1)) it is equivalent to (0,0,0,0), i.e. these vectors placed tip-to-tail take us right back to the origin. Indeed, any (n,n,n,n) = (0,0,0,0). This identity property allows us to reduce any quadray 4-tuple (a,b,c,d) to lowest terms by subtracting the lowest valued scalar (n,n,n,n) from the vector sum (a,b,c,d), where n is nonzero (if the lowest coordinate is already 0 -- i.e. none are negative -- then we're done). By these means, all quadrays are reduced to 4-tuples consisting of one or more zeros, with the rest of the coordinates all positive scalars. For example: (-10, 5, 0, 8) - (-10, -10, -10, -10) = (0, 15, 10, 18) ( 5, 9, 1, 6) - ( 1, 1, 1, 1) = (4, 8, 0, 6) -10 and 1 are the "lowest scalars" in their respective 4-tuples, hence the "identity element" reduction to lowest terms (akin to reducing fractions to lowest terms -- for pedagogical purposes). Polyhedra in the IVM Given that quadrays point to the 4 vertices of the regular tetrahedron of edge length 2, with an angle between them of acos(-1/3), polyhedra embedded in the face-centered-cubic lattice (fcc) or isotropic vector matrix (ivm) tend to have whole number coordinates. Indeed, all fcc vertices are themselves linear combinations of {2,1,1,0} where { } means "all permutations of". These are the coordinates of a regular Octahedron, dual to the duo-tet cube, in quadray 4-tuples (a,b,c,d): POINTID ACOORD BCOORD CCOORD DCOORD O1A 1.0000000 0.0000000 0.0000000 1.0000000 O1B 1.0000000 0.0000000 1.0000000 0.0000000 O1C 1.0000000 1.0000000 0.0000000 0.0000000 O1D 0.0000000 1.0000000 0.0000000 1.0000000 O1E 0.0000000 1.0000000 1.0000000 0.0000000 O1F 0.0000000 0.0000000 1.0000000 1.0000000 The duo-tet cube (C1) consists of a tetrahedron (T1) and its dual (T2) with the following quadray coordinates: POINTID ACOORD BCOORD CCOORD DCOORD T1A 1.0000000 0.0000000 0.0000000 0.0000000 T1B 0.0000000 1.0000000 0.0000000 0.0000000 T1C 0.0000000 0.0000000 1.0000000 0.0000000 T1D 0.0000000 0.0000000 0.0000000 1.0000000 T2A 0.0000000 1.0000000 1.0000000 1.0000000 T2B 1.0000000 0.0000000 1.0000000 1.0000000 T2C 1.0000000 1.0000000 0.0000000 1.0000000 T2D 1.0000000 1.0000000 1.0000000 0.0000000 The space-filling rhombic dodecahedron, being the set of vertices of the duo-tet cube + its dual, the octa O1, has vertices of these two sets combined. The above listings are from ALLPOINTS (catalog of points). To generate polyhedra, sets of edges connecting these cataloged points are required. Here are the edges of the rhombic dodecahedron, taking from SHAPES, a related table. Columns ID1 and ID2 are populated with vertices already cataloged (above) in ALLPOINTS. SHAPEID ID1 ID2 R1 O1A T1A R1 O1A T2B R1 O1B T1A R1 O1B T2B R1 O1A T2C R1 O1A T1D R1 O1F T1D R1 O1F T2B R1 O1B T2D R1 O1B T1C R1 O1F T1C R1 O1F T2A R1 O1D T1D R1 O1D T2A R1 O1D T2C R1 O1D T1B R1 O1C T1A R1 O1C T2D R1 O1C T1B R1 O1C T2C R1 O1E T1C R1 O1E T2D R1 O1E T1B R1 O1E T2A R1 O1E T1C Volumes of IVM Polyhedra The quadrays volume method is defined around Euler's for the volume of a tetrahedron given its 6 edges, as modified by de Jong to return a value of 1 for the 2x2x2 tetrahedron, where '2' is in fcc sphere radii. If we call the distance from 1 fcc sphere center to its neighboring center (12 options) an interval of measure 1, then our tetrahedron is 1x1x1. It has a volume of 1, as per Fuller's modeling of 3rd powering in his synergetic geometry (a philosophical language more than a math). Given the above volume method, the volumes of the so-far introduced polyhedra is as follows: Tetrahedron (T1 and dual T2): 1 Duotet Cube C1 (T1+T2): 3 Octahedron O1 (dual of duo-tet): 4 Rhombic dodecahedron R1 (C1+O1): 6 Quadrays were originally introduced on Synergetics-L by David Chako, and evolved in a neoCartesian direction by Kirby Urner. Kirby Major references: http://www.teleport.com/~pdx4d/quadrays.html http://www.teleport.com/~pdx4d/quadshapes.html http://www.teleport.com/~pdx4d/quadvols.html http://www.teleport.com/~pdx4d/quadphil.html --------------------------------------------------------- Kirby T. Urner http://www.teleport.com/~pdx4d/kirby.html 4D Solutions http://www.teleport.com/~pdx4d/ [PGP OK] --------------------------------------------------------- ========================================================================= Date: Fri, 10 Jul 1998 08:22:09 -0500 Reply-To: List for the discussion of Buckminster Fuller's works Sender: List for the discussion of Buckminster Fuller's works From: anthony kalenak Subject: Re: An Overview of the Quadray Coordinate System Content-Type: Text/Plain; Charset=US-ASCII Content-Transfer-Encoding: 7Bit MIME-Version: 1.0 (WebTV) Kirby, Thanks for the primer. It will take a while to absorb it, become conversant in it and to lose my (xyz) mind set. I have questions: Is there a naming convention or order for the axis' ? And when you say the polyhedra are imbedded, does that mean (0,0,0,0) is at their center. Thanks, Tony Kalenak ========================================================================= Date: Fri, 10 Jul 1998 08:55:06 -0700 Reply-To: List for the discussion of Buckminster Fuller's works Sender: List for the discussion of Buckminster Fuller's works From: Kirby Urner Subject: Re: An Overview of the Quadray Coordinate System In-Reply-To: <2027-35A61581-6924@mailtod-142.iap.bryant.webtv.net> Mime-Version: 1.0 Content-Type: text/plain; charset="us-ascii" At 08:22 AM 7/10/98 -0500, you wrote: >Kirby, > Thanks for the primer. >It will take a while to absorb it, become conversant in it and to lose >my (xyz) mind set. >I have questions: >Is there a naming convention or order for the axis' ? I've been using (a,b,c,d). At http://www.teleport.com/~pdx4d/quadrays.html I go around the "base" clockwise with (1,0,0,0) (0,1,0,0) (0,0,1,0) and then put (0,0,0,1) at the "apex" (terms in quotes because base/apex is all how you look at it of course). >And when you say the polyhedra are imbedded, does that mean (0,0,0,0) >is at their center. > No, not necessarily. Using combinations of {2,1,1,0} vectors you can navigate to any IVM sphere center. I did a graphic using quadray coordinates showing spheres in a VE packing (cuboctahedral) with a little rhombic dodecahedron around each sphere. See: http://www.teleport.com/~pdx4d/images/rdpack.gif Kirby ========================================================================= Date: Fri, 10 Jul 1998 04:20:53 GMT Reply-To: List for the discussion of Buckminster Fuller's works Sender: List for the discussion of Buckminster Fuller's works From: Kirby Urner Organization: 4D Solutions Subject: Re: CubeWorld: adding dimensions MIME-Version: 1.0 Content-Type: text/plain; charset=us-ascii Content-Transfer-Encoding: 7bit kramsay@aol.com (KRamsay) wrote: >If you want to compute distances with these coordinates, I suppose >the easiest way is to project onto the plane {(a,b,c,d):a+b+c+d=0}. >All you need to do is to subtract the average from each coordinate. >The usual distance formula in R^4 then works. > Based on this post, it's not clear to me whether you realize that these (a,b,c,d) coordinates are not in R^4. See 'An Overview of the Quadrays Coordinate System' posted below for more info, if interested. >they really don't have a good idea of how flexible we are. True, I >have heard intelligent criticism of mathematicians for inflexibility, >but by people who have more substantial knowledge of the mind-set they >are criticizing. > I think the quadray game per se is pretty cogent and not likely to encounter much resistence from mathematicians. >From a programming point a view, I found it easer to take my all whole number coordinates for FCC sphere centers and create little rhombic docahedra as the domains of the unit-radius FCC spheres using my all whole numbers for these vertices too -- easier than messing with the XYZ 3-tuples that is. Of course the ray-tracing software I was using to do the final rendering is XYZ based, so I had to convert to XYZ upon writing the ray-tracing script But given those methods are built in to my class definitions, this didn't involve much overhead. The result: http://www.teleport.com/~pdx4d/images/rdpack.gif >more vertex than edge. My friend got to show him that vertices-edges >really counted the number of connected components, which I guess the >instructor thought was pretty cool. > Certainly Synergetics is invested in ye ol' Eulerian V+F=E+2, which for omnitriangulated systems also gives N:F:E = 1:2:3 where N=V-2. For the cuboctahedron, the number of vertices in layer f is 10 ff + 2, which, by jitterbugging, turns into an icosahedron of the same frequency (f) i.e. same number of vertices. This was initially interesting in the 1960s when Casper-Klug were first discovering the 5-fold symmetry of virus protein shells, noticed the resemblance to Fuller's domes, and went to him for some math relating to capsomere counts (Fuller came back with 10 ff + 2, coming from his original sphere packing studies). But Fuller was a maverick, not a peer-accepted mathematician (Coxeter at least was generous with his time), and when it came time for Scientific American to do with write-up (article by Horne), the whole connection to Synergetics was dropped in favor of a link to the work of Arthur Goldberg (which was also relevant, definitely, but not the same as the information in Synergetics, which should have been linked to as well -- but making that link just didn't seem "safe enough" at the time I guess). See: http://www.teleport.com/~pdx4d/virus.html Deja vu with the fullerenes, although this time the connection stuck, because of the naming convention. Synergetics is now in no danger of obscurity, is exploding everywhere on the web (and it's about time too!). See: http://www.inetarena.com/~pdx4d/synergetica/eja1.html Kirby --------------------------------------------------------- Kirby T. Urner http://www.teleport.com/~pdx4d/kirby.html 4D Solutions http://www.teleport.com/~pdx4d/ [PGP OK] --------------------------------------------------------- ========================================================================= Date: Fri, 10 Jul 1998 15:54:44 GMT Reply-To: List for the discussion of Buckminster Fuller's works Sender: List for the discussion of Buckminster Fuller's works From: Kirby Urner Organization: 4D Solutions Subject: Re: CubeWorld: adding dimensions MIME-Version: 1.0 Content-Type: text/plain; charset=us-ascii Content-Transfer-Encoding: 7bit Robin Chapman wrote: >I heartliy agree that one should choose one's coordinate system with regard >to the problem at hand. Indeed in a previous altercation with Urner I said >"As a slave of hypercross dogmatics I am forced to choose the most appropriate >coordinate system for the problem at hand (Cartesian, affine, projective, >trilinear, polar, spherical, etc.) while no doubt you as liberated from >this sterile dogma are free to use quadray coordinates for any problem >whatsoever." > And I told Chapman best to just characterize his own position without trying to characterize mine. I'm not averse to using n-tuples to play with polytopes (e.g. I'm studying Stuart Kaufmann's "The Origins of Order" wherein binary strings label vertices of a hypercube and "Hamming distance" measures intervals between) and have used various gizmos (e.g. homogenous coordinates) for doing projective computer graphics (the standard way). I use quadrays as a pedagogical device to investigate an alternative usage patterns involving the "dimension" concept -- not to exclude established patterns (as if I could or wanted to) but to make more room for Fuller's usage, which was self-consistent enough to merit follow-through by interested scholars (e.g. philosophers). I've also coded various quadray-savvy class definitions around data tables holding 4-tuple vertices and edges and used these to generate ray-tracings. The project was aesthetically satisfying. Quadrays "fit the grain" of what Fuller called the isotropic vector matrix, the skeleton of edges connecting sphere centers in the FCC lattice. I use "hypercross dogmatics" to circle a cultural nexus wherein a specialized inner circle becomes a priest caste to awed laypersons largely because of a nonsensical proposition: that four (or more) mutual orthogonals has any meaning as a visualization, that we are somehow 'trapped in 3D' by our inferior senses (except maybe a lucky few with a kind of special vision). To counter this confusing mess of metaphors, cliches, algebraic methods, propaganda, and bona fide visualizations which are indeed helpful for doing polytope geometry, I employ some synergetics, showing people how they might get free of the whole business (yet still keep a hold on any of the math that might be useful or engaging -- but perhaps using different figures of speech to make it more smoothly operational). Kirby --------------------------------------------------------- Kirby T. Urner http://www.teleport.com/~pdx4d/kirby.html 4D Solutions http://www.teleport.com/~pdx4d/ [PGP OK] --------------------------------------------------------- ========================================================================= Date: Fri, 10 Jul 1998 19:41:49 GMT Reply-To: List for the discussion of Buckminster Fuller's works Sender: List for the discussion of Buckminster Fuller's works From: Kirby Urner Organization: 4D Solutions Subject: Re: In case you missed the last one... MIME-Version: 1.0 Content-Type: text/plain; charset=us-ascii Content-Transfer-Encoding: 7bit "WmWallace!" wrote: >The Bible also describes Peter, a disciple of Jesus, as carrying a >sword. Remember when he "removed" the ear of the soldier's assistant >at the garden when they came to take Christ away? He took the weapon >out to protect the Lord. <> Interesting invocation of Biblical themes and hyperlinking to USA's protecting of imperial Christendom against those Commie athiests -- and in response to someone bringing up genocide against native Americans no less. So perfect, so pat. Post Cold War, maybe the fork in Christianity (western vs. eastern patriarchies, Rome vs. Byzantium) and the more mystical bent of the latter, brings native Americans closer to Russians such that USA will feel safer about its Christian assets and do that swords into plough shares thing more successfully. Quakers, with strong NavAm ties and high tech holdings, a useful bridge (one of many). Atheist suppresion of eastern mysticism resulted in a lot of "over the edge" science growing up behind the "Iron Curtain" -- Carlos Castaneda had nothing on those paranormalists with their "tensegrity" (lighter-weight, less oppressive) blueprints for tomorrowland's cathedrals (aka religious sites, focii for pilgrims -- Christocentric included). >Boy, if my nation asked me to volunteer again for service I would. >There is a difference between you and I and it isn't just skin color. >You cannot pick and choose your war. You serve your nation when >called upon to do so--PERIOD. > More difficult is to detect when your nation and its ideals are being twisted around by some derelict crowd with less integrity and intelligence than those who set an earlier course. In the transition from FDR to Nixon, for example, when do your blow the whistle? Or do we think real dissent is always by definition highly illegal (in which case a police state is our lot)? Counterintelligence on the home front: a delicate business sometimes (starts within -- one can be overtaken by insidious mob psychologies that, in retrospect, turn out to be downright unAmerican). >BWho's going to make that assessment? You? What basis for this >reasoning would you use? The media? The government? See where I'm >going with this one? Your statement lacks thought. What if everyone >decided to say, "I'll fight if I think it's a good enough cause..." or >"...if the nation is truly in peril, I'll fight!" When they idiots >lack the access to the classified information (which cannot be >released to the general public, as I'm sure you would advocate, >because there might be a SPY in the crowd--imagine that!) which would >allow them to make an uneducated guess, since they have no training in >analyzing/evaluating that raw information. > Note USA has freedom and democracy as designed-in features, with secrecy sometimes necessary for the preservation of same. But circular logic whereby "idiots" must admit their subservience to a caste of "in the know" professionals (with privileged access to situation rooms), which latter dictate the whys and wherefores of a war (hot, warm or cold) in which the "idiots" must fight -- such a state of affairs is oft times (if not always) symptomatic of a democracy deceased. So then do we recognize our USA as behind the call to arms, and when do we work the grass-roots against thuggery? Thanks to open sources, our emerging high tech ability to cross-check data from all walks in a hurry, the situation room people have progressively less of an edge, are having a harder time proving that their "secrets" aren't public knowledge, already circulated among those keeping a look out (NGOs seem to have some pretty well placed sources, judging from their success as "watch dogs" of late). Again, when do you recognize "when in the course of human events..." it becomes necessary to stop unquestioningly "following your betters"? Founders were clear the USA would need a lot of built-in fail-safes (and even those weren't enough, the design was flawed from the beginning, lots added later, more to go). If we'd left it to the unquestioning, the authoritarians, we'd still be a part of the UK. Anyway, I'm glad the USA won against LAWCAP in Vietnam in the final analysis (I'm using somewhat byzantine logic here, I realize). > >WmWallace! ^^^^^^^^^^ dim bulb! Kirby --------------------------------------------------------- Kirby T. Urner http://www.teleport.com/~pdx4d/kirby.html 4D Solutions http://www.teleport.com/~pdx4d/ [PGP OK] --------------------------------------------------------- ========================================================================= Date: Fri, 10 Jul 1998 19:45:33 GMT Reply-To: List for the discussion of Buckminster Fuller's works Sender: List for the discussion of Buckminster Fuller's works From: "Brian M. Scott" Organization: Cleveland State University Subject: Re: CubeWorld: adding dimensions On Fri, 10 Jul 1998 15:54:44 GMT, pdx4d@teleport.com (Kirby Urner) wrote: >I use "hypercross dogmatics" to circle a cultural nexus wherein >a specialized inner circle becomes a priest caste to awed laypersons >largely because of a nonsensical proposition: that four (or more) >mutual orthogonals has any meaning as a visualization, that we are >somehow 'trapped in 3D' by our inferior senses (except maybe a >lucky few with a kind of special vision). How appropriate: you use a silly neologism to describe something that exists only in your imagination. Brian M. Scott ========================================================================= Date: Fri, 10 Jul 1998 21:04:43 GMT Reply-To: List for the discussion of Buckminster Fuller's works Sender: List for the discussion of Buckminster Fuller's works From: Kirby Urner Organization: 4D Solutions Subject: Re: CubeWorld: adding dimensions MIME-Version: 1.0 Content-Type: text/plain; charset=us-ascii Content-Transfer-Encoding: 7bit scott@math.csuohio.edu (Brian M. Scott) wrote: >How appropriate: you use a silly neologism to describe something that >exists only in your imagination. > >Brian M. Scott The neologism is actually pretty clever, as several have remarked. It incorporates a religion meme plus aptly describes what's at the heart of "4-D" Euclideanism: 4 or more mutual orthogonals, crossed at the origin. The graphic of the little hooded monk fits right in. That what I'm fighting is more than just a figment of my own imagination is well documented at my website, where I link to exhibits symptomatic of this dogma's pop cultural sway. For example: "We cannot see the multidimensional reality because our senses are limited to three dimensions, yet the higher- dimensional environment has a more substantial reality than our world." From: http://home.sprynet.com/sprynet/jowolf/ If you saw the recent PBS math show, 'Life by the Numbers', then you saw us do a segment with a mathematician staring at a tesseract on his computer screen, chatting about whether these polytopes "really exist" in higher dimesnional space (as if this were an empirical question and not a grammatical one), and then wandering down the street to a church, staring at a stained glassed window, playing up the religious meme while continuing the "higher dimensions" meditation. The companion volume by Keith Devlin repeats the dogma that we're "trapped" in 3 dimensions (as if the hypercross were an empirical datum escaping physiological detection owing to limitations of our neurological design -- versus a prima facie nonsensical metaphor (which we can do without and still get mileage from the algebra, less cryptic and obfuscating visualizations)). Just read Abbott's 'Flatland' again if you think 'hypercross dogmatics' is just something I made up, and not a prevalent, easily tapped cultural phenomenon (traced in great detail through such scholarly works as Linda Henderson's book: "The Fourth Dimension and Non-Euclidean Geometry in Modern Art" http://www.amazon.com/exec/obidos/ASIN/0691101426/002-2219567-7879451 (she was interviewed for the PBS show as well)). After 'Flatland' we got a generation of people determined to "see beyond 3D" with more or less positive claims re their ability to do so (with few skeptical inquirers applying their same bogus- detectors to these hypercrossers as to paranormalists of other varieties -- because the hypercross shrine is "too close to home", supports superstitions that highly educated PhDs are allowed to indulge, are loathe to have debunked as this would expose their ethnocentrism and hypocrisy). My essay, which defines what I'm talking about, provides exhibits, discusses my alternative viewpoint, is at on the web at http://www.teleport.com/~pdx4d/hypercross.html (cited many times) It's part of my Synergetics on the Web, because while Fuller used '4D' as a key term, his usage is not in the Euclidean tradition ala Coxeter and Conway nor in the NonEuclidean tradition ala Einstein and Riemann. People who try to study Synergetics frequently get hung up on this point, trying to filter his thinking through what they learned in school for from reading popularizations. It's an uphill battle to establish a separate thread from the aforementioned, wherein '4D' has an internally consistent usage without being either 3D + Time or 'dim n' orthonormal Cartesianism. Quadrays are likewise a part of 'Synergetics on the Web' (winner of a Dr. Matrix award for science excellence, rave-reviewed at the IBM website long ago) and have been somewhat helpful in combatting conflicting gestalts, undermining deeply engrained prejudices, as a prerequisite to having any conceptual space to study something different (i.e. Synergetics). Seems to me you're over-anxious to be derogatory about my thinking while doing zero work to even inform yourself of what that thinking might be. This is the hallmark of a sloppy, lazy ideologue, not a mathematician, or serious-minded scholar of any variety for that matter. Kirby --------------------------------------------------------- Kirby T. Urner http://www.teleport.com/~pdx4d/kirby.html 4D Solutions http://www.teleport.com/~pdx4d/ [PGP OK] --------------------------------------------------------- ========================================================================= Date: Sat, 11 Jul 1998 04:00:49 GMT Reply-To: List for the discussion of Buckminster Fuller's works Sender: List for the discussion of Buckminster Fuller's works From: Kirby Urner Organization: 4D Solutions Subject: 1960s - 1990s: synergetics and the virus meme MIME-Version: 1.0 Content-Type: text/plain; charset=us-ascii Content-Transfer-Encoding: 7bit [ from Synergetics on the Web: http://www.teleport.com/~pdx4d/synhome.html ] Sphere Packing and Capsomere Counts Sometime in the 1960s virologists first approached Fuller with a puzzle: new x-ray diffraction patterns revealed that many viruses were similar in structure to geodesic domes. The protein sheaths housing the RNA were 5-fold symmetric, icosahedral structures, and the number of capsomeres numbered 12, 42, 92... Virologists wondered whether Fuller recognized these numbers from his explorations with geodesic domes. He answered with his sphere-packing formula for the number of spheres in the outer layer of an expanding cuboctahedral packing: 10F^2+2, where F=1,2,3.. and is the number of intervals between sphere centers along an outermost edge. That Fuller's investigations were proving relevant, and that 10F^2+2 in particular was matching empirical data, made the front page of the New York Herald Tribune. Given that the jitterbug transformation turns a cuboctahedral layer into an icosahedral one, the geometric basis for the number of viral capsomeres was clear. However, other common capsomere counts were not accounted for by the cuboctahedral numbers, as when the capsomeres 'wrap' around an icosahedron in a skewed pattern. Virologists Casper and Klug derived a formula that fit even more of the data, which they subsequently connected back to the geometric investigations of Arthur Goldberg, a mathematician. When Dr. Robert Horne wrote a groundbreaking article for Scientific American about these matters, he chose not to credit Fuller for having discovered anything new, although students of synergetics (including Arthur Goldberg) realized at the time that Fuller's pioneering investigations, like Goldberg's, also derived from more generalized principles -- in Fuller's case these were generalizations about sphere packing in a variety of conformations, not just the cuboctahedral. Armed with Goldberg's 1922 paper, virologists felt they were off the hook vis-a-vis hard-wiring anything from Fuller's synergetic geometry into their discipline. Many felt relieved because Fuller, something of a maverick (regarded as such even by architects), and without the academic credentials expected of a scientist, might only serve to undermine the status quo if admitted into the literature as a recognized contributor in such professional circles. The idea that virology might also serve as a useful access point leading to a more generic synergetics- informed curriculum, linking in turn to many other disciplines, at the time seemed quasi-irrelevant, if not downright alien, to these rather narrowly focused specialists. With the subsequent discovery of a new allotrope of carbon in the 1980s, again showing five-fold symmetric icosaspherical geometry (variably frequenced hexa-pents), the opportunity to provide a useful curriculum access point to synergetics again arose. This time, by naming the newly discovered C60 molecule buckminsterfullerene (and other frequencies fullerenes) its discoverers helped forge a chemistry-synergetics link (see E.J. Applewhite's The Naming of Buckminsterfullerene for more on this story). The Scientific American has subsequently published an article about synergetics and five-fold symmetry in its Japanese edition (dinosaurs on the cover), focusing on Yasushi Kajikawa's modular decompositions of well-known five-fold symmetric shapes (e.g. the icosahedron). It's cover story in January, 1998 was also devoted to a central synergetics theme, tensegrity (as a principle for understanding cell structure), which likewise belongs to Ken Snelson. More relevant to the this virus thread than tensegrity, however, was a story in the previous issue (December, 1997) about metal atoms clustering in icosahedral and cuboctahedral conformations -- no link to Fuller's groundbreaking sphere-packing studies was included, even in the notes section. For further reading: A Case of Deja Vu in The Invention Behind the Inventions: Synergetics in the 1990s Memo to Ivars Peterson re Fuller & viruses in his Jungles of Randomness Review of Hugh Aldersey-Williams' chapter on Fuller in his book The Most Beautiful Molecule about buckminsterfullerene Some further discussion including w/ Hugh Aldersey-Williams Kroto on Fuller and the naming of buckminsterfullerene [ for graphics and active hyperlinks version, see http://www.teleport.com/~pdx4d/virus.html ] --------------------------------------------------------- Kirby T. Urner http://www.teleport.com/~pdx4d/kirby.html 4D Solutions http://www.teleport.com/~pdx4d/ [PGP OK] --------------------------------------------------------- ========================================================================= Date: Sat, 11 Jul 1998 01:55:40 GMT Reply-To: List for the discussion of Buckminster Fuller's works Sender: List for the discussion of Buckminster Fuller's works From: "Brian M. Scott" Organization: Cleveland State University Subject: Re: CubeWorld: adding dimensions On Fri, 10 Jul 1998 21:04:43 GMT, pdx4d@teleport.com (Kirby Urner) wrote: >Seems to me you're over-anxious to be derogatory about my thinking >while doing zero work to even inform yourself of what that thinking >might be. This is the hallmark of a sloppy, lazy ideologue, not a >mathematician, or serious-minded scholar of any variety for that >matter. I've looked at your site. I've carried on correspondence with you. I've seen too many of your posts in sci.math. I've seen a lot of self-glorifying hype and demonizing of an 'inner circle' that doesn't exist; you're an expert at leading the cheering section while you tilt at windmills that exist only in your own mind. I've seen a mathematical triviality presented as the salvation of our youth from the dead hands of Euclid and Descartes. On the other hand, I've never seen much understanding on your part of what mathematics and mathematicians are about. You appear to be quite energetic, but you're certainly an ideologue, not a mathematician, and you've presented no evidence of scholarship. Brian M. Scott ========================================================================= Date: Sat, 11 Jul 1998 07:55:53 GMT Reply-To: List for the discussion of Buckminster Fuller's works Sender: List for the discussion of Buckminster Fuller's works From: Kirby Urner Organization: 4D Solutions Subject: Re: CubeWorld: adding dimensions MIME-Version: 1.0 Content-Type: text/plain; charset=us-ascii Content-Transfer-Encoding: 7bit scott@math.csuohio.edu (Brian M. Scott) wrote: >I've looked at your site. I've carried on correspondence with you. >I've seen too many of your posts in sci.math. I've seen a lot of >self-glorifying hype and demonizing of an 'inner circle' that doesn't >exist; you're an expert at leading the cheering section while you tilt >at windmills that exist only in your own mind. I've seen a >mathematical triviality presented as the salvation of our youth from >the dead hands of Euclid and Descartes. On the other hand, I've never >seen much understanding on your part of what mathematics and >mathematicians are about. > "Demonize" is inaccurate. Demons are fiendishly clever, worthy opponents, at least in my cosmology. My technoinvective tends toward "paid hack" and "oblivious numbskull" at its ugliest -- not what I'd call demonizing. I'm fond of Euclid and Descartes, have posted admiringly of both and used some of their contributions in my own thinking. Both of these guys are heros in my book. I've labeled this quadrays apparatus "NeoCartesian" out of respect for a master. Fuller comes along some centuries later and suggests drilling our kids in orthonormal thinking to the exclusion of doing much with 60-degree sphere packing is part of the problem, and suggests we remember that ancient Greek Euclidean stuff was originally scribed in sand on the beach of a spherical planet i.e. the doctrine of "infinitely expanded, infinitely thin planes" is really dispensible metaphysics, without which 'The Elements' will survive just fine (I'd argue we could recast most if not all of Euclid's theorems minus both "infinity" and "continuity" as necessary assumptions). That seemed an interesting angle. I decided to give Fuller the benefit of the doubt and explore his syllabus in detail, in part to get to the bottom of why we never heard much about him at Princeton (where I spent a lot of time in the philosophy and religion departments -- some math (eigenvectors with Dr. Thurston), lots of computers (fond of Iverson's APL), and some Woodrow Wilson School (Dr. Kahler sorry to lose me to philo)). I reached the conclusion (in the 1980s) that in many important respects Fuller was on target with his analysis: academia has become way over-specialized, rewarding people for narrowing their focus to record-setting extremes. Synergetics has fallen through the cracks not because Fuller was a crackpot as because people like Hugh Kenner, a renouned James Joyce scholar but also the author of 'Geodesic Math and How to Use It' are ever fewer and further between. We just don't make 'em like we used to I guess. By this measure (of falling away from a commitment to comprehensivity in thought) the "doctor of philosophy" degree has degraded beyond all recognition -- otherwise we'd have more experienced synergetics readers in our philosophy departments by now. Not demonizing. Just a sad state of affairs -- and dangerous. If academia won't (wouldn't) handle Fuller, then who will (did)? http://www.teleport.com/~pdx4d/bio.html gives some clues. Also, I've not presented quadrays as "the salvation of our youth". On the contrary, at my website you'll find this quote from an email sent in October of 1997: I think this quadrays thread is worth bringing to the attention of a larger audience as it addresses a perceived lack which has dogged Synergetics from the beginning: people consider it incomplete because largely devoid of algebraic content. I've never subscribed to this view, as I see Fuller's goal was to work at a primitive level using what he called 'conceptual mathematics' -- his language is operational even without all those algebraic gizmos we've come to know and love ever since Descartes and before. But this new quadrays thread doesn't hurt our cause, even if some of us consider it unnecessary. [italics added] ^^^^^^^^^^^^^^^^^^^^^^^ >You appear to be quite energetic, but you're certainly an ideologue, >not a mathematician, and you've presented no evidence of scholarship. > Mathematicians can be ideologues of course, but I've never claimed to be a mathematician (even if I've taught aspects of the subject and gotten paid for doing so). You're free to splat out your opinion re "no evidence of scholarship" of course, but I think it unbelievably biased and contrary to the very evident facts. I rest content to let others judge whether I have presented any evidence of scholarship. As you can guess, I get a fair amount of fan mail, am not suffering for a lack of ego food. I append a recent post to sci.physics as further evidence that I am not villainizing Euclid and really do have kids' best interests at heart when I do my curriculum writing. If you are serious about education, as probably you are, then I think we'd do better to look for common ground and possible areas of collaboration, since I've already passed the qualifying tests I care about (administered by masters I respect) and am not about to take a few rotten tomatoes from the sci.math peanut gallery as a sign to call it quits. On the other hand, I'm more inclined to spend my time where my work is appreciated. Some mathematicians are more willing to work with me peer-to-peer and in an atmosphere of mutual respect. Plus some work does more to keep my family eating and able to procure stuff then squandering my time posting to newsgroups. So if it looks like I'm tapering off here on sci.math, take that as a sign that I'm not a complete idiot. There's certainly work to be done, and math is a big part of it. With or without your assistance, we're gonna make it happen and have fun besides. So stay tuned (or don't). Kirby Curriculum writer 4D Solutions ======== Newsgroups: alt.education,k12.chat.teacher,k12.chat.junior,sci.physics Subject: Curriculum notes (afterschool polymath for underserved youth) From: pdx4d@teleport.com (Kirby Urner) Date: Mon, 06 Jul 1998 20:11:01 GMT Notes for upcoming meeting with youth coordinators, American Friends Service Committee, in Seattle -- presenting re the 1998 Math Makeover Campaign (sponsored, in part, by the Philosophers' Network) Primary references: http://www.inetarena.com/~pdx4d/ocn/ http://www.inetarena.com/~pdx4d/ocn/calculus2.html http://www.teleport.com/~pdx4d/makeover1.html -------------- Philosophy for young people (curriculum notes): The focus here is getting "beyond flatland" early, meaning returning to those "scribing in sand" demonstrations by coming to "Euclid's world" from space [1], i.e. from spatial geometry, wherein surfaces are clearly aspects of volumetric topologies. Classes focus on Sun->Earth economy with energy transfer from fusion to "big cycle" weather/climate and biomass formation (e.g. agriculture, wilderness). The geometry of electromagnetic waves linked to Archimedes screw (irrigation) as precursor to latter phase-in of cross-product (curl). Field trip to local alternator farm (e.g. Bonneville dam) if feasible. Use Earth as link to spherical geometry, projecting polyhedra from inside as "shadow-castings" e.g. spherical tetrahedron gives 4 equal regions on the surface, each of area equal to spherical cross-section.[2] Projecting icosahedron gives 20 spherical triangles setting stage for world map projection and overview of resources (emphasize sufficiency, if intelligence in the wings).[3] Zoom in on a beach in Greece and show ancient greek philosophers with ruler and compass using 'Elements'-style postulates and constructing theorems (do some). Relate "points" to grains of sand, "plane" to sandy beach. Emphasize locally flat aspect of Earth, given relatively tiny dimensions of humans, and Greek propensity to use post-and-lintel (e.g. Parthenon) as precursor of western civ fixation on "orthogonal" as "normal" even though it isn't, outside human designs.[4] De-emphasize points as "zero dimensional" or planes as "infinitely expansive" (important for historical context and backward compatibility, but not for drilling).[5] Zoom in further on beach sand and idealize as close-packed spheres. Explore packing 12 around 1 (2 ways) one way giving cuboctahedron. Use to set stage for concentric hierarchy w/ tetrahedral and octahedral voids in 2:1 ratio (population) and 1:4 volume. Cuboctahedron = 8 tetrahedra + 6 1/2 octahedra for volume 20. Jitterbug as bridge to 5-fold (e.g. icosahedron, rhombic triacontahedron). Do volumes again with cube as unit and compare. Discuss cube as model of 3rd powering. Do again with tetrahedron as 3rd powering model. Emphasize philosophy of math as self-consistent games, some tightly coupled, some relatively isolated.[6] Regarding axioms, note their definitional nature without dwelling too much on "self-evidence" (not really a necessary stipulation). Look at "real numbers" as "rationals" plus "irrationals" then revisit through eyes of another culture, e.g. a so-called "Persian math" with different categories: symbols as "terminal" versus "algorithmic" (bears a family resemblance to "rational" and "irrational", certainly).[7] Discuss definitions as cultural artifacts, not "cast in stone for all time" (perhaps concluding with Ozymandius poem).[8] NOTES: [1] picturing from Al Gore's L1 webcam for example [2] Exercise: 8000 miles diameter w/ pi r^2 gives approx 16,000,000 x 3 = 48,000,000. Earth surface area roughly 48,000,000 x 4 = 192,000,000 square miles. [3] computer algorithm by Robert Gray, global data from WorldSat http://www.teleport.com/~pdx4d/dymax.html [4] sections of virus, buckyballs (C60), stickyballs (C36) relevant (good intro to 5-fold symmetry segment) [5] genesis of '3D' might be retold using the tetrahedron: show 3-edge zigzag "snake" defines complement, and therefore concept of volume. http://members.xoom.com/Urner/images/genesis3d.gif [6] [Aldous Huxley quote in Stuart Kaufmann book goes here] [7] http://members.xoom.com/Urner/images/persian.gif [8] http://www.lgmicro.com/ozymandius.htm --------------------------------------------------------- Kirby T. Urner http://www.teleport.com/~pdx4d/kirby.html 4D Solutions http://www.teleport.com/~pdx4d/ [PGP OK] --------------------------------------------------------- ========================================================================= Date: Sat, 11 Jul 1998 08:22:47 -0700 Reply-To: List for the discussion of Buckminster Fuller's works Sender: List for the discussion of Buckminster Fuller's works From: PAC Organization: gte.net Subject: Re: CubeWorld: addinng dimensions PAC wrote in message <6o12i9$9u2$1@news-2.news.gte.net>... > >Kirby Urner wrote in message <35a3ff6e.182529497@news.teleport.com>... >>"PAC" wrote: > It is rather comic book in dealing with dimensions like this, but // >universes and other such would follow along these lines more than dimensions >as entities being differentiated by varying degrees . Actually, this I should correct myself here being that I think I remember (not really familiar with his work) that Bohm used a sublimated (in this case parallel and integrated though) model of // universes (not dimensions in the traditional way, but still...) whereby the unfolding/enfolding nature of the dimensions would allow two different dimensions to be accessible at the same time being that one would collapse when the other was active thereby circumventing the problem of two separate dimensional realities both existing at the same time. > If dimensions are totally sublimated (seemingly the typical model) into >each other then we really are just dealing with a difference of degrees >between them and regardless of the strange curvatures involved from tacking >one dimension to another, if we are dealing with any type of dimensional >continuum, which I think is assumed, then any lower dimension is pretty much >rendered non-existent compared to a higher one, the lower one being totally >subsumed, and certainly more problematical for any sentient creatures to >have access to a lower one but not a higher one as often stated > As far as I see it, we re basically dealing with one final combined >dimension and regarding any other as separated from the continuum would be >false except for artificial evaluations. So then the issue becomes why are >we giving dimensions special status beyond saying that, for instance, the >number eight is one greater than the number 9? Why would it then be assumed >that reality consists of 11 dimensions as opposed to an infinite number of >them combined into a final expanse? Unless, perhaps, everything combines to > one totality in reverse order as the dimensions increased. Alternatively, >some kind of special purpose fandangled multi-twisting hyper-crossed shape >of some superior relevance. > This basically boils down to the rather simple idea that in a 3d graph, >given any type of continuum, which is usually assumed, 2d does not exist >except as artificially extracted, and cannot be applied as a separate >existent in space as is somewhat assumed when dealing with the 11 dimensions >that exist as "separate" physical realities. Cubed out, Phil C. ========================================================================= Date: Sun, 12 Jul 1998 12:16:06 -0700 Reply-To: List for the discussion of Buckminster Fuller's works Sender: List for the discussion of Buckminster Fuller's works From: Patrick Salsbury Subject: Re: Cookie recipe - free with good reason! Comments: To: cath sheard , Sandra Robinson Comments: cc: Stewart & Sharyn Crilley , Rob Lusher , Rowan Crawford , chat In-Reply-To: <01bda625$f0e9d920$LocalHost@cathandtony> Mime-Version: 1.0 Content-Type: text/plain; charset="us-ascii" At 01:57 PM 7/3/98 +1200, cath sheard wrote: >There is a Neiman-Marcus cookie recipe at the very bottom of this message. >Enjoy! > Man, is Neiman-Marcus *STILL* overcharging for that damned recipe? They were selling that thing for $400 when I got on the internet 10 years ago! I'm at least glad to see the price has come down a bit! (Tongue firmly in cheek. This is an urban legend. And a REALLY OLD one, too. The recipe is real, though, and you can make real cookies from it. As I recall, they were a bit dry...) Pat ___________________Think For Yourself____________________ Patrick G. Salsbury - http://www.sculptors.com/~salsbury/ Check out the Reality Sculptors Project: http://www.sculptors.com/ ========================================================================= Date: Fri, 10 Jul 1998 23:46:32 -0700 Reply-To: List for the discussion of Buckminster Fuller's works Sender: List for the discussion of Buckminster Fuller's works From: "jamie@iname.com" Subject: You got to see this page Comments: To: "geodesic@ubvm.cc.buffalo.edu" Hi geodesic@ubvm.cc.buffalo.edu You got to check this page out http://www.vivaerotica.com/sex/ ========================================================================= Date: Sun, 12 Jul 1998 12:25:25 -0700 Reply-To: List for the discussion of Buckminster Fuller's works Sender: List for the discussion of Buckminster Fuller's works From: Patrick Salsbury Subject: Dome building party! In-Reply-To: <003801bda0bc$bd71f5a0$dcdae3a5@kelp220.cruzio.com> Mime-Version: 1.0 Content-Type: text/plain; charset="us-ascii" Hey, Joe, We're thinking of having a dome-building party at my new dome, to put together a model of the geodesic emergency shelter that I've been babbling about for years. I've got a pile of colorful, corrugated plastic sitting across the room from me, and we're going to cut it into panels and assemble a shelter. This all might be happening next Sat., the 18th. And I now live just off of Summit Rd., about 15 miles from Soquel. (Right up San Jose-Soquel Rd.) If you're interested, send me a note, or call 408-353-8247 (408-ELF-TAGS) Talk to you later! Pat ___________________Think For Yourself____________________ Patrick G. Salsbury - http://www.sculptors.com/~salsbury/ Check out the Reality Sculptors Project: http://www.sculptors.com/ ========================================================================= Date: Sun, 12 Jul 1998 12:45:24 -0700 Reply-To: List for the discussion of Buckminster Fuller's works Sender: List for the discussion of Buckminster Fuller's works From: Patrick Salsbury Subject: Re: Dome building party! Comments: cc: dave@fqa.com In-Reply-To: <3.0.3.32.19980712122525.006c5d1c@mailhost.sculptors.com> Mime-Version: 1.0 Content-Type: text/plain; charset="us-ascii" At 12:25 PM 7/12/98 -0700, you wrote: >Hey, Joe, > We're thinking of having a dome-building party at my new dome, to put >together a model of the geodesic emergency shelter that I've been babbling >about for years. I've got a pile of colorful, corrugated plastic sitting >across the room from me, and we're going to cut it into panels and assemble >a shelter. > This all might be happening next Sat., the 18th. And I now live just off >of Summit Rd., about 15 miles from Soquel. (Right up San Jose-Soquel Rd.) > > If you're interested, send me a note, or call 408-353-8247 (408-ELF-TAGS) > > Talk to you later! > > >Pat Well, I didn't *mean* to blast that all across the planet, just to Joe Moore, who I know live's close. But if any other dome-heads are in the Bay Area and want to help, drop me a line.... :-) Pat ___________________Think For Yourself____________________ Patrick G. Salsbury - http://www.sculptors.com/~salsbury/ Check out the Reality Sculptors Project: http://www.sculptors.com/ ========================================================================= Date: Sun, 12 Jul 1998 20:36:29 -0400 Reply-To: List for the discussion of Buckminster Fuller's works Sender: List for the discussion of Buckminster Fuller's works From: John Belt Subject: Re: HAPPY BIRTHDAY and ANNIVERSARY In-Reply-To: MIME-Version: 1.0 Content-Type: TEXT/PLAIN; charset=US-ASCII Hello List Members, Today is Bucky's Birthday. RICHARD BUCKMINSTER FULLER July 12, 1895-July 1, 1983 Following is a repost i made one year ago from Critical Path. After the repost are a few Fuller quotes from "I Seem To Be A Verb" and in order to celebrate his life and work i thought i would ask list members to dig through some of your books and articles and post some favorite material or quotes by Fuller. Maybe some good discussion might come from the posting and it would also give other list members who might not have much print material of Fuller's some information they would appreciate and use as well as prompt a few new discussion threads. I encourage each and every member to make at least one post during the next two weeks, especially those of you who have been reading only to become visible to the list. The last time i checked there were about 290 subscribers to the list, let's hear from all members. Thanks, jb --------------------------------------------------------------------- John Belt, Design Faculty Phone: (Office)315-341-2868 Department of Technology (Studio)315-341-2867-voice mail SUNY Oswego Fax: 315-341-3363 Oswego, NY 13126 Home: 315-342-2280 --------------------------------------------------------------------- On Sat, 12 July 1997, John Belt wrote: > To Allegra and Family, Buckminster Fuller Institute and List Members > > HAPPY BIRTHDAY and HAPPY WEDDING ANNIVERSARY to Bucky and Anne > > > from inside cover of Critical Path: > > "Those whom God hath joined together let no one put asunder." > To ANNE HEWLETT FULLER on this, our 63rd Wedding Anniversary > and my 85 Birthday---July 12, 1980 > > Being on this list is to celebrate, may we continue the celebration. > > enjoy, > john belt ....................................................................... ..............................July 12th,1998........................... ........Quotes from I SEEM TO BE A VERB, by R. B. Fuller with ........ ........with Jerome Agel and Quentin Fiore......... Bantam Book 1970---out of print "The most important fact about Spaceship Earth: An instruction book didn't come with it." "I live on Earth at present, and I don't know what I am. I know that I am not a category. I am not a thing-a noun. I seem to be a verb, an evolutionary process- an integral function of the universe." "I was born cross-eyed. I could see only large patterns, houses, trees and outlines of people-and all coloring was blurred. I could see two dark areas on human faces, but I could not see a human eye or a teardrop or a human hair. Not until I was four years old, in 1889, was it discovered that my cross-eyeness was caused by my being abnormally farsighted. Lenses fully corrected my vision. Despite my new ability to apprehend details, my childhood's spontaneous dependence only upon big patterns has persisted." "The most poetical experiences of my life have been those moments of conceptual comprehension of a few of the extraordinary generalized principles and their complex interactions that are apparently employed in the governance of universal evolution." "Man is a complex of patterns, or processes. We speak of our circulatory system, our respiratory system, our digestive system, and so it goes. Man is not weight. He isn't the vegetables he eats, for example, because he'll eat seven tons of vegetables in his life. He is the result of his own pattern integrity." "Whenever I draw a circle, I immediately want to step out of it." "I always start with the universe: An organization of regenerative principles frequently manifest as energy systems of which all our experiences, and possible experiences, are only local instances." "I am convinced that creativity is a priori to the integrity of universe and that life is regenerative and conformity meaningless." "Man can approximate the magnificent efficiencies and economies of the macro-micro tensional integrities of nature." "I always say to myself, what is the most important thing we can think about at this extraordinary moment." "The new life needs to be inspired with the realization that the new advantages were gained through great gropes in the dark by unknown, unsung intellectual explorers." "The intellectual integrity and infinite order of the universe obviously are vastly greater than man. Man is an invention within it. What one did about this understanding would have to be through design. I decided I must not be a persuader, but a doer." "Bite you tongue. Get a cinder in your eye. When you feel good, you feel nothing." "My objective has been humanity's comprehensive welfare in the universe. I could have ended up with a pair of flying slippers." "What I am trying to do. As a conscious means of hopefully competent participation by humanity in its own evolutionary trending while employing only the unique advantages inhering exclusively to the individual who takes and maintains the economic initiative in the face of the formidable physical capital and credit advantages of the massive corporations and political states I seek through comprehensively anticipatory design science and its reduction to physical practice to reform man also intend thereby to accomplish prototyped capabilities of doing more with less whereby in turn the wealth-regenerating prospects of such design-science augmentations will induce their spontaneous and economically successful production by world-around industrialization's managers all of which chain reaction-provoking events will both permit and induce all humanity to realize full lasting economic and physical success plus enjoyment of all the Earth without one individual interfering with or being advantaged at the expense of another." The above quotes of R. B. Fuller taken from the first eight pages of I SEEM TO BE A VERB. ========================================================================= Date: Sun, 12 Jul 1998 22:16:55 -0400 Reply-To: List for the discussion of Buckminster Fuller's works Sender: List for the discussion of Buckminster Fuller's works From: "3104702913@iname.com" <3104702913@INAME.COM> Subject: HERE IS THE PAGE YOU WERE ASKING ME FOR http://www.geocities.com/MadisonAvenue/Boardroom/3050/ -------------------- 3104702913@iname.com sent you this message using WorldMerge, the fastest and easiest way to send personalized email messages to your customers, subscribers, leads or friends. For more information, visit http://www.coloradosoft.com 792214 ========================================================================= Date: Sun, 12 Jul 1998 17:45:34 GMT Reply-To: List for the discussion of Buckminster Fuller's works Sender: List for the discussion of Buckminster Fuller's works From: Kirby Urner Organization: 4D Solutions Subject: Synergetics 101: Quadrays in Philosophy MIME-Version: 1.0 Content-Type: text/plain; charset=us-ascii Content-Transfer-Encoding: 7bit [from Synergetics on the Web http://www.teleport.com/~pdx4d/synhome.html] ====== Investigations into the Linear Algebra Concepts used in the XYZ and Quadray Language Games by Kirby Urner First posted: November 20, 1997 Last updated: November 20, 1997 In xyz, the 3 positive basis vectors line the edges of one of eight sectors -- lets call it the alpha sector (not 'quadrant' because we have eight of them -- octant OK). To have tip-to-tail vector addition get us outside the alpha sector and into the rest of space, we need to reverse the positive vectors, which reversal operation we accomplish by multiplying the positives by -1. The result is 6 rays (3 positive and 3 negative) arranged like a "jack" (as in the game). If you paint them all black, it's not evident which three are positives, nor which is the alpha sector. You see 6 spokes stemming from a common hub i.e. from the origin, or (0,0,0). In the game of quadrays, 4 positive basis vectors carve space into four quadrants. To get beyond a given sector, simply scale and add the vector already outside it. No multiplication by -1 is needed to map all of volume. If you paint the rays black, it's not evident which quadrant is called alpha but then it doesn't really matter, since all 4 rays are positive; the symmetry is simpler than in xyz, wherein you have this "pure" +++ --- versus "mixed" ++- +-+ -++ --+ -+- +-- signage in the various octants. You see 4 spokes stemming from a common hub i.e. from the origin, or (0,0,0,0). An xyz player might say 3 quadrays are basis vectors (any 3) and the fourth is a linear combination of those 3. This assumes we're following the rule that vector reversal is just another scalar operation which introduces no new basis rays (only 3 of the xyz spokes are considered 'basic' i.e. the positive ones). But in quadrays, any vector pointing oppositely to a basis vector is itself a linear combination of the other three basis vectors e.g.: -(1,0,0,0) = (0,1,0,0) + (0,0,1,0) + (0,0,0,1) = (0,1,1,1) This means "vector reversal" is accomplished by the original basis rays themselves, not through introducing multiplication by -1. The fourth quadray is a linear combination of the other three only if vector reversal is slipped in as primitive and essential to the game. But in quadrays, we don't need to give vector reversal such a primitive status. By making all four rays equally basic, negative numbers are what become inessential. In other words, all points P(a,b,c,d) in the surrounding volume may be readily addressed by elongating/contracting the four basis rays and adding them tip-to-tail, with no negatives entering into the coordinate addressing scheme. A preliminary step involving negative mirroring to get additional spokes, as in xyz, is not required. So the quadray player doesn't see a fourth vector as a linear combination of the other three, but on the contrary, as the very reason why "negative mirroring" is inessential. It's the xyz system of 6 spokes which looks overbuilt and dependent upon redundant "mirror opposites" to map volume. And it's the xyz apparatus which therefore seems less "basic" or "primitive" overall, vis-a-vis the quadray system of only 4 spokes and no negative mirroring. Plus quadrays easily pair to give six vectors in the xyz orientation, which gives xyz the appearance of a construction within quadray space. xyz as a whole is derivative. In sum, the xyz player needs two operations: vector grow/shrink and vector reversal, in support of tip-to-tail vector addition, in order to reach all points, whereas the quadray player only needs the grow/shrink operation, and not vector reversal, to have vector addition perform adequately. Of course, the xyz player lumps both vector reversal and vector elongate/ contract under the heading of a single operation, called scalar multiplication. But the argument can be made that an operation which reverses a vector's direction is simply not of the same kind as one which alters the length but not the orientation of a vector. The reorienting "mirroring" function should be distinguished from the non-reorienting "scaling" function. To reiterate, the negation operator (-) performs a distinctly different role in xyz space, creating mirror vectors without which the positives alone are helpless to reach allspace. We should perhaps treat with some suspicion this claim that a mirrored basis ray is not itself a basis ray, since once created there's no way to tell them apart, or at least there shouldn't be, since the positive half of the number line is as much a "mirror" of the negative half as the other way around. Take a jack and spray paint one vector red and the oppositely pointing vector green. It's not clear why one has priority or should be seen as having produced the other. So why should only the red (or green) vector be designated a "basis vector" and the other as the operationally derived "reflection" of the one true oppositely pointing twin? Cartesianism seems laced with a cultural "positives are better" bias, which leaves the negatives out of accounts as "derivative" or "second rate", even though these negatives are equally relied upon and betray no detectable differences other than in sign and orientation. Perhaps its the asymmetry of (-)(-) = + and (+)(+) = + that makes positives and negatives come across as having a higher and lower rank. To nod twice is to be even more affirmative whereas to say "not no" is to negate the negation and return a positive. Positives don't self negate while negatives do. ~(~p) = p, but so does +(+p), if defined at all. Turning to philosophy, we find "truth" playing the role of the "positive" with the operation of negation conventionally depending upon positive or affirmative statements as targets to operate upon. The proposition "All seagulls eat rats" (p) is conventionally negated as "Some seagulls don't eat rats" (~p). The negation lacks the power and authority of the positive, comes across as a mere "exception to the rule" -- enough to negate the truth of the positive obviously, but not to come off as symmetrically bold in its own right, something more like "All rats eat seagulls" or "All seagulls avoid rats like the plague". Basically, negative numbers play second banana to the positives in much of the curriculum, following this paradigm of symbolic logic, are regarded less as numbers in their own right than as positives being operated upon by a symbol (-). When moved into the realm of geometry, this convention makes less sense, because both +x and -x are equally important, as directions, and there's no clear reason to regard one as operationally more dependent upon the other than vice versa. Yet in conventional linear algebra this is made to be the case. The xyz positives are predefined as "basis vectors" while the negatives are seen as operationally derived by vector reversal and are therefore not considered equally basic. Quadrays put all four directions on an even playing field, not marking any as less important, less basic, more derivative. Vector reversal is defined, but as shorthand for a positive operation making no use of "second banana" mirror vectors. For further reading: An Introduction to Quadrays Quadrays and the Concentric Hierarchy Memo re this paper to Dr. Benacerraf, Chair, Princeton Philosophy (Nov 30, 1997) Memo to Dr. Paul Ernest, University of Exeter (April 10, 1998) On Ludwig Wittgenstein's Contribution to a Pragmatic Philosophy Memo re teaching linear algebra and computing Synergetics versus HyperCross Dogmatics ====== [for original version w/ graphics and activated hyperlinks see http://www.teleport.com/~pdx4d/quadphil.html] --------------------------------------------------------- Kirby T. Urner http://www.teleport.com/~pdx4d/kirby.html 4D Solutions http://www.teleport.com/~pdx4d/ [PGP OK] --------------------------------------------------------- ========================================================================= Date: Sun, 12 Jul 1998 18:05:31 GMT Reply-To: List for the discussion of Buckminster Fuller's works Sender: List for the discussion of Buckminster Fuller's works From: Kirby Urner Organization: 4D Solutions Subject: Synergetics 101: RBF, a bio MIME-Version: 1.0 Content-Type: text/plain; charset=us-ascii Content-Transfer-Encoding: 7bit [from Synergetics on the Web http://www.teleport.com/~pdx4d/synhome.html] ====== R. Buckminster Fuller: A 20th Century Philosopher by Kirby Urner Originally posted: May 11, 1998 Last updated: May 13, 1998 R. Buckminster Fuller (b. July 12, 1895, d. July 1, 1983) is perhaps most easily pigeon-holed as the last of the New England Transcendentalists, although Fuller himself always resisted being pigeon-holed. His philosophy is centered around the human potential to overcome whatever "reflex conditioning" might have entrapped our humanity in counterproductive scenarios. His focus on "intuition" as coming from the mind, which is beyond the realm of brain-banked experiences, is what most clearly puts him in the transcendentalist tradition, along with a host of New England mannerisms and a life-long base of operations on Bear Island in Maine -- now his grave site and that of his wife, Anne Hewlett Fuller. Also, his great aunt, Margaret Fuller Osoli (1810-1850), was one of the first to publish the writings of Emerson and Thoreau in her magazine The Dial and her writings made an impact on the young Fuller early in his intellectual career. Although the family had a four-generation tradition of sending its sons to Harvard, Fuller was too much the wild romantic to settle in and was expelled for treating an entire New York dance troupe to champagne on his own tab. The family sentenced him to hard labor in a Canadian cotton mill, where he sobered up quite a bit, but he still didn't like Harvard upon giving it a second try and was again expelled. He later returned to Harvard as the Charles Eliot Norton Professor of Poetry (1962). Given his nautical background as a boy messing about with boats around Bear Island, Fuller was attracted to the navy, and managed to achieve a command with family assistance (1917). His marriage to Anne Hewlett was in grand military style. His native genius as an inventive soul was recognized (he developed a winch for rescuing pilots downed over water) and this led to an appointment at the Annapolis Naval Academy (1918). At Annapolis, under the tutelage of retired admirals, Fuller felt very much at home, and began to germinate his "Great Pirates" narrative, wherein the big picture thinking then offered to young officers was a culmination of a long tradition of "thinking globally, acting locally" on the part of high seas figures, many of them pirates, and many of them lost to history because operating invisibly, over the horizon from those who kept the historical accounts (mostly landlubbers). A few years after his honorable discharge, Fuller attempted to make money using his father-in-law's invention, a morterless brick building system, but failed in this enterprise (1926). This failure, which led to joblessness in Chicago, coupled with the trauma of losing his first child Alexandra to prolonged illness in 1922, pushed Fuller to the brink in 1927. He considered suicide but, as he put it, resolved to commit 'egocide' instead, and turn the rest of his life into an experiment about what kind of positive difference the 'little individual' could make on the world stage. He called himself 'Guinea Pig B' (B for Bucky) and resolved to do his own thinking, starting over from scratch. Hugh Kenner likens this to Descartes' resolve to shut himself in a room until he'd discerned God's truth -- a kind of archetypal commitment to a solitary journey. In Operating Manual for Spaceship Earth (1969) he refined his Great Pirates narrative to account for what he considered a chief element of the human predicament -- overspecialization. At one time, the story goes, the grand strategist pirates had instituted strict compartmentalization as a way of keeping their own grip on power, keeping those under them partly in the dark and informed only on a "need to know" basis. The big picture was only for an elite inner circle. But as legions of specialists pioneered technologies operating in hitherto unsuspected regions of the frequency spectrum, the strategic frontier moved outside the scope directly accessible to the naked human senses. The once-comprehensivist bosses lost experiential contact with the new realities and with their passing came a loss of any anchoring comprehensivist viewpoint in a curriculum now continuing on "auto pilot" to further subdivide and overspecialize. Synergetics and Synergetics 2 (1975, 1979) subtitled 'explorations in the geometry of thinking' encapsulated Fuller's attempt to restore the possibility of a comprehensivist viewpoint within a dangerously overspecializing curriculum -- the kind of thing any would-be great pirates of the future would need to read. Synergetics, short for synergetic-energetic geometry, systematizes its concepts around a core polarity variously labeled as: synergy vs. energy growth vs. decay tension vs. compression syntropy vs. entropy gravity vs. radiation. These paired tendencies 'always and only co-occur' and do not come across as moral catagories in any primary sense, nor should Synergetics be regarded as a theological work, despite its transcendentalist proclivities. The ethical direction in synergetics is towards "omnieconomical design" with nature's "technologies" setting the standard. Our humanly contrived inventions work to approach nature's ideals and as we become more adept at using basic principles to best advantage, our designs accomplish more with with less physical time/energy expenditures -- a long term trend Fuller labeled "ephemeralization" (historian Arnold Toynbee used "etherealization" to mean the same thing). The implosive or structuring tendency (e.g. syntropy) has an edge in the grand scheme of things, however, as it operates "circumferentially" in an embracing, constrictive capacity, whereas the explosive or destructuring tendency (e.g. radiation) broadcasts outwardly in all directions from some center. The same amount of force organized circumferentially is more effective, because the network collaborates with itself, with all members drawing towards the same focus. Radial energies seek individual freedoms without regard for a whole and in physical terms reach a top speed en vacuo of 186,000 miles per second, the normal state for unfettered energy of zero rest mass. 'Tensegrity' or 'tensional integrity' provides a unifying context for this central polarity. In tensegrity structures, all the compression elements become islanded entities, not touching one another, yet contributing to the overall shape. Tension wires, which tend towards increasing invisibility with slenderness, run between the compression elements, playing the role of an implosive, syntropic, gravitational force. In the language of synergetics, the compression islands are the linear semi-metaphorical verities, local and partial attempts to capture truth, with a sense of the whole emerging thanks to the invisible cohering power of the mind, which is attuned to the exceptionless principles running through all the brain-sorted special case events (1005.50-56). It was over this concept of 'tensegrity' that early divisions over the issue of Fuller's character and integrity came to the foreground. Ken Snelson, a star pupil at Black Mountain College (1948), at first enchanted by Bucky's spell, became highly disillusioned when it appeared that Fuller planned to abscond with the "tensegrity" idea without properly crediting his student. Fuller's reputation for egomania and improperly seizing upon others' ideas as his own may be traced to this Fuller-Snelson split, and led many to question whether the geodesic dome, widely credited to Fuller (who took out a number of patents around the idea) was another case in point. Walter Bauresfeld had hit on the same strategy in 1922, for use in constructing planetaria. Alexander Graham Bell had also made extensive use of the octet truss circa 1907, another one of Fuller's key concepts (also patented). Fuller's own archives, maintained since his death in 1983 by the Buckminster Fuller Institute (BFI) and his estate (EBF), details his side of the story and he seems to have died with a clear conscience regarding these matters -- realizing they would remain bones of contention. His collaboration with Werner Erhard (late 1970s on), a self-styled "est Trainer" who shared his home-grown philosophy of the mind using a hard-hitting seminar format, marked another chapter fraught with controversy. Fuller, as per usual, took pains to fully document the relationship for his Chronofile (an exhaustive record of the Guinea Pig B experiment), making it especially clear that Erhard's group in no way ever funded or underwrote any of his activities. On the contrary, Fuller wanted to be seen as giving Erhard, many years his junior, a welcome boost from an independent platform. Fuller's contribution has for the most part not penetrated to academia's required reading syllabi within any department as of this writing (May, 1998), in part because Fuller himself remained largely aloof to speciation within the university system, and therefore was never embraced by any professional peer group, except by architects. Given its non-acceptance within academia, Synergetics eventually went out of print, which proved a blessing as it allowed Robert Gray, with the estate's permission, to put both volumes in interleaved format, as per Applewhite's numbering scheme, on the World Wide Web. One might argue the architects had little choice but to recognize Fuller, given the dramatic visibility of the geodesic domes. However, with the realization that the Bauersfeld domes were also geodesic, the move to disown Fuller, by casting him as a mere "popularizer" even with regard to his best known invention, was seen by some as a kind of poetic justice, apt punishment for his failing to sufficiently credit his contemporaries. Mathematicians have tended to dismiss synergetic geometry as trivial or insufficiently analytical even though Synergetics is dedicated to H.S.M. Coxeter, perhaps this century's greatest geometer. Coxeter himself remains ambivalent about Synergetics, more for philosophical reasons than because of anything strictly to do with geometry. Philosophers have not accepted Synergetics as a work in their domain at all, despite Fuller's own claim to have accomplished "the integration of geometry and philosophy in a single conceptual system providing a common language and accounting for both the physical and metaphysical." (251.50) Philosphers tend to be put off by the geometry and engineering content, which appears non-germane to their discipline. Fuller's commitment to evolving a comprehensivist, philosophical language goes against the grain of late 20th century academic thinking. Synergetics might have fared better in a Renaissance environment, as a form of Neo-Platonism for example, and before "natural philosophy" had been carved up into so many subdisciplines. However, a recent issue of Architecture New York (ANY #17) devoted entirely to Fuller's legacy suggests his philosophy may be a source of creative ferment in new Continental brews (i.e. in European, romance language schools of thought). Although not embraced by academia, Fuller did attract some loyal and long term collaborators to his save-the-world crusade -- his book Utopia or Oblivion (1969) spells out what he considered to be the only options. His closest collaborator on the Synergetics volumes, E.J. Applewhite, had joined Fuller shortly after a stint in the Navy, to assist with personnel and logistics around the DDU (dymaxion deployment unit) in Wichita, Kansas (1945). Ed later joined the CIA (1947), rising to the position of deputy inspector general before retiring under DCI Richard Helms during president Johnson's term -- well before the Nixon-ordered purge of Ivy Leaguers, about which Nixon had a complex (Ed was from Yale). Ed and his wife June, whom he met in the agency, settled in a Georgetown apartment, which became a new base of operations for working with Fuller, on the Synergetics volumes especially. Applewhite's wryly humorous Cosmic Fishing (1977) details the process of coaching Fuller through this very busy period and struggling with Macmillan to keep the ball rolling. Hugh Kenner, James Joyce scholar, professor of literature, and erstwhile columnist for Byte magazine, was another key player in Bucky's universe. Kenner wrote Geodesic Math and How to Use It (1976) one of the first and most thoughtful 'how to' books for early dome pioneers, and a biography Bucky (1973). Kenner also gave Fuller some airplay in The Pound Era (1973), his narrative account and weaving together of poetic threads in the 20th century. Kenner also wrote the intro to Applewhite's Cosmic Fishing. Post-synergetics, Fuller produced Critical Path (1979) and its short sequel Grunch of Giants (1980) as culminating volumes designed to show how a new chapter of human history might take off with the application of "design science" to human affairs. True to form, he attached some degree of teleological inevitability to these developments, provided humanity managed to not blow itself up before it attained a new level of maturity. Cosmography (1992) was published posthumously, with final editing by Kiyoshi Kuromiya, Fuller's adjuvant (catalyst) on Critical Path as well. Fuller had a lot of faith in the young to eventually come to grips with their situation aboard Spaceship Earth (his coin) and saw his role as one of providing big picture viewpoints with a minimum of misinformation -- a self-perception many of his critics consider ironic in light of the off-beat speculation and analysis contained in these later works. Col. L. Fletcher Prouty hailed Critical Path as an important book, but then he was the career Washington insider upon whom the shadowy "Man X" in Oliver Stone's movie JFK was modeled. President Ronald Reagan awarded Fuller a Medal of Freedom in 1983, capping a long series of prizes and honorary degrees. Some efforts are being made to link to synergetics from more established philosophy of mathematics syllabi, by way of Ludwig Wittgenstein's investigations in particular. Fuller's "operational mathematics", inspired by P.W. Bridgman, synchronizes well with Wittgenstein's "meaning through use" doctrine. Key terms in synergetics (e.g. "dimension" and "4D") gain their meaning through the usage patterns containing them, giving the work as a whole the appearance of a gear-works or machine -- a "tautology" in the sense that "it works" (or doesn't, according to critics). To the list of aforementioned polar pairs, we might add the sense vs. nonsense dichotomy as used in Wittgenstein's Tractatus, and come to understand "tensegrity" as a metaphor for "the world" (more customary in philosophical circles than Fuller's "Universe"). Kirby Urner (the author of this account) has been spearheading these efforts to dovetail synergetics with a more mainstream style of philosophy via his growing body of writings on the World Wide Web. Fuller's apolitical approach to grand strategizing, which features his own nationless world projection as a game board, has been continued by the World Game Institute (WGI), among other entities, under the leadership of Medard Gabel. The WGI gymnasium-sized map has been upgraded using imagery provided by Tony DeVarco of WorldSat, and using Robert Gray's computer algorithms. Peter Meisen's group (GENI) has continued lobbying to have more critical gaps closed in the global electrical grid, and organized a centennial event around Fuller and design science in San Diego (1995) which brought together a lot of key players continuing the work (Tony Gwilliam, Amy Edmondson, Don Richter, Barbara Marx Hubbard, Bonnie and Tony DeVarco, Harold Kroto, Robert Snyder and Allegra Fuller Snyder...). Jay Baldwin, co-founder of the Whole Earth Catalog, recently authored Bucky Works (1996), which details some of his ongoing projects around the 'garden of Eden dome' and its skin of argon-filled translucent pillows, made of Tefzel (a DuPont product). A burgeoning network of interlinked websites, plus a growing interest in 'tensegrity' in academic circles, as evidenced by a cover story in Scientific American (January, 1998) and a feature on "Mathematics and Tensegrity" in The American Scientist (March-April 1998), suggests that a Fuller-invested curriculum is very much alive and growing. Arthur Loeb at Harvard, contributor to Synergetics (intro and addendum) and his pupil Amy Edmondson, author of A Fuller Explanation (1987) have likewise helped connect a somewhat dense and difficult philosophy to a more mainstream and interdisciplinary syllabus. Finally, Fuller's "concentric hierarchy", a system of nested polyhedra centered around a unit-volume tetrahedron, which lives at the core of Fuller's metaphoric language of synergetics, has gained a following among some classroom teachers, who find it an easy on-ramp for kids wanting to explore spatial geometry. The concentric hierarchy fits into a sphere packing environment and associated lattice dubbed the "isotropic vector matrix" by Fuller (equivalent to the octet truss) and successfully streamlines and systematizes a lot of "inter-geared" concepts. The "skeleton key" to all of these aspects of the ongoing work is a centralizing philosophy, synergetics. As our western calendars roll over to mark a new millenium, perhaps we will use the occasion to make a fresh beginning, in part by exploring more deeply and appreciatively what this pioneering 20th century conceptual engineer has helped to set in motion on behalf of his fellow beings. For further reading: To/from Dr. Jim Fieser, Encyclopedia of Philosophy (May, 1998) To Ivars Peterson re Fuller as Philosopher (May 15, 1998) >From Ed Applewhite (May 13, 1998) Memo to Dr. Paul Ernest, University of Exeter (April 10, 1998) To/from Dr. Benacerraf, Chair, Princeton Philosophy (Nov 30, 1997) Letter to Josef Hasslberger (October 13, 1997) To/from Dr. Peter Suber, Earlham College (September, 1997) Letter to John S. Burr, '53, Chairman, Annual Giving (June 21, 1988) ===== [for the original version with hyperlinks activated, see http://www.teleport.com/~pdx4d/bio.html] --------------------------------------------------------- Kirby T. Urner http://www.teleport.com/~pdx4d/kirby.html 4D Solutions http://www.teleport.com/~pdx4d/ [PGP OK] --------------------------------------------------------- ========================================================================= Date: Mon, 13 Jul 1998 07:08:18 GMT Reply-To: List for the discussion of Buckminster Fuller's works Sender: List for the discussion of Buckminster Fuller's works From: Robin Chapman Organization: Deja News - The Leader in Internet Discussion Subject: Re: CubeWorld: adding dimensions In article <35a6c35a.1087037@news.csuohio.edu>, scott@math.csuohio.edu (Brian M. Scott) wrote: > On Fri, 10 Jul 1998 21:04:43 GMT, pdx4d@teleport.com (Kirby Urner) > wrote: > > >Seems to me you're over-anxious to be derogatory about my thinking > >while doing zero work to even inform yourself of what that thinking > >might be. This is the hallmark of a sloppy, lazy ideologue, not a > >mathematician, or serious-minded scholar of any variety for that > >matter. > > I've looked at your site. I've carried on correspondence with you. > I've seen too many of your posts in sci.math. I've seen a lot of > self-glorifying hype and demonizing of an 'inner circle' that doesn't > exist; you're an expert at leading the cheering section while you tilt > at windmills that exist only in your own mind. I've seen a > mathematical triviality presented as the salvation of our youth from > the dead hands of Euclid and Descartes. On the other hand, I've never > seen much understanding on your part of what mathematics and > mathematicians are about. > > You appear to be quite energetic, but you're certainly an ideologue, > not a mathematician, and you've presented no evidence of scholarship. Brian, There's no point in arguing with Urner. If you refute one ridiculous argument he comes back with ten more, even more ludicrous. It appears that his sense of identity is tied with being a member of an "outsider" group in opposition to mainstream culture, but in his case he seems to have had to invent such a group for himself. Strangely enough, the nearest he comes to coherent argument is appeals to authority (Fuller, Wittgenstein). A little earlier in the thread he said > I vote we give up discussing any Synergetics on sci.math, > permanently . I never expected him to actually do so :-( Best to ignore him. Robin Chapman + "They did not have proper Department of Mathematics - palms at home in Exeter." University of Exeter, EX4 4QE, UK + rjc@maths.exeter.ac.uk - Peter Carey, http://www.maths.ex.ac.uk/~rjc/rjc.html + Oscar and Lucinda -----== Posted via Deja News, The Leader in Internet Discussion ==----- http://www.dejanews.com/rg_mkgrp.xp Create Your Own Free Member Forum ========================================================================= Date: Mon, 13 Jul 1998 15:54:42 GMT Reply-To: List for the discussion of Buckminster Fuller's works Sender: List for the discussion of Buckminster Fuller's works From: Kirby Urner Organization: 4D Solutions Subject: Re: CubeWorld: adding dimensions MIME-Version: 1.0 Content-Type: text/plain; charset=us-ascii Content-Transfer-Encoding: 7bit >> I vote we give up discussing any Synergetics on sci.math, >> permanently . > >I never expected him to actually do so :-( > Certainly not with propaganda like yours to keep the fires burning (I posted my offer, after finding Brian had started a synergetics thread in this NG, only to find two new threads, including a long Gospel Hour parody -- funny -- started by yourself). >Best to ignore him. > You post that you won't read or respond to my posts (not a problem), but are quick to jump in and "2nd the motion" when someone else makes a critical remark. This is nothing like open-minded debate among scholars. Ignoring the thread is one thing, but taking a side, characterizing the opposition, while adopting a see & hear no evil "wise monkey" stance vis-a-vis actually knowing thy enemy is just setting yourself up to look foolish. I don't see myself as an outsider by the way (quite the contrary). But I'm coming to look at you more along those lines, given your inability to live up to your own ideals as an academic, your self-indulgence of your pet knee-jerk reflexes instead of opting for a life of the mind. You seem to think you're some kind of gatekeeper and I'm supposed to win your tacit approval before posting stuff to sci.math (to which you are a prolific contributor). If that's the case, give it up -- an idle fantasy. Nor have I seen you "refute" anything I've posted, just whine when I don't accept your opinions as gospel and dare to rebut instead. Well excuuuuuse me for having a different point of view. Kirby --------------------------------------------------------- Kirby T. Urner http://www.teleport.com/~pdx4d/kirby.html 4D Solutions http://www.teleport.com/~pdx4d/ [PGP OK] --------------------------------------------------------- ========================================================================= Date: Mon, 13 Jul 1998 17:48:51 GMT Reply-To: List for the discussion of Buckminster Fuller's works Sender: List for the discussion of Buckminster Fuller's works From: "Brian M. Scott" Organization: Cleveland State University Subject: Re: CubeWorld: adding dimensions On Mon, 13 Jul 1998 07:08:18 GMT, Robin Chapman wrote: >There's no point in arguing with Urner. If you refute one ridiculous argument >he comes back with ten more, even more ludicrous. Agreed - after that last post I didn't even bother to read the response. (If I want pointless argument, there are much more entertaining folks over in sci.archaeology!) Brian M. Scott ========================================================================= Date: Mon, 13 Jul 1998 17:49:33 -0700 Reply-To: List for the discussion of Buckminster Fuller's works Sender: List for the discussion of Buckminster Fuller's works From: Brian Hutchings Subject: embedding the hyperbolic plane in 4D (yeeha) <> Brian Hutchings 13-JUL-1998 17:49 r001806@pen2.ci.santa-monica.ca.us the Whitney embedding theorem guarantees a closed manifold, up to 5 dimensions?... wow, cool. as for your equations, your second "3D" one is the "twisted cylinder", which jibes with your dyscription! (it's a favorite "semi-ruled" surface o'mine, for reasons which are unclear .-) thus quoth: (sin u, cos u, sin v, cos v) is a flat plane rolled into a torus without stretching in 4D. In 3D, you can't bring the ends of a cylinder together without stretching. (u,v sin u, v cos u) is a suface with negative curvature everywhere, but not constant. It is a spiral staircase surface generated by a line moving like a propeller. Wwhat about rotating a circle around its centre in 4D, for example: ((sin u)(sin v), (sin u)(cos v), (cos u)(sin v), (cos u)(cos v)) which has guu=gvv=1, guv=0, ds^2=du^2+dv^2, g=16(sin u)(cos u)(sin v)(cos v) or perhaps some other subset of the hypersphere? Brian Calvert --Shakespeare -- ain't he still dead ?!? http://www.tarpley.net http://inet.uni-c.dk/~sch-inst/radio.html Support the Citizens Protection Act, HR#3396 (McDade-Murtha) !! ========================================================================= Date: Mon, 13 Jul 1998 22:15:34 GMT Reply-To: List for the discussion of Buckminster Fuller's works Sender: List for the discussion of Buckminster Fuller's works From: Kirby Urner Organization: 4D Solutions Subject: Re: CubeWorld: adding dimensions MIME-Version: 1.0 Content-Type: text/plain; charset=us-ascii Content-Transfer-Encoding: 7bit scott@math.csuohio.edu (Brian M. Scott) wrote: >On Mon, 13 Jul 1998 07:08:18 GMT, Robin Chapman >wrote: > >>There's no point in arguing with Urner. If you refute one ridiculous argument >>he comes back with ten more, even more ludicrous. > >Agreed - after that last post I didn't even bother to read the >response. (If I want pointless argument, there are much more >entertaining folks over in sci.archaeology!) > >Brian M. Scott Look at these two! Calling my positions ridiculous (after doing much of their own sloppy characterizations of what these are) and than patting each other on the back for refusing to even read what I say in response. How ethically bankrupt their commitment to free and open public debate is what I say. Take pot shots and then close your eyes and ears to the person you've shot at, and encourage others to do the same. This is the irresponsible strategy of a losing cause I'd say. Good thing we skeptical inquirer folks showed up to catch these bozos and their dubious techniques in action. For the record. Kirby --------------------------------------------------------- Kirby T. Urner http://www.teleport.com/~pdx4d/kirby.html 4D Solutions http://www.teleport.com/~pdx4d/ [PGP OK] --------------------------------------------------------- ========================================================================= Date: Mon, 13 Jul 1998 19:26:20 -0700 Reply-To: List for the discussion of Buckminster Fuller's works Sender: List for the discussion of Buckminster Fuller's works From: Kirby Urner Subject: Re: embedding the hyperbolic plane in 4D (yeeha) In-Reply-To: <199807140049.RAA00871@pen2.ci.santa-monica.ca.us> Mime-Version: 1.0 Content-Type: text/plain; charset="us-ascii" At 05:49 PM 7/13/98 -0700, you wrote: ><> Brian Hutchings 13-JUL-1998 17:49 > r001806@pen2.ci.santa-monica.ca.us > > the Whitney embedding theorem guarantees a closed manifold, Does this have anything at all to do with "the discussion of Buckminster Fuller's works" or is this just another classic Hutchings ESL (empty show of learning)? Mile wide, inch deep: Shakespearian clown with a fat bottom. Kirby ========================================================================= Date: Mon, 13 Jul 1998 22:28:51 -0500 Reply-To: spammers.eat.used.kitty.litter.coolbear@earthlink.net Sender: List for the discussion of Buckminster Fuller's works From: Jonathan Thompson Subject: Gedesics in the field of transportation devices MIME-Version: 1.0 Content-Type: text/plain; charset="iso-8859-1" Content-Transfer-Encoding: 7bit I thought I would take up John Belt on his challenge, having remained a watcher ro quite a while since the last time I posted on the newsgroup. Other than as part of the structure for the Wellesly Bomber (maybe that is spelled wrong, don't have it in front of me) does anyone know of a solid instance where geodesic structures have been utilized for vehicles? There seems to be a dearth of relative articles about such things. The closest I've seen so far is the patent for the Topp-Flite golfBall having a geodesic patterned dimple pattern to get maximum lift derived. There is an airship made by a Cnadian Company that I saw in Popular Science in the mid 80's that used a giant sphere (I believe 420 feet in diameter) spun to create lift utilizing the Magnus Effect, but no mention about it being Geodesic in nature. The sphere is made of Kevlar. Have there even been geodesic balloons made for passenger usage? Does anyone happen to know if there might have been any geodesic structuring utilized in the Zeppelin airships? Remove the comment about kitty litter to reply! spammers.eat.used.kitty.litter.coolbear@earthlink.net ========================================================================= Date: Mon, 13 Jul 1998 20:51:37 -0800 Reply-To: bward@metro.net Sender: List for the discussion of Buckminster Fuller's works From: Bruce Ward Organization: chh yeh right… Subject: Re: CubeWorld: adding dimensions MIME-Version: 1.0 Content-Type: text/plain; charset=us-ascii Content-Transfer-Encoding: 7bit Whew! Talk about getting to watch the priesthood of hypercross dogmatics in action... thank you, mssrs. Chapman & Scott! I'm 51. I picked up Operating Manual for Spaceship Earth during winter of '66-'67 in Syracuse while studying Russian for the USAF. Thought it might be sci-fi. Wrong. Hooked. While Bucky was alive I went to hear him speak more than 30 times. I have mor than twnty volumes of his, or related, work. My first copy of Synergetics was sent to me directly from MacMillan because I made myself a nuisance when it wasn't printed on schedule. My formal math training is limited to high school algebra and geometry. My informal, continuing self education has allowed me to understand and use celestial navigation, and build 2 domes, several tensegrity models, 20 boats from 8 to 51 feet long, and more "boxes" for people to try to live in than I care to count. Got mouths to feed, you give the customer what he wants. Nobody ever went broke underestimating the tastes of the american consumer. The greatest difficulty I found in learning to think in terms of dynamic triangulated relationships was getting past or setting aside the xyz co-ordinate monkeybars. (it is NOT a system) Learning Synergetics is learning to speak mathmatics in a different language. One cannot converse naturally in the new language while still thinking in the old. And the old squares and cubes are hammered in early, often, hard and relentlessly. Not only are they difficult to put aside due to early age conditioning, but attempts to put them aside in public discourse are met with derision and obfuscation by the priesthood and blank stares by the laity. At age 51, I am convinced that what the Mystery behind Nature is doing has very little to do with cubeworld. We continue to cripple young minds with garbage data, and continue to punish (flunk) those intelligent enough to see through the nonsense. Watching vested (read 'clutched') "profess"ors trash concepts that don't fit in their status quo 'box' is hilarious; kind of like watching a catholic priest telling You to abide by the Golden Rule while he directs the Inquisition. The scary part is that we entrust our children to these licensed and titled fools. ========================================================================= Date: Tue, 14 Jul 1998 00:23:31 EDT Reply-To: List for the discussion of Buckminster Fuller's works Sender: List for the discussion of Buckminster Fuller's works From: Zac Elston Subject: Re: CubeWorld: adding dimensions Mime-Version: 1.0 Content-type: text/plain; charset=US-ASCII Content-transfer-encoding: 7bit In a message dated 98-07-13 23:48:21 EDT, (Bruce Ward) writes: > We continue to cripple young minds with garbage data, and continue to > punish (flunk) those intelligent enough to see through the nonsense. speaking of which..is there anything out there besides the Zome tools to teach kids about triangular geometry? In my quest for tools to test out designs with I have hit every single toy and model store in the DC, Nova area. Absoultly no one has anything that might be used for exploring geodesic construction. Even fewer knew what what geodesic was. The Nature Company once sold a glow-n-the-dark geodesic set with flexable plastic hexagons and pentagons that one could snap together....but no longer. Zome's a recool, but do they really have the corner on the market? I've been using 3/8" wooden dowls with eye screws in the ends. it's a cheap setup (8 foot octet arch for 4 dollars) and works great once you manage to get it together but I'm having trouble believing that no one sells anything to use in this field. -zac ========================================================================= Date: Mon, 13 Jul 1998 23:48:38 -0700 Reply-To: List for the discussion of Buckminster Fuller's works Sender: List for the discussion of Buckminster Fuller's works From: Chuck Knight Subject: Re: Gedesics in the field of transportation devices Comments: To: coolbear@earthlink.net MIME-Version: 1.0 Content-Type: text/plain; charset=us-ascii Content-Transfer-Encoding: 7bit > don't have it in front of me) does anyone know of a solid instance where > geodesic structures have been utilized for vehicles? There seems to be a dearth It depends on how you define geodesic. If you mean the reduction of a surface to triangular facets, then all the following examples will be relevant. Otherwise, only one of them. An experimental "bubble boat" designed to study the integrity of spherical bubbles for underwater use, used a truncated icosahedron pattern. Think soccer ball. This was from "Popular Science" in the 1970's. The stealth bomber and "facetcraft" are both airplanes which use trianglarly faceted skins and geodesic patterning...but not purely geodesic. Bucky's dymaxion car (if memory serves) used a triangulated space frame which closely resembled a geodesic pattern. The "basketweave" net used on hot air balloons could be said to be a geodesic structure...though this is a stretch. And, I'm sure that there is a geodesic construct being used on at least some of the satellites, etc...not exactly vehicles, but they do move! Oh...oh...oh... Didn't one of those early electric cars (UrbaCar?) use a fully triangulated body structure? The thing literally looked like a wedge. > of relative articles about such things. The closest I've seen so far is the > patent for the Topp-Flite golfBall having a geodesic patterned dimple pattern to > get maximum lift derived. There is an airship made by a Cnadian Company that I > saw in Popular Science in the mid 80's that used a giant sphere (I believe 420 > feet in diameter) spun to create lift utilizing the Magnus Effect, but no > mention about it being Geodesic in nature. The sphere is made of Kevlar. This spherical airship was a failure...in operation, the flexible spherical envelope set up an oscillation...a rippling in the fabric...which almost destroyed the craft. However, L.T.A.S. Corporation (solar powered airships) uses geodesic rigid envelopes in its rigid airships...shaped like "saucers" and use vectored thrust. Instead of "turning" the entire craft around, you simply point the gondola in another direction. Lots more efficient. > Have there even been geodesic balloons made for passenger usage? Does anyone I have a design in mind for an ultralight "saucer" airship that would use non-rigid panels...a truncated icosahedron, appropriately distorted. It would have an open gondola, and *could* conceivably be human powered. I've been designing it with input from Mike Walden, of L.T.A.S. Whether it ever gets built is a different story. > happen to know if there might have been any geodesic structuring utilized in the > Zeppelin airships? The newest Zeppelin uses a gigantic triangulated truss for its main support structure. But, its skin and supporting ribs are NOT geodesic. -- Chuck Knight ========================================================================= Date: Mon, 13 Jul 1998 23:55:00 -0700 Reply-To: List for the discussion of Buckminster Fuller's works Sender: List for the discussion of Buckminster Fuller's works From: Chuck Knight Subject: Re: CubeWorld: adding dimensions Comments: To: Zac Elston MIME-Version: 1.0 Content-Type: text/plain; charset=us-ascii Content-Transfer-Encoding: 7bit > speaking of which..is there anything out there besides the Zome tools to teach > kids about triangular geometry? In my quest for tools to test out designs Funny you should mention this. I picked up (at a thrift store) an old set of tinkertoys. Every connector has 4 or 8 radially arranged holes, so I couldn't even make a triangle! I bought them to use as a pattern for model connectors...looks like I'll have to do a little more engineering than I thought. > with I have hit every single toy and model store in the DC, Nova area. > Absoultly no one has anything that might be used for exploring geodesic You know, a very viable product might be an "extension" to the basic Tinkertoy set, which includes connectors for geodesic modelling. What child does not have a set of Tinkertoys (and consequently what parent?) lying around the house? -- Chuck Knight P.S. So, who's up to the challenge of designing these things with me? ========================================================================= Date: Tue, 14 Jul 1998 01:33:02 -0700 Reply-To: List for the discussion of Buckminster Fuller's works Sender: List for the discussion of Buckminster Fuller's works From: Brian Hutchings Subject: Re: embedding the hyperbolic plane in 4D (yeeha) MESSAGE from ="List 14-JUL-1998 0:12 At 05:49 PM 7/13/98 -0700, you wrote: ><> Brian Hutchings 13-JUL-1998 17:49 > r001806@pen2.ci.santa-monica.ca.us > > the Whitney embedding theorem guarantees a closed manifold, Does this have anything at all to do with "the discussion of Buckminster Fuller's works" or is this just another classic Hutchings ESL (empty show of learning)? Mile wide, inch deep: Shakespearian clown with a fat bottom. Kirby - - - - - <> Brian Hutchings 14-JUL-1998 1:33 r001806@pen2.ci.santa-monica.ca.us I'm sure, it does; we are dealing, as they say, with "low dimensions", as contrasted with generical "n+1" s[aces, inductively aglomerating (not really; the Riemannian manifolds are determined, characteristically, by physical experiments, as with the Weber-Gauss uncovery of what we now refer to as the "strong force"; they embody characteristic curvatures & singularities. there is also an inherited "platonical" question, although the "shadows in caves" metaphor undermines it a bit, as to whether all such questions are resolvable in terms of naively visual terms, or "straightforward visualization". since I agree that my knowledge of classical literature, thus of "learnedly ignorant" metaphor is severely limited, I also admit that the "show is empty" -- although i tire of the "bubbling virtual void" speak; don't you? (butt, the drawings of the spear-shaker, that I have seen, were somewhat clownish. it is very hard to say, or i have no reference to't, that these are not, nerely, latter-day oligarchical elisions, a la the (Earl of) Oxford Society, to capture the republican brilliance, in a cage of smug heraldry; also, he might look like that !-) -- Shakespeare ... yuck -- he's really getting putrid! http://www.tarpley.net ========================================================================= Date: Tue, 14 Jul 1998 00:44:09 GMT Reply-To: List for the discussion of Buckminster Fuller's works Sender: List for the discussion of Buckminster Fuller's works From: "Brian M. Scott" Organization: Cleveland State University Subject: Re: CubeWorld: adding dimensions On Mon, 13 Jul 1998 15:54:42 GMT, pdx4d@teleport.com (Kirby Urner) wrote: >after finding Brian had started a synergetics >thread in this NG Liar. Brian M. Scott ========================================================================= Date: Mon, 13 Jul 1998 21:55:40 -0700 Reply-To: List for the discussion of Buckminster Fuller's works Sender: List for the discussion of Buckminster Fuller's works From: David Freedman Subject: Re: 1960s - 1990s: synergetics and the virus meme please tell meddie galbe that dale klause just celebrated his 60th birthday nad old friend can remain in touch love gigi 707-762-0665 ========================================================================= Date: Tue, 14 Jul 1998 11:08:14 EDT Reply-To: List for the discussion of Buckminster Fuller's works Sender: List for the discussion of Buckminster Fuller's works From: Lucy Kaplan Subject: Remove Mime-Version: 1.0 Content-type: text/plain; charset=US-ASCII Content-transfer-encoding: 7bit Please remove me from your mailing list. ========================================================================= Date: Tue, 14 Jul 1998 11:30:40 EDT Reply-To: List for the discussion of Buckminster Fuller's works Sender: List for the discussion of Buckminster Fuller's works From: Zac Elston Subject: Re: CubeWorld: adding dimensions Mime-Version: 1.0 Content-type: text/plain; charset=US-ASCII Content-transfer-encoding: 7bit In a message dated 98-07-14 01:05:51 EDT, cknight@FLASH.NET writes: > Funny you should mention this. I picked up (at a thrift store) an old > set of tinkertoys. Every connector has 4 or 8 radially arranged holes, > so I couldn't even make a triangle! same thing with any erector set derivative (except for the old steel versions). The newer plastic versions from Kennex (sp) have only 45deg angles. You can force curvature through some twisting but that's about it. and don't even think about getting equallateral dimensions from anything sold today. > You know, a very viable product might be an "extension" to the basic > Tinkertoy set, which includes connectors for geodesic modelling. What > child does not have a set of Tinkertoys (and consequently what parent?) > lying around the house? yes it would, but maybe the rest of the world doesn't think so. My theory however is that if the product is in enough hands ...it will become more understood and desired therefor paying off the cost of production. However...and here is were one would begin to compete with the ZomeTool product, how fancy do you design the connectors? Zometools are great and are designed for the exact purpose this conversation is discussing. I personally would like to see the costs come down to Lego costs and then we might see something revolutionary. I started with small wooden balls from a craft store ($.19 retail). These can be drilled with 5 or 6 holes fitting the tinkertoy diameter, but where do you stop? Do you want a connector that accepts every entry point? would it be better to have classes of connectors? mode I II or III? Color coded for platonic class? just thinking out loud here.... > P.S. So, who's up to the challenge of designing these things with me? I'm game :) as an aside.. how about something bigger? I want something like http://www.8020.net/ -zac ========================================================================= Date: Tue, 14 Jul 1998 12:43:33 -0700 Reply-To: List for the discussion of Buckminster Fuller's works Sender: List for the discussion of Buckminster Fuller's works From: Chuck Knight Subject: TinkerDomes Comments: To: Zac Elston MIME-Version: 1.0 Content-Type: text/plain; charset=us-ascii Content-Transfer-Encoding: 7bit > > You know, a very viable product might be an "extension" to the basic > > Tinkertoy set, which includes connectors for geodesic modelling. > > yes it would, but maybe the rest of the world doesn't think so. My theory > however is that if the product is in enough hands ...it will become more > understood and desired therefor paying off the cost of production. Plus, it wouldn't have to be marketed as a "geodesic modelling kit," but simply as a supplemental connector kit compatible with Tinkertoys. Marketing would be everything! However, pictures on the box, showing complex structures...a geodesic dome, a dna double helix, maybe a molecule or two, would force people to start thinking about the limitations of the basic set which currently shows a "square" ferris wheel. > However...and here is were one would begin to compete with the ZomeTool > product, how fancy do you design the connectors? Zometools are great and are > designed for the exact purpose this conversation is discussing. Who said anything about competing directly with Zometool? That's a higher end modelling product, specifically designed for the purposes of exploring polyhedra. My basic concept wouldn't compete with them at all. I'm talking about TINKERTOYS!!! Anyone know the lengths of the sticks available in a complete Tinkertoy set? The one I bought wasn't even close to being complete. > I started with small wooden balls from a craft store ($.19 retail). These can > be drilled with 5 or 6 holes fitting the tinkertoy diameter, but where do you > stop? Do you want a connector that accepts every entry point? would it be > better to have classes of connectors? mode I II or III? Color coded for > platonic class? just thinking out loud here.... I think something a little more flexible would be a better design. (literally) I was thinking of a flexible rubber set of connectors, consisting of a rubber tinkertoy-style "disk" connector with 5 or 6 holes in it. That would allow some flexibility in the angles, while still allowing enough rigidity to "hold" the struts in place. With so many flexible polymers available, it's just a matter of choosing the right one. (The ones used for plastic "pencil erasers" would probably be a good choice) > > P.S. So, who's up to the challenge of designing these things with me? > > I'm game :) So, what do you think of my basic concept? I have a few variants already designed...in my mind's eye...but I'm not sure how easy they would be to actually mass produce. Shouldn't be too hard. > as an aside.. how about something bigger? I want something like > http://www.8020.net/ No reason that the basic concept could not be scaleable. ;-) One step at a time. -- Chuck Knight ========================================================================= Date: Tue, 14 Jul 1998 15:17:34 EDT Reply-To: List for the discussion of Buckminster Fuller's works Sender: List for the discussion of Buckminster Fuller's works From: Zac Elston Subject: Re: TinkerDomes Mime-Version: 1.0 Content-type: text/plain; charset=US-ASCII Content-transfer-encoding: 7bit In a message dated 98-07-14 14:45:05 EDT, you write: > However, pictures on the box, showing complex structures...a geodesic > dome, > a dna double helix, maybe a molecule or two, would force people to start the basic freckled carrot-top 4 year old sitting next to a double helix as tall as he is...LOL. > Anyone know the lengths of the sticks available in a complete Tinkertoy > set? The one I bought wasn't even close to being complete. I think it's 1 2 4 and 6 inches, but I can get a set on the way home today. > I think something a little more flexible would be a better design. > (literally) I was thinking of a flexible rubber set of connectors, > consisting of a rubber tinkertoy-style "disk" connector with 5 or > 6 holes in it. That would allow some flexibility in the angles, while you need one with three in there as well. i'm concerned with the tinker toy motif because of the mass of tinker toy spans. The flexable design does solve the inherent math but what about the the actual useage. i think rubber parts might be a little to complex for small children. Or is this an Adult Only toy addition (timmy's toys and Dad's addons?) limiting the structures to isohederal? what about octahedreal (4 joints)? I like the idea but it would need beta testing of course. next step would be to find a prototype house to make product. -zac ========================================================================= Date: Tue, 14 Jul 1998 16:15:09 GMT Reply-To: List for the discussion of Buckminster Fuller's works Sender: List for the discussion of Buckminster Fuller's works From: Kirby Urner Organization: 4D Solutions Subject: Re: CubeWorld: adding dimensions MIME-Version: 1.0 Content-Type: text/plain; charset=us-ascii Content-Transfer-Encoding: 7bit scott@math.csuohio.edu (Brian M. Scott) wrote: >On Mon, 13 Jul 1998 15:54:42 GMT, pdx4d@teleport.com (Kirby Urner) >wrote: > >>after finding Brian had started a synergetics >>thread in this NG > >Liar. > >Brian M. Scott On my newsreader I can still scroll up to the July 5 thread started by dodecagona@aol.com (Brian Hutchings). My participation on bit.listserv.geodesic and sci.philosophy.meta under this heading dates back to July 1 at least (included sci.math in my posts -- CubeWorld started here after all, but Brian's posts were to sci.math exclusively, so it took me awhile to discover them, as this wasn't the venue in which I was tracking). I wasn't claiming all my synergetics-related posts to sci.math started with or stem from Brian's thread. Clearly not true. After discovering Brian's new thread, I posted my vote to keep synergetics off sci.math (you can read the post, under Brian's July 5 start). Then I found Chapman had started two more threads bashing my contributions. At this point, I've changed my mind. You can expect me to participate on sci.math (sometimes with regard to synergetics, which includes mathematical content) indefinitely. Kirby --------------------------------------------------------- Kirby T. Urner http://www.teleport.com/~pdx4d/kirby.html 4D Solutions http://www.teleport.com/~pdx4d/ [PGP OK] --------------------------------------------------------- ========================================================================= Date: Tue, 14 Jul 1998 18:47:46 GMT Reply-To: List for the discussion of Buckminster Fuller's works Sender: List for the discussion of Buckminster Fuller's works From: Kirby Urner Organization: 4D Solutions Subject: Synergetics 102: Beyond Flatland MIME-Version: 1.0 Content-Type: text/plain; charset=us-ascii Content-Transfer-Encoding: 7bit [from the Oregon Curriculum Network website: http://www.inetarena.com/~pdx4d/ocn/] ======= The original version of the essay below was first published to geometry-research at the Swarthmore Math Forum in April of 1998. Beyond Flatland: Geometry for the 21st Century by Kirby Urner First posted: April 22, 1998 Last modified: May 7, 1998 PART I: Pascal's Tetrahedron Agglomerating equi-radiused spheres outwardly from a central sphere in concentric cuboctahedral layers gives an isotropic Barlow packing more commonly known as the face-centered cubic or fcc. The packing subsumes the tetrahedral arrangement used to stack cannon balls, called the 'brass monkey' by some in USA civil war days, and commonly used for fruit-stacking in grocery stores. The nuclear sphere plus layers out to one of the cuboctahedron's 8 trianglar facets defines a tetrahedral packing. This packing is the volumetric analog of a triangulated peg board, sometimes used as in the game of pachinko to vector falling balls, with Pascal's triangle describing 'by how many paths' a given peg might be reached, with 'how many' = 'the likelihood of ending up somewhere' -- turns out to be a Gaussian distribution or bell-shaped curve. 1 1 1 1 2 1 1 3 3 1 1 4 6 4 1 By the same token, a tetrahedral packing, with an apexial entry point and fall-pattern with 3 choices per peg, to the base corners of a tet, defines "Pascal's Tetrahedron" of countable pathways, again with a kind of peak-shaped statistical outcome. 1 1 1 1 1 1 1 2 2 3 3 4 4 1 2 1 3 6 3 6 12 6 1 3 3 1 4 12 12 4 1 4 6 4 1 Pascal's Tetrahedron also describes the structure of diamond crystals, where the carbon atoms arrange in stacked tetrahedra. Another feature of the fcc pegboard is the fact that any four pegs not in the same plane define a tetrahedron of whole number volume, relative to a unit tetrahedron defined by four close-packed fcc spheres. This is true for skew as well as regular tetrahedra. If the spheres have unit radius, then each sphere center is distance 2 from 12 surrounding centers, but this 2 also = 1 interval or 1 diameter, so the unit volume tetrahedron is likewise a model of 1x1x1 or 1^3, measuring in intervals. Successive layerings of 1,3,6,10... spheres (as in Pascal's Tetrahedron) present a tetrahedron of 0,1,2,3... intervals along an edge respectively, and its volume of 1^3, 2^3, 3^3..., demonstrates the third power growth rate of volume with respect to linear distance increase. Triangles may likewise be used consistently to model 2nd powering; instead of "squaring" and "cubing" we might say "triangling" and "tetrahedroning". The volume of a tetrahedron, calibrated by this unit-volume tet of 1-interval edges, may be computed using an expression similar to one obtained by Euler: only the 6 edge lengths are needed as input. References: Urner, Chako. Pascal's Tetrahedron. Snelson. Diamond graphics from 'Portrait of an Atom' Chako, Gray, de Jong, Urner. Whole numbered fcc Tets. Fuller. Triangle & Tet as 2nd & 3rd powering models. de Jong. Sublimation Theorem. Math Forum Pascal's Triangle page. Urner on the Binomial Theorem. PART II: The Octet Truss The most isotropic Barlow packing of 12 spheres around every 1 in a cuboctahedral conformation, serves as a basis for explorations in crystallography. Considered as a skeletal arrangement of edges, all length 2 and interconnecting adjacent unit radius sphere centers, we get a spaceframe known to engineers as the octet-truss. Alexander Graham Bell was among the first to study the octet-truss circa 1907 for its relevance to large scale structures, such as towers and giant kites. Fuller made use of the same spaceframe in his geometric investigations, naming it the isotropic vector matrix. The octet truss defines tetrahedral and octahedral voids, twice as many of the former, with a volume ratio of 1:4 respectively. A second octet truss interpenetrates the first by centering all its vertices on octahedral voids. A third and fourth take up half the tetrahedral voids apiece. The four trusses may be paired to give two sets of vertices arranged in a cubic pattern, ala XYZ, with one set having vertices at the centers of the other's cubes. This pattern is known as body-centered cubic or bcc in crystallography. As Kepler once discovered, spheres packed in an fcc lattice may expand to become rhombic dodecahedra, thereby filling all the interspheric voids. An octet truss is a skeletal spaceframe with all edges perpendicular to rhombic facets. The spheres inscribed in the rhombic dodecas "kiss" at these face centers. The rhombic dodecahedron's 14 vertices occupy the centers of the 8 tetrahedral and 6 octahedral voids surrounding any fcc sphere. Its volume is 6 relative to the tetrahedron's, thereby providing the beginnings of our concentric hierarchy: Shape Volume ----- ------ Tetrahedron 1 Cube 3 Octahedron 4 Rh Dodecahedron 6 Cuboctahedron 20 Table 1: Concentric Hierarchy The volume 3 cube inscribes as the short diagonals of the rhombic dodecahedron and runs between the pair of octet trusses in complementary sets of tetrahedral voids. The volume 4 octahedron inscribes as the long diagonals of the rhombic dodecahedron and defines the vertices of a fourth octet truss paired with the first i.e. the one defined by the rhombic dodecahedron centers. The above concentric hierarchy shapes may all be fractured into "common denominator" modules, a minimal set of which consists of the A and the B mods, irregular tetrahedra with left and right mirrored versions (or inside-out versions), both of volume 1/24. Left and right A mods, plus a B mod of either hand, make a minimum tetrahedral space-filler or MITE of volume 1/8. All MITEs (MInimum TEtrahedra) are outwardly identical and interchangeable, regardless of the internal B's handedness. Eight MITEs make a Coupler of volume 1, another space-filler. Our more complete hierarchy now looks like this: Shape Volume ----- ------ A module 1/24 B module 1/24 MITE 1/8 Coupler 1 Tetrahedron 1 Cube 3 Octahedron 4 Rh Dodecahedron 6 Cuboctahedron 20 Table 2: Concentric Hierarchy References Childs, Chu. Synergetic Crystallography. Loeb. Contribution to Synergetics (1st print volume, Macmillan) Fuller, Urner. Concentric Hierarchy. Alexander Graham Bell. Octet-truss. DeVarco on Kepler and the Rhombic Dodecahedron. Fuller, Hawkins, Urner. A and B modules, MITE, Coupler. [1][2] PART III: The Jitterbug The 20-volumed cuboctahedron embeds in the fcc lattice and is defined by 12 unit-radius spheres packed around a nuclear sphere. Considered as a wireframe with flexible joints, it twist-contracts in either a clockwise or counter-clockwise direction by bringing pairs of vertices along the diagonals of its square faces closer together. When all edges are length 2, the icosahedron's volume is about 18.51 relative to the cuboctahedron's of 20. This transformation has been known since at least Newton's day and in the 20th century was picked up and popularized by Fuller, who dubbed it "the jitterbug" and continued its contraction to an octahedral phase and beyond. The jitterbug forms a useful bridge between 3,4-fold symmetric lattice shapes and the 5-fold symmetric world of non-periodic conformations. The jitterbug transformation may be computerized using STRUCK, a Java application for building structures using edges which push or pull exponentially when forced away from their pre-defined rest-lengths. STRUCK also permits sets of edges to smoothly alter their rest-lengths through time, as in this case of the jitterbug, where the diagonals of the cuboctahedron's six square faces go from 2 x root(2) to 2 (and onward to zero at octaphase). STRUCK optionally writes successive animation frames in POV format for ray-tracing and movie-making purposes. The fcc cuboctahedron is a subclass of fcc polyhedra (those with vertices aligned with the sphere centers in an fcc packing) known as Waterman polyhedra. Waterman polyhedra are those convex hulls consisting of all fcc vertices equidistant from a common fcc center. Because all such shapes may be tetrahedralized, we know their volume will be a whole number relative to our unit volume tetrahedron of 4 fcc spheres. Erickson has studied Watermans using STRUCK and Povray while Towle, another geometer-explorer (and Povray aficionado), employed Mathematica to visualize these shapes. Although the five-fold world is aperiodic, its constituent polyhedra are still amenable to modularization. Various schemes exist, among which one of the most ingenious is Koski's. Koski's mods derive from the golden cuboid, a brick with edges phi, 1 and 1/phi. These 3 edges plus distinct face and body diagonals give a set of 7 lengths, any six of which may be used in a tetrahedron. Given these base measuring cups, Koski allows each to grow or shrink by powers of phi, and finds the five-fold shapes have both algebraic and geometric equivalence to sums of such modules. Some five-fold symmetric shapes, the 30-faceted rhombic triacontahedron for example, may be tightly shrink-wrapped around the unit-radius fcc sphere, as is Kepler's four-fold symmetric rhombic dodecahedron. An interesting fact about the shrink-wrapped rhombic triacontahedron is how closely it misses having a volume of precisely 5. By shrinking its unit radius by a hair (~0.0005) we can make each of its 120 T-modules have a volume of precisely 5/120 or 1/24, the same as the A and B modules discussed above -- a useful mnemonic for fitting this five-fold symmetric shape into our growing concentric hierarchy. The T-mod is also the principal Koski mod, which he recursively disassembles into smaller and smaller phi-scaled versions of itself, down to his arbitrarily small "remainder tets". Shape Volume ----- ------ A module 1/24 B module 1/24 T module 1/24 MITE 1/8 Coupler 1 Tetrahedron 1 Cube 3 Octahedron 4 Rh Triacontahedron 5 Rh Dodecahedron 6 Icosahedron 18.51... Cuboctahedron 20 Table 3: Concentric Hierarchy With the above concentric hierarchy in mind, a geometry student can look at an octet truss and superimpose an easily memorable system of scaled shapes. Both four- and five-fold symmetric members are represented, with a bridging transformation, and are concentric and hierarchically arranged. Many of the shapes are also dual pairs, which pairs may then be combined to give additional shapes. For example, the cube and octahedron are duals, and combine to give the rhombic dodecahedron. Given the streamlining effects of merging fcc packing with the octet truss and a concentric hierarchy of easy-to-remember volumes, the essentials of this curriculum are likely to gravitate down to lower grade levels, such that all of the above will be in some form accessible to an average 14 year old. Using TV, the internet, and film, it should be possible to communicate this primary level information quickly to a fairly large and global audience. We hope to have this job completed or well underway by the end of 1998. References: Erickson on Waterman Polyhedra. Synergetics-L archives in Reference.com de Jong. STRUCK. Erickson. SpringSpace. Koski. five-fold shapes modularlized w/ phi-scaled cuboid tets [1] [2] [3] Fuller, Grip-Kitrick, Urner. The volume 5 RT. [1] [2] [3] Snelson on Tensegrity Fuller, Urner. Concentric Hierarchy. Urner. Jitterbug animation using STRUCK and Povray. Hawkins. Jitterbug GIF. Fuller, Applewhite, Gray. Synergetics (web version) Hart. Duals and dual combinations. Erickson. Duals and other STRUCK animations. 1998 Math Makeover Campaign Return to Topics for Exploration Oregon Curriculum Network ======== [original version with graphics and activated hyperlinks at http://www.inetarena.com/~pdx4d/ocn/urner.html] --------------------------------------------------------- Kirby T. Urner http://www.teleport.com/~pdx4d/kirby.html 4D Solutions http://www.teleport.com/~pdx4d/ [PGP OK] --------------------------------------------------------- ========================================================================= Date: Tue, 14 Jul 1998 14:11:58 -0500 Reply-To: List for the discussion of Buckminster Fuller's works Sender: List for the discussion of Buckminster Fuller's works From: Jim Ferry Organization: Center for Simulation of Advanced Rockets Subject: Re: CubeWorld: adding dimensions Mime-Version: 1.0 Content-Type: text/plain; charset=us-ascii Content-Transfer-Encoding: 7bit Just in case any of you were wondering why this (out of control) thread bears the name CubeWorld . . . it split off from a thread in which I announced this page of mine: http://www.uiuc.edu/ph/www/jferry/cube/CubeWorld.html This site contains a few cheerful facts about the surface gravity of a large cube, so is irrelevant to the topic of this thread, namely, bickering. So as to remain on topic, let me add: Everyone sucks! (oh, except me, that is). | Jim Ferry (your imaginary friend) | Center for Simulation | +------------------------------------+ of Advanced Rockets | | http://www.uiuc.edu/ph/www/jferry/ +------------------------+ | jferry@expunge_this_field.uiuc.edu | University of Illinois | ========================================================================= Date: Tue, 14 Jul 1998 19:05:55 GMT Reply-To: List for the discussion of Buckminster Fuller's works Sender: List for the discussion of Buckminster Fuller's works From: Kirby Urner Organization: 4D Solutions Subject: Calculus 102: A Humanistic Approach to Primitive Concepts MIME-Version: 1.0 Content-Type: text/plain; charset=us-ascii Content-Transfer-Encoding: 7bit [from the Oregon Curriculum Network website: http://www.inetarena.com/~pdx4d/ocn/] ======= The Calculus: Primitive Concepts by Kirby Urner Originally posted: June 13, 1998 Last modified: June 19, 1998 The application of humanities techniques in the domain of teaching mathematics results in the practice of building associative semantic networks around idiom, alliteration, and word plays, as a way of anchoring the more crypto-compressed notational nuggets which traditionally populate a math text. Naturally this approach can only be modelled as a special case application, given the diverse cultural makeup of our classrooms. The model at right uses idioms from USA culture, such as "chunka change", alliterating on the ch to reinforce the "geeky greek" (more alliteration) concept-symbol DELTA. The associational link to Delta Airlines is likewise regional (as a teacher, I'd rather sync brandname visibility with content, tastefully, seamlessly, and drop the disruptive commerical break format). This reliance on idiom may seem overly idiosyncratic, and can be, if malpracticed, but ideally does not get in the way of making what may be the less familiar or "long distance" links to connected concepts of "quantum" and "voxel" -- examples of key terms with many technical applications in math-oriented science and engineering disciplines which may have little role in a student's everyday speech patterns at this point in her training. In this training, the ch sound was likewise used to spread discrete events in time, as the smoke puffs from a choo choo train (or chugga chugga -- the sound of an engine expending energy over time), which time interval relates to an angular change of a second hand on a clock (delta t). This primitive link of DELTA to a time-distance interval sets the stage for students who later read Einstein's introduction to special relativity for lay audiences (perhaps in translation), which is very much geared towards thought experiments having to do with trains. The train metaphor likewise primes the pump for subsequent discussions of the Doppler Effect and pitch changes. The explanation of SIGMA notation in terms of computerized do-loops, and of the Riemann Sum as a smoothing of the SIGMA sum, with quanta becoming relatively infinitesimal in the context of the operative coordinate frame, is fairly traditional. A more recent innovation is this building of a tetrahedron from the flatlander DELTA and using this to symbolize a volumetric increment, or an energy increment. At the pump, a gas droplet (volumetric increment) has a monetary value, and droplets flow into the tank at a specific rate (drops/sec or $/sec). Given gas quanta signify BTUs, we are likewise metering a rate of energy flow (horsepower, watts), equivalent to the physics concept of power (energy/time). This linking of monetary units to energy units will be useful for later readings in general systems theory. In more British-informed cultures, we would likely say "petrol" in place of "gas". In this coordinate frame, June 13, 1998 in Portland, Oregon, USA president Clinton was in the neighborhood (commencement speech at Portland State University). The target audience for this brainstorming session consisted of high school aged youth participating in the Latin-America Asia-Pacific Program (LAAP) of the American Friends Service Committee (AFSC). The emphasis in the humanities approach is on hooking mathematical operators to direct experience, which in this USA culture means film and television. Energy, the potential to transmit information (a kind of work), propagates omnidirectionally by means of electromagnetic waves, as shown at right by televisions spherically positioned to receive around a broadcasting source. Differentiation slices life into changes per time interval (frames of action), with the time-indexed "function" concept tying in the notion of a gear-works, some law-abiding mechanism that plays by the rules -- including those of plot development. Events open the door to other possible events within our partially overlapping scenarios or chronologies. A "shell" of energy conveys a "slice of life" to the screen, where integration (projection) happens smoothly enough (30 frames/second) to sustain the perception of continuity. A television is a remotely controlled device taking instructions through encyphered (programmed) energy, either broadcast, or wave-guided by wires, from the studio or live news event. "Solid state" circuitry decodes the carrier frequency (channel) and aims the cathode rays (or activates the matrix) to make screen pixels change their color and intensity in sync with whatever recorded events. Fuller Schoolers such as myself tend to link the 2nd powering of a particle's velocity in energy bookkeeping (e.g. E=Mc2) to surface area, such that we see a divergent "ripple" conveying matter-jiggling potential to energy-importing TV receivers. Cosmologically, we posit "conservation of sense" (aka intelligence) might be operating in tandem with energy conservation, and convergently vis-a-vis radiation's inherently uninhibited expansiveness, in which case an eternally regenerative scenario Universe might be a scientifically tenable concept. You may choose to drop such speculative philosophizing from your own presentations of course. Brainstorming more along these lines, I'm seeing the use for the "programmed bulb" as a curriculum artifact, by which I mean a point light source, like a star, but "programmed" in the sense of conveying information, e.g. providing a channel for transmitting bytes from server to client, from TV studio to TV receiver. I put it out in space so we get the full sphere of the expanding program bubble, not a "cell" or "dome" as when putting such bulbs just slightly above the surface of the planet (e.g. on a broadcast or cell phone tower). I like this idea because I think students spontaneously relate to "frequency" in terms of Mhz, a measure of CPU speed (e.g. 233) -- a kind of generic notion of "vibration" or "clock speed" already linked to the notion of "processing" or "throughput". Hence a high frequency bulb is able to discharge energy faster than a lower frequency one, because compressing more information into its broadcast. There's nothing really new here, but instead of going towards gamma rays we're thinking about the "data throughput potential" associated with high frequency transmissions i.e. "high buzz means more bits in the same time frame" (we might talk about "encyclopedias/second"). This gives students a handle on the difference between intensity (amplitude) and frequency (hertz), in that a low sound can be soft or loud (more or less intense) or a red light (fixed frequency) dim or bright (where bright means visible from a greater distance), but no matter how loud or bright, if the frequency is fixed, the rate of information transfer is likewise limited (unless we parcel out the content and send multiple packets on the same frequency, now having more bandwidth to play with -- but here we're assuming all additional amplitude is redundant information, converting the additional intensity into longer distance transmissions, not greater content). Given the photoelectric effect, we find that atoms are tuned to this vibrational dimension (frequency) and will not resonate at specific frequencies (by releasing photons) unless receiving on those frequencies. Intensity will influence the number of photons released at a given frequency, sure, but only a higher frequency will unlock corresponding higher frequency energies in a black body. Like begets like. An analogy is the tourist who speaks no French and asks "where is the bathroom?" in English. The victim of this interrogation conveys (or feigns) incomprehension, so the tourist simply repeats the question, only in a much louder tone of voice. This "intensity" or "amplitude" parameter might be linked to the notion of "brute strength" -- you get louder or more insistent but don't up the information content. Again, conservation of energy suggests a fatter pipe will make up for the slower throughput, so if we accumulate energy with no more leakage one way (AM) than the other (FM), we'll have enough total income to hit the high notes when retransmitting even if none were heard -- but will this high note capability atrophie if we don't use it? Atoms don't lose their spunk, but other designs certainly "get out of shape" through non-use of certain features. For example, capacity for languages -- "use it or lose it" seems to be the rule of thumb in so many of nature's deals. If your elders don't pass on whatever skill, it may be lost for generations, or forever (languages die out, and with them ways of life). Consider an episode in Star Trek (Next Generation) where the only way to escape certain disaster is to reprogram some circuits very quickly. Brute strength just won't do it -- sorry Whorf. So we call in Commander Data, who almost instantly sees what's needed and starts punching buttons at a rate even the fasted typist could not emulate. The amount of energy expended is perhaps less than the amount it would take to turbolift 1 crew member 3 decks, or to power the holodeck for 1 minute (simple bar scene), but the frequency of its translation, from Data's positronic brain to the ship's computer, was very high. This is a measure of power, or energy/time, and was the only expression of power that would serve -- brute strength would have been irrelevant. With these concepts in place, I think we can bring "intelligence" into the mix and give student-recruits a feel for how a "potentially explosive situation" might be dissipated or defused, provided we have enough analysts assigned to collecting and processing information about the events in question. Intelligence is the "high frequency" escape valve for energy that needs to go somewhere. If you close off this avenue, then "kaboom" (low frequency, low intelligence, high amplitude event) is the more likely result. To put it another way, a definite quantity of energy has a frequency spectrum and an amplitude spectrum for freedoms, and depending on the receivers in the neighborhood, will be able to keep amplitude within acceptable thresholds if given a chance to do high speed data feed. We needn't raise our voices and pound the table if the working atmosphere permits intelligent give and take -- more than mere posturing or scoring points for some hypothetical audience of dumbed-down third party observers. What may be the case is some systems "sense" when being received at high frequencies (or not) and deliver energy in this region of the spectrum accordingly -- this would go against our bias that "increased amplitude will always do the trick". It's not unusual in field studies to have a "sink" (receiver) set up a gradient such that energy is effectively "drained" from surrounding bodies. In other words, don't think of a receiver as just a passive ear, but as a "suction device" which tries to find ways to exercise its true potential. Owners of very fast computers are somewhat driven to buy games which take maximum advantage of their computers' capabilities -- give their machines a workout. To scan or listen is to likewise elicit, to encourage or promote broadcasts on the same frequency. But lets not leave this subject with Commander Whorf in a lowly, unappreciated position. In many situations, brute strength, power in the sense of amplitude, at whatever frequency (maybe low), is a positive and necessary form of expression. The stories are not all about technogeeks circumventing strong players (in other dimensions) using various dweeby cyphers that "the knuckleheads" can't grok. On the contrary, many stories are about ordinary folk with no "special training" or academic degrees networking to revector energy (aka finances) in ways that keep the technogeeks from blowing everything sky high because they feel "misunderstood" or "resent the unintelligent" or whatever sick and twisted form of misanthropy feeds their mad scientist fantasies of making others pay. Commander Whorf isn't chief of security because he's stupid, but because he has integrity and courage, and sometimes just repeating yourself, only this time more loudly, is just the ticket. For further reading: More Curriculum Notes Project Earthala: Brainstorming with Friends about the AFSC AFSC Portland Office Humanistic Mathematics Differentiation and Integration Professor Lazowska's 1996 lecture re the Information Revolution Some Information Theory The Concept of Hypertoons Rewiring ideas about electricity (curriculum reform) Math Makeover: Meeting with AFSC LAAP youth Phase, Frequency, Amplitude, and all that.. (see Java applet) Einstein's Special Relativity as a Windows helpfile R. Buckminster Fuller: 20th Century Philosopher Synergetics re Information [200.00] [ 1075.00] Delta Airlines Editorial Cartoons re Loud 'n Dumb, Technogeeks, Manliness South Asians Against Nukes Return to Topics for Exploration Oregon Curriculum Network ======== [original version with graphics and activated hyperlinks at http://www.inetarena.com/~pdx4d/ocn/calculus2.html] --------------------------------------------------------- Kirby T. Urner http://www.teleport.com/~pdx4d/kirby.html 4D Solutions http://www.teleport.com/~pdx4d/ [PGP OK] --------------------------------------------------------- ========================================================================= Date: Tue, 14 Jul 1998 20:09:11 GMT Reply-To: List for the discussion of Buckminster Fuller's works Sender: List for the discussion of Buckminster Fuller's works From: Kirby Urner Organization: 4D Solutions Subject: Re: CubeWorld: adding dimensions MIME-Version: 1.0 Content-Type: text/plain; charset=us-ascii Content-Transfer-Encoding: 7bit Jim Ferry wrote: >Just in case any of you were wondering why this (out of control) >thread bears the name CubeWorld . . . it split off from a thread >in which I announced this page of mine: > True enough, though someone quickly renamed your thread, went for 'addinng dimensions' at which point I chimed in with my 'hypercross dogmatics' material, given such content such as below from 1998/07/01 (none of the text mine): > Spatial dimensions are geometric > while sensual ones are perceptual. If a geometery is not observed, has no effect on anything that can be observed it by definition may not exist. There are spacial geometries we perceive, directly or indirectly, and these are the only ones we can claim to actually exist. So, there is a 1:1 match between concieved dimensions and known existing dimensions. I clued other NGs re my angle (I hang out in sci.philosophy.meta some) and some of the subsequent posts have not been posted to sci.math (e.g. Bruce Ward's of yesterday, to bit.listserv.geodesic only) -- while others were exclusively to sci.math, thanks mainly to Brian. Some of the posts which I thought didn't make it to sci.math actually did (not that it matters to anyone). Good, fine. Given the sensitivity of people who start threads feeling subsequent replies owe it to the starter to stay on topic, I'm doing more to create new threads of my own. I apologize if I have interfered with CubeWorld in any way and will post no further messages under this particular thread (many new ones started below, including the infamous Hypercross essay). Kirby --------------------------------------------------------- Kirby T. Urner http://www.teleport.com/~pdx4d/kirby.html 4D Solutions http://www.teleport.com/~pdx4d/ [PGP OK] --------------------------------------------------------- ========================================================================= Date: Tue, 14 Jul 1998 16:52:27 -0700 Reply-To: List for the discussion of Buckminster Fuller's works Sender: List for the discussion of Buckminster Fuller's works From: Brian Hutchings Subject: Beyond Flatland <> Brian Hutchings 14-JUL-1998 16:52 r001806@pen2.ci.santa-monica.ca.us that's very interesting, Kirby; although it as yet unclear, since I have just used the two, dual hexahedral matrices, to define the IVM/fcc (or dual of the "honeycomb" of rh.dodecah.) as for the "Waterman spheres", that is a question, I'd wondered about, for years, before reading of them, recently. then, I saw Jong's applet in St via your site, and I was startled by the patterns of each layer, although still cross-eyed -- and no *fusion*, either. I must say, the conjecture as to whole-tetragonal-unit volumes, like that of the tetraga made amongst any 4 vertices of the lattice, is a good one, and surely elementary, but I have never carried it through (clearly, though, the former could be proved *via* the latter, perhaps also *iff*, I suspect); it's a whole leap beyond Bucky's sphere-centered "shells", and an obvious "n+1" kind o'question, considering them (like, what are the numbers of vertices at each dostance ?-) the other cool thing was Snelson's small-circle model of the atomic orbitals, which I'd heretofore only seen, in a single picture, seen once (or hallucinated) in New Scientist! thus quoth: The octet truss defines tetrahedral and octahedral voids, twice as many of the former, with a volume ratio of 1:4 respectively. A second octet truss interpenetrates the first by centering all its vertices on octahedral voids. A third and fourth take up half the tetrahedral voids apiece. The four trusses may be paired to give two sets of vertices arranged in a cubic pattern, ala XYZ, with one set having vertices at the centers of the other's cubes. This pattern is known as body-centered cubic or bcc in crystallography.... The volume 3 cube inscribes as the short diagonals of the rhombic dodecahedron and runs between the pair of octet trusses in complementary sets of tetrahedral voids. The volume 4 octahedron inscribes as the long diagonals of the rhombic dodecahedron and defines the vertices of a fourth octet truss paired with the first i.e. the one defined by the rhombic dodecahedron centers.... The fcc cuboctahedron is a subclass of fcc polyhedra (those with vertices aligned with the sphere centers in an fcc packing) known as Waterman polyhedra. Waterman polyhedra are those convex hulls consisting of all fcc vertices equidistant from a common fcc center. Because all such shapes may be tetrahedralized, we know their volume will be a whole number relative to our unit volume tetrahedron of 4 fcc spheres. -- Shakespeare -- no! http://www.tarpley.net http://inet.uni-c.dk/~sch-inst/radio.html Citizens Protection Act -- yes! ========================================================================= Date: Tue, 14 Jul 1998 20:28:01 GMT Reply-To: List for the discussion of Buckminster Fuller's works Sender: List for the discussion of Buckminster Fuller's works From: Kirby Urner Organization: 4D Solutions Subject: Synergetics 102: Versus HyperCross Dogmatics MIME-Version: 1.0 Content-Type: text/plain; charset=ISO-8859-1 Content-Transfer-Encoding: 8bit [from the Synergetics on the Web site: http://www.teleport.com/~pdx4d/synhome.html] ======= Synergetics Versus HyperCross Dogmatics by Kirby Urner Originally posted: August 11, 1997 Last updated: November 13, 1997 Synergetics does not buy into hypercross dogmatics. The standard curriculum "ball of wax" you need to grasp, if you want to sound well trained in late 20th Century western (meta)physics, includes hypercross dogmatics, by which I mean the preaching that human sensory apparatus, with or without instrumental enhancements, is, by some flaw in its design, locked out of certain critical perceptual realms knowable only vicariously via sophisticated hypercross mathematics. Hypercross mathematics posits a fourth axis perpendicular to the three already mutually orthogonal X, Y, and Z axes. On the face of it, this proposition of a fourth orthogonal appears patently nonsensical, positively absurd, but the hypercross dogmatists say this initial skepticism is a knee-jerk manifestation of a human failing, that because of our fallen state we simply have no experiential access to the mysterious "fourth dimension" (a space of four mutually orthogonal axes), nor to the many additional hyperdimensional realms, each characterized by yet one more nonexperiential perpendicular. The brutal truth, we are told, is we are perceptually trapped in "three dimensions". To understand what this means, we are to read a favorite tract of the hypercross dogmatists: Flatland by Edwin A. Abbott. Mathematics, on the other hand, is clearly able to demonstrate the "reality" of these hyperdimensional realms, and those with special powers do have a kind of privileged and intuitive access to hyperdimensional truth. People like Einstein and Penrose are known for their uncanny ability to perform as guides to these ethereal trans-experiential domains. So if you want to be acknowledged for your academic prowess and authoritative metaphysics (physics with an inventive, yet acceptable spin), you must school your imagination to accept this hard core orthodoxy of the hypercross, otherwise you will be banned from the inner sanctum. As stated at the outset, Synergetics does not buy in to hypercross dogmatics. Synergetics doesn't buy the standard "dimension talk" at all, let alone its hyperinflated, dogmatic versions. Once down to primitive conceptual volume, no further paring away of dimensionality is conceivable -- we don't have fewer dimensions than it takes to think of volume. Points, lines and planes all occur within this identical shared context -- are nonexperiential without it. And in Synergetics, the emphasis is on experiences, on special case phenomena, as the front and center means by which we come to grips with the generalized, exceptionless principles. We simply have no experience of "Flatland" and all our attempts to experience it start with an irreducible, primordial sense of being observers within a containment -- observers with memories and an awareness of otherness and interaction. But what about hyperdimensional sphere packing and its already proved relevance to many branches of science and mathematics? Surely we don't mean to throw out decades of useful research into higher dimensional polytopes. The algebra and symbolic processing behind all the hyperdimensional sphere packing talk is useful programming, designed to operate with discrete locations in computer memory. Computer memory may be mapped using any kind of addressing logic, n-tuples, URLs, street names... with class methods defined to work in coordination with whatever invented schema. So to expand 3-tuple XYZ addressing to n-tuples, along with analogous definitions of 'sphere adjacency' (a term that remains operationally meaningful relative to methods for working with a 'dim 5' or 'dim 10' memory scheme) is not a problem, as long as we recognize the importance of metaphor and analogy within our operational mathematics. The problem starts when we become fixated on the "literal reality" of hyperdimensional sphere packings and begin beating ourselves (or our students) over the head with the dogma that we are dumb or inferior creatures because we cannot physically see the "dim 24" spheres that our computer programs seem to suggest are "really there" somewhere. Locations in a logical space may have any number of addressing elements (i.e. coordinates) -- and the analogy between such a "logical space" and the space of visual-tactile experiences is embedded in metaphors. Connections between any two experiences, regardless of when-where they occurred, are edges, to which edges the properties of tension (pull) and compression (push) may be applied. A tetrahedron, in principle, consists of any four events no matter when or where these occur. So Synergetics certainly retains our sense of intervals, connections, relationships and of a logical space, a memory, wherein any number of data storage and retrieval schemes get used to identify and characterize the interconnected, discrete, special-case events. The space of web pages is metaphorically such a polyvertexial structure of edges (links) and vertices (pages) -- a topology, a network. Synergetics is certainly not without its networks, its websites, its grand centrals, with connections converging-diverging everywhichway. But none of this experiential geometry of thinking requires us to buy that human experience is "trapped in 3D", or that the addressing schemes we require to spread our nets of hyperlinks throughout Universe must center around the hypercross: four or more mutual orthogonals. In fact, Synergetics suggests that we not base our simplest spatial thinking on perpendiculars at all, let alone more than three. The paradigm network containment with the fewest edges and vertices is the tetrahedron, which is more suggestive of 60 degrees than 90 degrees, although it is true that opposite edges of the regular tetrahedron run at 90 degrees to one another (without intersecting). Because Synergetics is a work in the humanities, semi- metaphorical verities are its bread and butter. Students trained in Synergetics are able to write and use computer programs which expand the usual 3-tuple XYZ addressing schema via n-tuples without getting so superstitious about the "hidden realities" which such operational mathematics is supposedly accessing altogether outside our powers to sensorially and experientially comprehend them. On the contrary, our senses are expanded by metaphor just as our mathematics is expanded by analogy and extrapolation. Our powers to visualize and otherwise experience are not being left in the dust owing to failings in the human design, but are keeping pace, because we recognize the symbolic nature of mathematics is not different in kind from the symbolic nature of the humanities, wherein hyperlinks have long sustained our stream of consciousness, even as our experiential networks have grown increasingly complicated and intricate. Synergetics consists of hyperlink networks minus any investment in hypercross dogmatics. Synergetics is polemical against the standard "dimension talk" and therefore is free-standing outside the whole standard "ball of wax" which places such dogmatics at its core. Exhibits re HyperCross Dogmatics: 4-D Dreams: Flatland and Star Trek? Quest for Utopia The Fourth Dimension by Cliff Pickover (is God 4-D?) We cannot see the multidimensional reality because our senses are limited to three dimensions The tesseract animation on Tom Getty's page really is fine (you don't need to join a religion to appreciate its great works of art) For further reading: The meaning of 4D in Synergetics FTP: On Redefining "Dimension" in Synergetics (rich text format) or MS Word 6.0 format More on "Dimension" at the Swarthmore Math Forum Let's End the Reign of Hypercross Dogmatics (newsgroup posting) Re "engineering mathematics" within the Fuller School (Swarthmore Math Forum) The Geometry Junkyard (lots of links to hypercross junk) A short review of Life by the Numbers (book and PBS TV series) Flatland by Edwin A. Abbott Investigations into Linear Algebra Concepts... Hypertoon Synergetics GST: Proposed New Low Level Associations for the System Concept ======== [original version with graphics and activated hyperlinks at http://www.teleport.com/~pdx4d/hypercross.html] --------------------------------------------------------- Kirby T. Urner http://www.teleport.com/~pdx4d/kirby.html 4D Solutions http://www.teleport.com/~pdx4d/ [PGP OK] --------------------------------------------------------- ========================================================================= Date: Tue, 14 Jul 1998 14:51:13 -0700 Reply-To: UncleAl0@ix.netcom.com Sender: List for the discussion of Buckminster Fuller's works From: Uncle Al Organization: The Noble Krell Subject: Re: Calculus 102: A Humanistic Approach to Primitive Concepts Mime-Version: 1.0 Content-Type: text/plain; charset=us-ascii Content-Transfer-Encoding: 7bit Kirby Urner wrote: > > [from the Oregon Curriculum Network website: > http://www.inetarena.com/~pdx4d/ocn/] > > ======= > > The Calculus: Primitive Concepts > > by Kirby Urner > Originally posted: June 13, 1998 > Last modified: June 19, 1998 > > The application of humanities techniques in the domain of > teaching mathematics results in the practice of building > associative semantic networks around idiom, alliteration, and > word plays, as a way of anchoring the more crypto-compressed > notational nuggets which traditionally populate a math text. [snip] Dare one speculate what transpires when one needs to take a derivative of a one variable linear function? Compromise of beauty in search of single-valued empirical truth is an obscenity - it would superannuate entire Liberal Arts faculties. A tenured Social Sciences professor at the University of Victoria was last summer found to be growing and selling Northern Lights cloned hydroponic boo to her students. Last I heard, her censure or dismissal hinged upon whether she was asking fair market price of her students UVic university administration was at a total loss as to a mechanism for acquiring unbiased market data. Uncle Al suspects further dialectic, dialog, and critique was called for. Needs more study. The RCMP was after her for tapping hydro before her meter. Doesn't make for much of a War on Drugs, does it? Then again, marijuana is the biggest single economic product in British Columbia, with ZERO impact upon the environment, no government subsidies, and a vast hard currency trade with the south (the US). Beats the Hell out of beneficiating Athabasca tar sands. (Marvelous stuff, that Nortehrn Lights. Proton and C-13 NMR showed single isomer purity, /_\-9-THC. If potheads in closets with grow lights can Mendelian breed a 30 wt-% THC marijuana in their spare time, how come all those corporate idiots with $million budgets doing rice, wheat, and corn cannot get their act together over the past 30 years?) -- Uncle Al Schwartz UncleAl0@ix.netcom.com ("zero" before @) http://uncleal.within.net/ http://pw2.netcom.com/~uncleal0/uncleal.htm http://www.ultra.net.au/~wisby/uncleal.htm http://www.guyy.demon.co.uk/uncleal/uncleal.htm (Toxic URLs! Unsafe for children, Democrats, and most mammals) "Quis custodiet ipsos custodes?" The Net! ========================================================================= Date: Tue, 14 Jul 1998 19:57:17 -0700 Reply-To: "P. O. Box 2321" Sender: List for the discussion of Buckminster Fuller's works From: "P. O. Box 2321" Subject: Education Automation & Synergetics Online Comments: To: Synergetics Listserv MIME-Version: 1.0 Content-Type: TEXT/PLAIN; charset=US-ASCII I have the good fortune to live only a few blocks from Kirby Urner [1]. At the risk of umasking him before those who only know him through his techo-invectives online, he is a kind person who has aided my understanding of synergetics. After reading many books by and about Buckminster Fuller, I felt I was ready to read Synergetics & Synergetics 2. It took several months and I had to take notes but I did read them and I think I understood as much as I didn't understand. Since both volumes of Synergetics are now online [2] and could therefore be edited, I began a list of what I felt were ideas that at least deserved debate if not correction. Kirby encouraged me to develop my criticisms, but he also convinced me that Synergetics was 'a museum piece' that we should work from, not a base material we should continue to mold. He convinced me the text of Synergetics may not be perfect or finished or even correct in some cases but rather than tamper with it, we should use it as a springboard for new works. However, I just read something by Fuller that may serve as an argument for amending Synergetics. The following is from "Education Automation / Freeing the Scholar to Return to His Studies" (Southern Illinois University Press, Carbondale 1962). [begin quote] "This lecture [the text of this book consists of a transcription of a lecture] will be recorded as Southern Illinois University did my last lecture series of fifty-two hours in October 1960. They will make moving picture footage of the lecture as well as hi-fi tape recordings. Then the professor and his faculty associates will listen to this recording time and again. ""What you say is very good," his associates may comment, "but we have heard you say it a little better at other times." The professor then dubs in a better statement. Thus begins complete reworking of the tape, cleaned up, and cleaned up some more, as in the moving picture cutting, and new illustrative "footage" will be added on. The whole of a university department will work on improving the message and conceptioning of a picture for many months, sometimes for years. The graduate students who want to be present in the university and who also qualify to be with the men who have great powers and intellectual capability together with the faculty may spend a year getting a documentary ready. They will not even depend upon the diction of the original lecturer, because the diction of that person may be very inadequate to his really fundamental conceptioning and information, which should be superb. His knowledge may be very great, but he may be a poor lecturer because of poor speaking habits or false teeth. Another voice will take over the task of getting his exact words across. Others will gradually process the tape and moving picture footage, using communications specialists, psychologists, etc." [end quote] This passage suggests, to me, that Fuller would have approved of a re-working of Synergetics online. And this suggestions raises many questions and possibilities. I suggest that there should remain a 'core' version of Synergetics online, one that is identical to the first edition of the printed version (identical even down to any spelling or punctuation errors present in the first edition of the printed version). The value of a 'museum piece' edition of Synergetics is to chart the development of the theory as well as to mark its place in the development of mathematics / philosophy as a whole. In addition to this, there could be an 'expanded' version that incorporates only those corrections and amplifications that have been made by Fuller, Ed Applewhite and Arthur Loeb. I do not recall the specifics, but if I remember correctly Kirby said Fuller had some unpublished corrections or amplifications for Synergetics. If so, these could be incorporated into an 'expanded' Synergetics. I further suggest that there could be a third class of Synergetics, one which incorporates corrections and amplifications made by other students of the theory. This third class Synergetics would likely occur in many forms; there would be one or two versions that many developed together and many more versions that were developed by individuals. The Unix and Linux operating systems serve as a model for how Synergetics could be developed online: a core version under official control and alternate versions under public control. As with Unix and Linux, issues of copyright would come in to play were Synergetics to 'go public' as the above quote from Fuller suggests it should in the education of 21st Century students. 'Core' Synergetics exists online already. 'Expanded' Synergetics does not, and if it is to exist at all should be brought into being by those most versed in what Fuller, Applewhite and Loeb consider to be essential additions and corrections to the text. 'Public' Synergetics is, in some ways, occurring now in the mailing list 'synergetics-l' [3] and the archives for that list [4]. But in other ways it has yet to be attempted. Distinguishing between Fuller's words (which are copyrighted) and Fuller's ideas (which are, in his own words, the coordinate system of universe and impossible to copyright) should be undertaken with all due respect for Fuller's estate. I encourage further discussion of the appropriateness and process of amending, expanding and 'publicizing' Synergetics. [1] [2] http://www.servtech.com/~rwgray/synergetics/synergetics.html [3] http://www.inetarena.com/~pdx4d/Synergetics-L/synl.html [4] http://www.inetarena.com/~pdx4d/Synergetics-L/archives/recent/ [and] http://www.inetarena.com/~pdx4d/Synergetics-L/archives/compressed/ -- _________________________________________ | | | | | | | | | | (, | /\ | |] | (, | [- | |- | |- | <> | | Gg | Aa | Dd | Gg | Ee | Tt | Tt | Oo | ----------------------------------------- http://www.teleport.com/~box2321/go.html ========================================================================= Date: Wed, 15 Jul 1998 00:08:18 GMT Reply-To: List for the discussion of Buckminster Fuller's works Sender: List for the discussion of Buckminster Fuller's works From: Kirby Urner Organization: 4D Solutions Subject: Re: Calculus 102: A Humanistic Approach to Primitive Concepts MIME-Version: 1.0 Content-Type: text/plain; charset=us-ascii Content-Transfer-Encoding: 7bit Uncle Al related to Weird Al perchance? Whatchoo been smokin, dude? Kirby --------------------------------------------------------- Kirby T. Urner http://www.teleport.com/~pdx4d/kirby.html 4D Solutions http://www.teleport.com/~pdx4d/ [PGP OK] --------------------------------------------------------- ========================================================================= Date: Wed, 15 Jul 1998 02:50:12 GMT Reply-To: List for the discussion of Buckminster Fuller's works Sender: List for the discussion of Buckminster Fuller's works From: Harry H Conover Organization: The Internet Access Company, Inc. Subject: Re: Calculus 102: A Humanistic Approach to Primitive Concepts Kirby Urner (pdx4d@teleport.com) wrote: : : [from the Oregon Curriculum Network website: : http://www.inetarena.com/~pdx4d/ocn/] : : ======= : : The Calculus: Primitive Concepts : : by Kirby Urner : Originally posted: June 13, 1998 : Last modified: June 19, 1998 : : : The application of humanities techniques in the domain of : teaching mathematics results in the practice of building : associative semantic networks around idiom, alliteration, and : word plays, as a way of anchoring the more crypto-compressed : notational nuggets which traditionally populate a math text. : : Naturally this approach can only be modelled as a special case : application, given the diverse cultural makeup of our : classrooms. The model at right uses idioms from USA culture, : such as "chunka change", alliterating on the ch to reinforce : the "geeky greek" (more alliteration) concept-symbol DELTA. The : associational link to Delta Airlines is likewise regional (as a : teacher, I'd rather sync brandname visibility with content, : tastefully, seamlessly, and drop the disruptive commerical : break format). To put words into Uncle Al's mouth: "Are you on drugs, or simply stupid." While I share your pain, there is a plurality of kinder and more understanding psycobabble groups on the net, many members of which would joyously swab your forehead with conductive electrolytes jelly, and apply both electrodes and 120 volts of alternating current electricit until you comprend the basic truth of (and acknowledge the wisdom of) their agenda. Then too, there is the possiblity that, while verbose, you may be stupid, in which case (you not presenting a significant threat) everyone will ignore you. Harry C. ========================================================================= Date: Wed, 15 Jul 1998 03:20:54 -0700 Reply-To: List for the discussion of Buckminster Fuller's works Sender: List for the discussion of Buckminster Fuller's works From: Brian Hutchings Subject: what ever <> Brian Hutchings 15-JUL-1998 3:20 r001806@pen2.ci.santa-monica.ca.us I did not take Uncle Al's posting to be sggestive that Kirby is a member of the Hashashin/TwirlingDervishes/MuslimBrotherhood -- but he could be a Rasta -- nor of Al's own habituarium; both of these notions may be premature, however, and "further study" is definitely required! in any case, he is completely dysinfromed, perhaps by the Soroses of Earth, on the pristine nature of hardcore hempcropping, which can generaously be termed, Slash and Fall Ag; thou requirest **** (fertilizer). ========================================================================= Date: Wed, 15 Jul 1998 05:00:22 -0700 Reply-To: List for the discussion of Buckminster Fuller's works Sender: List for the discussion of Buckminster Fuller's works From: Brian Hutchings Subject: the Cup (saves face) <> Brian Hutchings 15-JUL-1998 5:00 r001806@pen2.ci.santa-monica.ca.us FLASH: just heard on KABC, all of the USAGs are combining in a "united front", supposedly to address the tobacco issue. however, it seems very probable, that they'll use this networking, to organize against HR#3396. so, do us all a favor, and call your Representative with warning & support, please! very late meeting, tonight, til 1. although I don't believe in "reporting" local news for Bush's NWO (e-Godz -- Olympians), I can relate my belated commemoration of French Independence Day, since they won that Big Match.... it is called, Bastille Day, after the campaign-stunt of the Duc d'Orleans, who paid some folks to lead the mob from behind -- to "liberate" 7 poor farts, most of whom'd have stayed, given conditions outside, I suppose; ecept for de Sade, though. the result was the promotion of Jacques Necker, the Ministre de Finance, to Prime Ministre, like giving Dracula the entire hospital, with "drawing" rights to all future bloodrives. Necker was the spouse of Madame de Stael, the organizer of the salon of the oligarchical Encyclopaedists and Enlightenment salesmen. --Shakespeare -- ain't he still dead ?!? http://www.tarpley.net http://inet.uni-c.dk/~sch-inst/radio.html Support the Citizens Protection Act, HR#3396 (McDade-Murtha) !! ========================================================================= Date: Thu, 16 Jul 1998 08:27:45 -0700 Reply-To: List for the discussion of Buckminster Fuller's works Sender: List for the discussion of Buckminster Fuller's works From: "Joe S. Moore" Subject: Re: what ever MIME-Version: 1.0 Content-Type: text/plain; charset="iso-8859-1" Content-Transfer-Encoding: 7bit Brian, I sure wish your email software had a spelling checker. **************************************** * Joe S. Moore * Independent Buckminster Fuller Scholar * joemoore@cruzio.com * Buckminster Fuller Virtual Institute * http://www.cruzio.com/~joemoore/ **************************************** -----Original Message----- From: Brian Hutchings Newsgroups: bit.listserv.geodesic To: GEODESIC@LISTSERV.ACSU.BUFFALO.EDU Date: Wednesday, July 15, 1998 03:18 AM Subject: what ever ><> Brian Hutchings 15-JUL-1998 3:20 > r001806@pen2.ci.santa-monica.ca.us > > I did not take Uncle Al's posting to be sggestive that > Kirby is a member of the Hashashin/TwirlingDervishes/MuslimBrotherhood > -- but he could be a Rasta -- nor of Al's own habituarium; > both of these notions may be premature, however, and > "further study" is definitely required! > in any case, he is completely dysinfromed, > perhaps by the Soroses of Earth, on the pristine nature > of hardcore hempcropping, which can generaously be termed, > Slash and Fall Ag; thou requirest **** (fertilizer). > ========================================================================= Date: Wed, 15 Jul 1998 12:27:56 EDT Reply-To: List for the discussion of Buckminster Fuller's works Sender: List for the discussion of Buckminster Fuller's works From: Zac Elston Subject: Smoke this Mime-Version: 1.0 Content-type: text/plain; charset=US-ASCII Content-transfer-encoding: 7bit In a message dated 98-07-14 23:24:09 EDT, pdx4d@TELEPORT.COM writes: > Uncle Al related to Weird Al perchance? > > Whatchoo been smokin, dude? What Al was smoking is obvious. This leads me to another rant concerning socialization and Fuller. Because many of Fuller's ideas and statements were so anti-establishment, and he was so vocal about them as well, he pulled a proverbial 'bullet in the foot" act with his own advancement. Even if his ideas were products of untold metal alpha-testing, Fuller's holier then now' attitude toward those who didn't see it his way served to distance himself from the population at large who had not the tools nor patience to look a little further. (I'm also convinced Fuller suffed from full blown Adult ADHD but that's another story.) Given that only the anti-establishment establishment would even give Fuller a second glance, I think it is little wonder we face the problems we face today with Fuller's work. That of getting past other people's noses. Now shoving aside all the problems inherent to Fullers designs in modern society (square holes and triangle blocks) I would like to make a comment to all those who think they have the answer. You might, but chances are no one will listen because it is not in the language they understand. Kirby's thesis on 'chunk-a-this' and how vocabulary shapes the global unconsciousness does foreshadow the spectrum one must observe when dealing with macro social concepts (or even concepts foreign to the society at large) Words not only pull people in to an idea, but also push them out of an idea. Before one goes off ranting how the world would be a better place if we all took a toke (or something equally anti-establishment), give some thought to who the audience is and how they might interpret such statements. As that of a scientist who is making a statement on the data at hand...or that of a poet, expressing a desire...or that of someone who hasn't thought at all. You might be right, but chances are no one will be listening because you just farted into the microphone some words that turned on all the alarms in everyone listening. (I hope that wasn't a Hutchings'ism) Yes, Fuller's ideas do tend to focus on community, sharing and type B personalities. Yes Pot is a drug that mixes well with socialization. But interchanging one counter culture idea with another tends to make people twitch and promotes false association of valid design principles with personal ideology. Friends don't let friends mix ideas. -zac ========================================================================= Date: Wed, 15 Jul 1998 11:25:03 -0600 Reply-To: List for the discussion of Buckminster Fuller's works Sender: List for the discussion of Buckminster Fuller's works From: "Lawrence E. Couey" Organization: FX Informationing Subject: Re: TinkerDomes MIME-Version: 1.0 Content-Type: text/plain; charset=us-ascii Content-Transfer-Encoding: 7bit I'm also working on an "extension" to the tinkertoy set. Still getting things setup. They also work well with Octettruss construction. What would people be willing to pay for a Geodesic Connector Extension set? Lawrence C. Chuck Knight wrote: > > > > You know, a very viable product might be an "extension" to the basic > > > Tinkertoy set, which includes connectors for geodesic modelling. > > > > yes it would, but maybe the rest of the world doesn't think so. My theory > > however is that if the product is in enough hands ...it will become more > > understood and desired therefor paying off the cost of production. > > Plus, it wouldn't have to be marketed as a "geodesic modelling kit," but > simply as a supplemental connector kit compatible with Tinkertoys. > Marketing > would be everything! > > However, pictures on the box, showing complex structures...a geodesic > dome, > a dna double helix, maybe a molecule or two, would force people to start > thinking about the limitations of the basic set which currently shows a > "square" ferris wheel. > > > However...and here is were one would begin to compete with the ZomeTool > > product, how fancy do you design the connectors? Zometools are great and are > > designed for the exact purpose this conversation is discussing. > > Who said anything about competing directly with Zometool? That's a > higher > end modelling product, specifically designed for the purposes of > exploring > polyhedra. My basic concept wouldn't compete with them at all. I'm > talking > about TINKERTOYS!!! > > Anyone know the lengths of the sticks available in a complete Tinkertoy > set? The one I bought wasn't even close to being complete. > > > I started with small wooden balls from a craft store ($.19 retail). These can > > be drilled with 5 or 6 holes fitting the tinkertoy diameter, but where do you > > stop? Do you want a connector that accepts every entry point? would it be > > better to have classes of connectors? mode I II or III? Color coded for > > platonic class? just thinking out loud here.... > > I think something a little more flexible would be a better design. > (literally) I was thinking of a flexible rubber set of connectors, > consisting of a rubber tinkertoy-style "disk" connector with 5 or > 6 holes in it. That would allow some flexibility in the angles, while > still allowing enough rigidity to "hold" the struts in place. > > With so many flexible polymers available, it's just a matter of > choosing the right one. (The ones used for plastic "pencil erasers" > would probably be a good choice) > > > > P.S. So, who's up to the challenge of designing these things with me? > > > > I'm game :) > > So, what do you think of my basic concept? I have a few variants > already > designed...in my mind's eye...but I'm not sure how easy they would be to > actually mass produce. Shouldn't be too hard. > > > as an aside.. how about something bigger? I want something like > > http://www.8020.net/ > > No reason that the basic concept could not be scaleable. ;-) One > step at a time. > > -- Chuck Knight -- --------------------------------------------- Lawrence E. Couey - Convivial Applied Theoretical Technologies/ FX Informationing - mailto:LECouey@INet-1.com --------------------------------------------- ========================================================================= Date: Wed, 15 Jul 1998 11:46:48 -0700 Reply-To: List for the discussion of Buckminster Fuller's works Sender: List for the discussion of Buckminster Fuller's works From: Michael Riversong Subject: Re: Smoke this Mime-Version: 1.0 Content-Type: text/plain; charset="us-ascii" I would add to this that drug use is a good way to compromise any social movement. Marijuana was used as a weapon against American troops in Viet Nam, for example, to devastating effects. Timothy Leary's promotion of LSD nearly destroyed Western civilization. Any student of Buckminster Fuller who in any way condones drug use (including psychiatric drugs such as Prozac) is destroying the future of design science. At 12:27 PM 7/15/98 EDT, you wrote: >In a message dated 98-07-14 23:24:09 EDT, pdx4d@TELEPORT.COM writes: > >> Uncle Al related to Weird Al perchance? >> >> Whatchoo been smokin, dude? > >What Al was smoking is obvious. > >This leads me to another rant concerning socialization and Fuller. Because >many of Fuller's ideas and statements were so anti-establishment, and he was >so vocal about them as well, he pulled a proverbial 'bullet in the foot" act >with his own advancement. Even if his ideas were products of untold metal >alpha-testing, Fuller's holier then now' attitude toward those who didn't see >it his way served to distance himself from the population at large who had not >the tools nor patience to look a little further. > >(I'm also convinced Fuller suffed from full blown Adult ADHD but that's >another story.) > >Given that only the anti-establishment establishment would even give Fuller a >second glance, I think it is little wonder we face the problems we face today >with Fuller's work. That of getting past other people's noses. > >Now shoving aside all the problems inherent to Fullers designs in modern >society (square holes and triangle blocks) I would like to make a comment to >all those who think they have the answer. You might, but chances are no one >will listen because it is not in the language they understand. Kirby's thesis >on 'chunk-a-this' and how vocabulary shapes the global unconsciousness does >foreshadow the spectrum one must observe when dealing with macro social >concepts (or even concepts foreign to the society at large) Words not only >pull people in to an idea, but also push them out of an idea. > >Before one goes off ranting how the world would be a better place if we all >took a toke (or something equally anti-establishment), give some thought to >who the audience is and how they might interpret such statements. As that of >a scientist who is making a statement on the data at hand...or that of a poet, >expressing a desire...or that of someone who hasn't thought at all. You >might be right, but chances are no one will be listening because you just >farted into the microphone some words that turned on all the alarms in >everyone listening. (I hope that wasn't a Hutchings'ism) > >Yes, Fuller's ideas do tend to focus on community, sharing and type B >personalities. Yes Pot is a drug that mixes well with socialization. But >interchanging one counter culture idea with another tends to make people >twitch and promotes false association of valid design principles with personal >ideology. > >Friends don't let friends mix ideas. > >-zac > > -- Michael Riversong P.O. Box 2775, Cheyenne, Wyoming 82003 ** (307)635-0900 Professional Harpist Author of MRiversong@earthlink.net http://home.earthlink.net/~mriversong ========================================================================= Date: Wed, 15 Jul 1998 12:05:08 -0700 Reply-To: List for the discussion of Buckminster Fuller's works Sender: List for the discussion of Buckminster Fuller's works From: Brian Hutchings Subject: warp factor naught <> Brian Hutchings 15-JUL-1998 12:05 r001806@pen2.ci.santa-monica.ca.us that is the apparently most-significant aspect of the hexahedral matrix or "XYZ"; it is self-dual, as the tetragon/tetrahedron is self-dual, "atomically". the fact that all of the vertices of the pair of duals, form the "isotropic" network of the centers of close-packed spheres, gives rise to its "4D-ness", as "mystaquenlly" proven in *Quantum*. the author had gathered results of number-crunchers, on "pre- and post-pythagorean triga" in various dimensions, and these clowns from IBM asserted some "4D" results, whereas they were easily shown to be "embedded" in the IVM. thus-related is my oldst conjecture, after "empirically" noticing the Pythag.Tetrahedron (cube-corner), that all of the integers are accounted-for, as the "squares" of the distances betweeen the vertices of the IVM. what is the first integer that is dysincluded in "XYZ" ?? (hint: it's less than a googleplex; empirically, using a *tablet* of standard "quadrille", I found that the IVM accounted all integers to something over a hundred (using the symmetry of the cuboctah., you only need to calculate the vertices that are within a 24th "sector" of the IVM .-) ========================================================================= Date: Wed, 15 Jul 1998 15:31:43 -0700 Reply-To: List for the discussion of Buckminster Fuller's works Sender: List for the discussion of Buckminster Fuller's works From: Chuck Knight Subject: Re: TinkerDomes Comments: To: "Lawrence E. Couey" MIME-Version: 1.0 Content-Type: text/plain; charset=us-ascii Content-Transfer-Encoding: 7bit > I'm also working on an "extension" to the tinkertoy set. Still getting > things setup. They also work well with Octettruss construction. I'll ask you about only one detail...I tend to find that inventors are rather tight lipped when it comes to unpublished inventions. But, are your connectors rigid or flexible? Our design is flexible...so the math of each and every conceivable angle does not come into play. > What would people be willing to pay for a Geodesic Connector Extension > set? I have no idea. I don't even know what Tinkertoys cost...I picked mine up at a thrift store for $.29! -- Chuck Knight ========================================================================= Date: Wed, 15 Jul 1998 15:20:50 GMT Reply-To: List for the discussion of Buckminster Fuller's works Sender: List for the discussion of Buckminster Fuller's works From: Kirby Urner Organization: 4D Solutions Subject: Re: Calculus 102: A Humanistic Approach to Primitive Concepts MIME-Version: 1.0 Content-Type: text/plain; charset=us-ascii Content-Transfer-Encoding: 7bit conover@tiac.net (Harry H Conover) wrote: >While I share your pain, there is a plurality of kinder and >more understanding psycobabble groups on the net, many members >of which would joyously swab your forehead with conductive >electrolytes jelly, and apply both electrodes and 120 volts >of alternating current electricit until you comprend the basic >truth of (and acknowledge the wisdom of) their agenda. > Sounds a lot like sci.math. >Then too, there is the possiblity that, while verbose, you >may be stupid, in which case (you not presenting a significant >threat) everyone will ignore you. > > Harry C. Did even bother to explore the website before jumping on the backlash bandwagon? -- if so, then clear evidence that in your case more humanities training is indicated. I back up my 'film metaphor' with coded methods for 'camera' and 'projector' objects (linked essay). Humanistic Math is not something I invented. Working a matrix or applying Stoke's Theorem is not something I eschew. This is just another layer or angle for my multicultural LAAP youth who lack intuitive "in yer bones" understanding of what the calculus is all about (film metaphor not just mine either -- Keith Devlin uses is my info, though I haven't seen his CDROM). We'll get to div and curl too, just with some different steps in between (still doing work). I've already gotten a rave review for my essay from Gene Fowler, ('Waking the Poet'), so I figure the audience I most want to reach is being well-served. Your knee-jerk ad hominem attacks just expose you for a sloppy thinker in severe need of better education (to respond in kind). Kirby Curriculum writer 4D Solutions --------------------------------------------------------- Kirby T. Urner http://www.teleport.com/~pdx4d/kirby.html 4D Solutions http://www.teleport.com/~pdx4d/ [PGP OK] --------------------------------------------------------- ========================================================================= Date: Wed, 15 Jul 1998 16:47:57 GMT Reply-To: List for the discussion of Buckminster Fuller's works Sender: List for the discussion of Buckminster Fuller's works From: Larry Mead Organization: University of Southern Mississippi Subject: Re: Calculus 102: A Humanistic Approach to Primitive Concepts Kirby Urner (pdx4d@teleport.com) wrote: : [from the Oregon Curriculum Network website: : http://www.inetarena.com/~pdx4d/ocn/] : ======= : The Calculus: Primitive Concepts : by Kirby Urner : Originally posted: June 13, 1998 : Last modified: June 19, 1998 : The application of humanities techniques in the domain of : teaching mathematics results in the practice of building : associative semantic networks around idiom, alliteration, and : word plays, as a way of anchoring the more crypto-compressed : notational nuggets which traditionally populate a math text. [verybigsnip] In other words, " To teach math to people who don't have skills using simple symbols, use a lot of words and pictures instead." Duh-uh. If this is the kind of speach used in teaching youngsters these days, no *wonder* no one can learn abstract reasoning. -- Lawrence R. Mead Ph.D. (Lawrence.Mead@usm.edu) Eschew Obfuscation! Espouse Elucidation! www-dept.usm.edu/~physics/mead.html ========================================================================= Date: Wed, 15 Jul 1998 15:46:08 -0700 Reply-To: List for the discussion of Buckminster Fuller's works Sender: List for the discussion of Buckminster Fuller's works From: "P. O. Box 2321" Subject: Re: Calculus 102: A Humanistic Approach to Primitive Concepts Comments: To: Larry Mead Comments: cc: Kirby Urner In-Reply-To: <6oimft$6gu$1@thorn.cc.usm.edu> MIME-Version: 1.0 Content-Type: TEXT/PLAIN; charset=US-ASCII On Wed, 15 Jul 1998, Larry Mead wrote: > If this is the kind of speach used in teaching youngsters these days, no > *wonder* no one can learn abstract reasoning. Try "speech." -- _________________________________________ | | | | | | | | | | (, | /\ | |] | (, | [- | |- | |- | <> | | Gg | Aa | Dd | Gg | Ee | Tt | Tt | Oo | ----------------------------------------- http://www.teleport.com/~box2321/go.html ========================================================================= Date: Wed, 15 Jul 1998 15:36:55 -0400 Reply-To: List for the discussion of Buckminster Fuller's works Sender: List for the discussion of Buckminster Fuller's works From: John Shonder Organization: Oak Ridge National Lab, Oak Ridge, TN Subject: Re: Calculus 102: A Humanistic Approach to Primitive Concepts Kirby Urner wrote in message <35acc494.122647960@news.teleport.com>... *snip* >This is just another layer or angle for my multicultural >LAAP youth who lack intuitive "in yer bones" understanding >of what the calculus is all about (film metaphor not just >mine either -- Keith Devlin uses is my info, though I haven't >seen his CDROM). We'll get to div and curl too, just with >some different steps in between (still doing work). > Are you saying students from Latin American and Asian-Pacific countries lack the ability to learn calculus the traditional way? I'm sure this will come as a surprise to all the successful mathematicians, engineers, and economists from those countries who did not have you to hold their hands for them. John Shonder ========================================================================= Date: Wed, 15 Jul 1998 19:43:46 GMT Reply-To: List for the discussion of Buckminster Fuller's works Sender: List for the discussion of Buckminster Fuller's works From: Harry H Conover Organization: The Internet Access Company, Inc. Subject: Re: Calculus 102: A Humanistic Approach to Primitive Concepts Kirby Urner (pdx4d@teleport.com) wrote: : conover@tiac.net (Harry H Conover) wrote: : : >While I share your pain, there is a plurality of kinder and : >more understanding psycobabble groups on the net, many members : >of which would joyously swab your forehead with conductive : >electrolytes jelly, and apply both electrodes and 120 volts : >of alternating current electricit until you comprend the basic : >truth of (and acknowledge the wisdom of) their agenda. : > : : Sounds a lot like sci.math. : : >Then too, there is the possiblity that, while verbose, you : >may be stupid, in which case (you not presenting a significant : >threat) everyone will ignore you. : > : > Harry C. : : Did even bother to explore the website before jumping on the : backlash bandwagon? -- if so, then clear evidence that in : your case more humanities training is indicated. Turning that around, there is clear evidence that in your case more computer science training is indicated. This is a Usenet netsgroup, which I read using a Unix newsreader named tin running under a Unix shell account on my ISP. Websites represent a totally different Internet medium or service than do newsgroups, and are generally best accessed through a totally different mechanism. Just as I do not view televison programs on my radio, or use my televison to receive FM stereo classical music broadcasts, I do not view websites with my newsreader nor do I post HTML to the newsgroups. Of course, there are those that, lacking a Unix shell account, access newsgroups using a web browser. While this is possible, there is a growing body of evidence that suggests this practice can lead to irreversible brain cramp and anal retentiveness, hence many experienced users continue to access the newsgroups using tools and mechanisms specific to the medium. Also, there are enough specious posts in the newsgroups that I don't need to move to the web to find more -- particularly since the web is a medium that lacks support to post a follow-up! Harry C. ========================================================================= Date: Wed, 15 Jul 1998 17:36:20 -0700 Reply-To: List for the discussion of Buckminster Fuller's works Sender: List for the discussion of Buckminster Fuller's works From: Brian Hutchings Subject: Calculus Naught <> Brian Hutchings 15-JUL-1998 17:36 r001806@pen2.ci.santa-monica.ca.us y'know, Harry, retentiveness is preferable to incontinence; eh?... I was just using a webreader, although I'm not sure, whether my postied replies actually made it (as the indicators zipped past, to fast; could have been errors), via Lynx, which is primarily textual, without add-ons, shich I just dyscovered has this facility (I'd recalled one, but forgotten that it was accessed via Lynx). I also tried to get Pine configures for NGs *and* my mail, but I wiped the configuration, for lack of error-trapping -- does anyone know, whether the circa-95 v3.91 is the final offering? I don't have a TV --thank God; I was raised on that ****-- but I'd love to have a tuner-card in my PC, with the proviso that the *picture* can be turned-off, leaving only the sound; there's a lot o'talking-head, or "radio with make-up professionals". as for "computer science" and "computer literacy", those jokes have lost their tender hilarity; my local community college has become, in part, a sweatshop for the inculcation of Windowless'00 (Da Kubikle), as well as a refractory remedial joint for The Basics, feeding into the local UC and USC and so on. back on the thread of spatial mensuration, I must again note that "Euclidean" mensuration is pre-co-ordinate-system: all of the constructions are done without ruler!... all of them, the spatial ones, are constructable as projections or cross-sections, as are the cubical matrices and the IVM. (see _Modern Pure Solid Geometry_ by nathan Altshiller-Court, recently republished by Chelsea in softback; I'd like to thank any of you that queried them, perhaps because of my characterization of it with a new title, _The Tetrahedron and How To Ab/Use It_, on "Syn-helL" .-) -- Shakespeare !! http://www.tarpley.net http://inet.uni-c.dk/~sch-inst/radio.html HR#3396 ?? ========================================================================= Date: Thu, 16 Jul 1998 04:39:23 GMT Reply-To: pcox4@bellsouth.net Sender: List for the discussion of Buckminster Fuller's works From: Randy Organization: Tension Structures Subject: Don't talk it, do it..... MIME-Version: 1.0 Content-Type: text/plain; charset=us-ascii Content-Transfer-Encoding: 7bit I've always found a lot of talk on geodesic and other Fuller-related forums, but very few people actually building anything other than domes. A lot of people talking about philosophy and world games and such, but very few applications are mentioned. Sometimes I wish Bucky and never patented the Geodesci Dome. It overshadows the underlying fundamental principles that are there. Fuller and Snelson and Otto (and others) developed real structural principles that can be used to BUILD things. Tensegrity and aspension can make incredible things. I am building some things using their underpinings. I will keep everyone informed, if you really want to know. Once you get through the initial confusion of tensegrity, an underlying simlicity and beauty becomes evident in the structure. ========================================================================= Date: Thu, 16 Jul 1998 03:04:35 -0700 Reply-To: List for the discussion of Buckminster Fuller's works Sender: List for the discussion of Buckminster Fuller's works From: Brian Hutchings Subject: "construtable" geometry citation <> Brian Hutchings 16-JUL-1998 3:04 r001806@pen2.ci.santa-monica.ca.us sorry, for the pedantical repetition, but I wanted the *good* part to be excerpted from the smalltalk. thus saith: back on the thread of spatial mensuration, I must again note that "Euclidean" mensuration is pre-co-ordinate-system: all of the constructions are done without ruler!... all of them, the spatial ones, are constructable as projections or cross-sections, as are the cubical matrices and the IVM. (see _Modern Pure Solid Geometry_ by nathan Altshiller-Court, recently republished by Chelsea in softback; I'd like to thank any of you that queried them, perhaps because of my characterization of it with a new title, _The Tetrahedron and How To Ab/Use It_, on "Syn-heL" .-) -- Shakespeare !! http://www.tarpley.net http://inet.uni-c.dk/~sch-inst/radio.html HR#3396 ?? ========================================================================= Date: Thu, 16 Jul 1998 07:27:43 GMT Reply-To: List for the discussion of Buckminster Fuller's works Sender: List for the discussion of Buckminster Fuller's works From: Robin Chapman Organization: University of Exeter Subject: Re: Calculus 102: A Humanistic Approach to Primitive Concepts In article <6oj080$lbk$1@sws1.ctd.ornl.gov>, "John Shonder" wrote: > > Kirby Urner wrote in message <35acc494.122647960@news.teleport.com>... > > >Keith Devlin uses is my info, though I haven't > >seen his CDROM). Can anyone understand this sentence? Robin Chapman + "They did not have proper Department of Mathematics - palms at home in Exeter." University of Exeter, EX4 4QE, UK + rjc@maths.exeter.ac.uk - Peter Carey, http://www.maths.ex.ac.uk/~rjc/rjc.html + Oscar and Lucinda -----== Posted via Deja News, The Leader in Internet Discussion ==----- http://www.dejanews.com/rg_mkgrp.xp Create Your Own Free Member Forum ========================================================================= Date: Thu, 16 Jul 1998 11:16:09 -0700 Reply-To: List for the discussion of Buckminster Fuller's works Sender: List for the discussion of Buckminster Fuller's works From: Brian Hutchings Subject: Re: Calculus 102: A Humanistic Approach to Primitive Concepts MESSAGE from ="List 16-JUL-1998 11:12 In article <6oj080$lbk$1@sws1.ctd.ornl.gov>, "John Shonder" wrote: > > Kirby Urner wrote in message <35acc494.122647960@news.teleport.com>... > > >Keith Devlin uses is my info, though I haven't > >seen his CDROM). Can anyone understand this sentence? Robin Chapman + "They did not have proper Department of Mathematics - palms at home in Exeter." University of Exeter, EX4 4QE, UK + rjc@maths.exeter.ac.uk - Peter Carey, http://www.maths.ex.ac.uk/~rjc/rjc.html + Oscar and Lucinda -----== Posted via Deja News, The Leader in Internet Discussion ==----- http://www.dejanews.com/rg_mkgrp.xp Create Your Own Free Member Forum - - - - - <> Brian Hutchings 16-JUL-1998 11:16 r001806@pen2.ci.santa-monica.ca.us yeah; monssieur Devlin uses his **** -- and he's also a verb! ========================================================================= Date: Thu, 16 Jul 1998 12:22:41 -0700 Reply-To: List for the discussion of Buckminster Fuller's works Sender: List for the discussion of Buckminster Fuller's works From: Brian Hutchings Subject: manifold destiny <> Brian Hutchings 16-JUL-1998 12:22 r001806@pen2.ci.santa-monica.ca.us hey, BC; could you explain what was meant of the Whitney theorem -- are these "up to" 5D manifolds, in some nD space, or 2D ones in 5D space, or What? thus quoth: the Whitney embedding theorem guarantees a closed manifold, up to 5 dimensions?... wow, cool. as for your equations, your second "3D" one is the "twisted cylinder", which jibes with your dyscription! (it's a favorite "semi-ruled" surface o'mine, for reasons which are unclear .-) thus quoth: (sin u, cos u, sin v, cos v) is a flat plane rolled into a torus without stretching in 4D. In 3D, you can't bring the ends of a cylinder together without stretching. (u,v sin u, v cos u) is a suface with negative curvat everywhere, but not constant. It is a spiral staircase surface generated by a line moving like a propeller. Wwhat about rotating a circle around its centre in 4D, for example: ((sin u)(sin v), (sin u)(cos v), (cos u)(sin v), (cos u)(cos v)) which has guu=gvv=1, guv=0, ds^2=du^2+dv^2, g=16(sin u)(cos u)(sin v)(cos or perhaps some other subset of the hypersphere? -- see "The End of History" chapter in the book on the Imperial President: http://www.tarpley.net ========================================================================= Date: Thu, 16 Jul 1998 11:50:53 -0400 Reply-To: List for the discussion of Buckminster Fuller's works Sender: List for the discussion of Buckminster Fuller's works From: Mike Markowski Organization: University of Delaware, Newark Subject: Re: Calculus 102: A Humanistic Approach to Primitive Concepts In article <6oka1e$jlb$1@nnrp1.dejanews.com>, Robin Chapman wrote: > >Can anyone understand this sentence? Yes. Your English is quite good. ;-) ========================================================================= Date: Thu, 16 Jul 1998 19:33:18 GMT Reply-To: List for the discussion of Buckminster Fuller's works Sender: List for the discussion of Buckminster Fuller's works From: pianoman@RADIX.NET Organization: RadixNet Internet Services Subject: Re: Calculus 102: A Humanistic Approach to Primitive Concepts Mime-Version: 1.0 Content-Type: text/plain; charset=us-ascii Content-Transfer-Encoding: 7bit >In other words, " To teach math to people who don't have skills using >simple symbols, use a lot of words and pictures instead." > >Duh-uh. > >If this is the kind of speach used in teaching youngsters these days, no >*wonder* no one can learn abstract reasoning. > >-- >Lawrence R. Mead Ph.D. (Lawrence.Mead@usm.edu) Agreed...Too much educational theory crap, not enough real work for the students... Dumb 'em down,down, and down again. Art ICQ#12900167 Remember, there are three kinds of mathematicians: Those who can count...and those who can't. ========================================================================= Date: Fri, 17 Jul 1998 00:28:23 -0600 Reply-To: List for the discussion of Buckminster Fuller's works Sender: List for the discussion of Buckminster Fuller's works From: "Lawrence E. Couey" Organization: FX Informationing Subject: Re: TinkerDomes Comments: To: Chuck Knight MIME-Version: 1.0 Content-Type: text/plain; charset=us-ascii Content-Transfer-Encoding: 7bit Chuck Knight wrote: > ...But, are your connectors rigid or flexible? Our design is > flexible... Currently my connectors are rigid, but current design can be fairly easily done in a more flexible material. > > > What would people be willing to pay for a Geodesic Connector Extension > > set? > > I have no idea. I don't even know what Tinkertoys cost... > I picked mine up at a thrift store for $.29! Hmmmm. I can't beat that, used Tinkertoys here run a couple of dollars (if they can be found!). I haven't figured out what my full costs are going to be. I'm talking to a friend who has a business that manufactures "crafts" stuff to see what he could manufacture the connectors for, in quantity. If you and everyone else could let me know what you are willing to "fork-over" for a set of connectors, or connectors and rods, then I'd know what my potential profit margin could be (maybe ;-). Lawrence C. -- --------------------------------------------- Lawrence E. Couey - Convivial Applied Theoretical Technologies/ FX Informationing - mailto:LECouey@INet-1.com --------------------------------------------- ========================================================================= Date: Fri, 17 Jul 1998 09:39:04 -0700 Reply-To: List for the discussion of Buckminster Fuller's works Sender: List for the discussion of Buckminster Fuller's works From: "P. O. Box 2321" Subject: Re: TinkerDomes In-Reply-To: <35AEEF07.CD91B8F6@inet-1.com> MIME-Version: 1.0 Content-Type: TEXT/PLAIN; charset=US-ASCII Tinker Toy connectors for geodesic structures are possible but perhaps not the most efficient use of materials. The slotted sticks need only a hole drilled through the center, or perhaps just a notch, and with some string or wire could be used for 'tensegrity' models. 'Bucky' by Hugh Kenner has some fine, simple 'tensegrity' instructions. 'Tensegrity' is Buckminster Fuller's term for Ken Snelson's sculptures and his imitations of them; Snelson called his work 'floating compression.' The form was discovered and developed by Snelson. It was later used by Fuller, largely without crediting Snelson. I saw what I believe was a Snelson sculpture in Buffalo, NY recently, and have seen another in Washington DC. One difference between Fuller's 'tensegrity' structures and Snelson's 'floating compression' sculptures is that Fuller proposed the possibility of objects that have not come into existence yet (aside from models), while Snelson has made works that exist (as finished pieces). See: http://www.teleport.com/~pdx4d/snelson.html -- _________________________________________ | | | | | | | | | | (, | /\ | |] | (, | [- | |- | |- | <> | | Gg | Aa | Dd | Gg | Ee | Tt | Tt | Oo | ----------------------------------------- http://www.teleport.com/~box2321/go.html ========================================================================= Date: Fri, 17 Jul 1998 12:44:39 EDT Reply-To: List for the discussion of Buckminster Fuller's works Sender: List for the discussion of Buckminster Fuller's works From: Zac Elston Subject: Re: TinkerDomes Mime-Version: 1.0 Content-type: text/plain; charset=US-ASCII Content-transfer-encoding: 7bit In a message dated 98-07-17 12:39:33 EDT, you write: > Tinker Toy connectors for geodesic structures are possible but perhaps not > the most efficient use of materials. The slotted sticks need only a hole > drilled through the center, or perhaps just a notch, and with some string > or wire could be used for 'tensegrity' models. I think that is going beyond the 4 year old's manipulation or patience level. -zac ========================================================================= Date: Sat, 18 Jul 1998 00:32:15 -0700 Reply-To: List for the discussion of Buckminster Fuller's works Sender: List for the discussion of Buckminster Fuller's works From: Brian Hutchings Subject: Re: TinkerDomes MESSAGE from ="List 17-JUL-1998 23:37 In a message dated 98-07-17 12:39:33 EDT, you write: > Tinker Toy connectors for geodesic structures are possible but perhaps not > the most efficient use of materials. The slotted sticks need only a hole > drilled through the center, or perhaps just a notch, and with some string > or wire could be used for 'tensegrity' models. I think that is going beyond the 4 year old's manipulation or patience level. -zac - - - - - <> Brian Hutchings 18-JUL-1998 0:32 r001806@pen2.ci.santa-monica.ca.us yeah, right; what's that new PBS kiddy show, Tubbies? ========================================================================= Date: Sat, 18 Jul 1998 00:37:16 -0700 Reply-To: List for the discussion of Buckminster Fuller's works Sender: List for the discussion of Buckminster Fuller's works From: Brian Hutchings Subject: previous subjectum (?) <> Brian Hutchings 18-JUL-1998 0:37 r001806@pen2.ci.santa-monica.ca.us it's uncharitable, to dyss Bucky's contribution to Snelson's uncovery; true, the essence was "all there" in his "flo-comp", but (as far as I have read, on his own website) it was kinda funky-rectalinear, til Bucky got through with it. ========================================================================= Date: Sat, 18 Jul 1998 18:21:50 -0700 Reply-To: List for the discussion of Buckminster Fuller's works Sender: List for the discussion of Buckminster Fuller's works From: Daniel Giaimo Organization: Netcom Subject: Re: Calculus 102: A Humanistic Approach to Primitive Concepts Kirby Urner wrote in message <35acc494.122647960@news.teleport.com>... >conover@tiac.net (Harry H Conover) wrote: > >>While I share your pain, there is a plurality of kinder and >>more understanding psycobabble groups on the net, many members >>of which would joyously swab your forehead with conductive >>electrolytes jelly, and apply both electrodes and 120 volts >>of alternating current electricit until you comprend the basic >>truth of (and acknowledge the wisdom of) their agenda. >> > >Sounds a lot like sci.math. > >>Then too, there is the possiblity that, while verbose, you >>may be stupid, in which case (you not presenting a significant >>threat) everyone will ignore you. >> >> Harry C. > >Did even bother to explore the website before jumping on the >backlash bandwagon? What website? >-- if so, then clear evidence that in >your case more humanities training is indicated. I happen to believe there is already way too much humanities training in most colleges, and the math and physics is already so dumbed-down that an average student with a moderate amount of perseverance, (a trait all too many students lack), can get an A+ with little work. > >I back up my 'film metaphor' with coded methods for 'camera' >and 'projector' objects (linked essay). Humanistic Math is >not something I invented. Working a matrix or applying >Stoke's Theorem is not something I eschew. > >This is just another layer or angle for my multicultural >LAAP youth who lack intuitive "in yer bones" understanding >of what the calculus is all about No one has said that "multicultural youth", as you put it, are incapable of learning mathematics except you. _No one_, regardless of ethnicity, has an intuitive "in yer bones" understanding of mathematics. As Von Neumann once said, "In mathematics, you don't understand things. You just get used to them." Mathematics doesn't need more humanistic baby-talk to make it more understandable. It needs more disciplined students who are ready to not understand things, and to work through that lack of understanding through perseverance and hard work. It also needs more math professors to demand that kind of level of work by not grading on these ridiculous curves where a 70 can get you an A+. >(film metaphor not just >mine either -- Keith Devlin uses is my info, though I haven't >seen his CDROM). We'll get to div and curl too, just with >some different steps in between (still doing work). > >I've already gotten a rave review for my essay from Gene Fowler, >('Waking the Poet'), so I figure the audience I most want to >reach is being well-served. You mean people who know nothing about mathematics nor care to learn? > >Your knee-jerk ad hominem attacks just expose you for a sloppy >thinker in severe need of better education (to respond in kind). And your ridiculous humanistic ideas just expose you as a non-thinker. > >Kirby >Curriculum writer We also need fewer humanist curriculum writers. >4D Solutions > >--------------------------------------------------------- >Kirby T. Urner http://www.teleport.com/~pdx4d/kirby.html >4D Solutions http://www.teleport.com/~pdx4d/ [PGP OK] >--------------------------------------------------------- -- --Daniel Giaimo Remove nospam. from my address to e-mail me. | rgiaimo@(nospam.)ix.netcom.com ^^^^^^^^^<-(Remove) ------------------------------------------------------------------------------- - "In a race between a rock and a pig, don't varnish your clams." --A Wise Elbonian ========================================================================= Date: Sun, 19 Jul 1998 00:49:51 -0500 Reply-To: List for the discussion of Buckminster Fuller's works Sender: List for the discussion of Buckminster Fuller's works From: anthony kalenak Subject: Re: TinkerDomes Content-Type: Text/Plain; Charset=US-ASCII Content-Transfer-Encoding: 7Bit MIME-Version: 1.0 (WebTV) I think this is a worthy pursuit, however I see a functional difficulty with the "tinkertoy" as a basis for geodesic modelimg. Geodesigc domes are continous tension structures. As I remember my set of tinketoys (30+ years ago), the connections have minimum resistance to tension. All my dome modeling and construction experience suggests to me that domes with tinkertoy type vertices are basically going to pull themselves apart. You are going to have to find a way to transfer tension thru the vertices yet allow kids (and kids at heart) to assemble and break them down easily. -Tony. ========================================================================= Date: Sun, 19 Jul 1998 01:16:57 -0600 Reply-To: List for the discussion of Buckminster Fuller's works Sender: List for the discussion of Buckminster Fuller's works From: "Lawrence E. Couey" Organization: FX Informationing Subject: Re: TinkerDomes MIME-Version: 1.0 Content-Type: text/plain; charset=us-ascii Content-Transfer-Encoding: 7bit anthony kalenak wrote: > > I think this is a worthy pursuit, however I see a functional > difficulty with the "tinkertoy" as a basis for geodesic > modelimg. My feeling (which is mine alone) is that for "Playing", "Tinkering", and just plain simple modeling, Tinkertoy type systems work okay. They're not the "finial say" in modeling, but are a stepping stone. One can quickly check out both a structural concept and an aesthetic concept. > Geodesigc domes are continous tension structures. As I > remember my set of tinketoys (30+ years ago), the > connections have minimum resistance to tension. All my > dome modeling and construction experience suggests to > me that domes with tinkertoy type vertices are basically > going to pull themselves apart. For me, the "minimum resistance to tension" is actually a plus at the stage I start my modeling from. (Sometimes I actually start my models from paper using Unit Origami techniques ;-) > You are going to have to find a way to transfer tension > thru the vertices yet allow kids (and kids at heart) to > assemble and break them down easily. I think what is needed is several systems that provide differing levels of... hhmmmm... tension-compression connections. A system like Tinkertoys that just slides together easily, a more advanced system having a "snap-together, snap-apart" which provides more tension-compression. Then the next level of tension-compression connectors would be something link Erector Sets. And so on, upto and including multiple Real Systems for putting together the Real Things. Not a tall order. Probably its something very simple. Once someone sees how its done. (Just wish I could see what it was... I get frustrated by with what I've got to work with now ). Lawrence C. -- --------------------------------------------- Lawrence E. Couey - Convivial Applied Theoretical Technologies/ FX Informationing - mailto:LECouey@INet-1.com --------------------------------------------- ========================================================================= Date: Sun, 19 Jul 1998 06:30:05 GMT Reply-To: List for the discussion of Buckminster Fuller's works Sender: List for the discussion of Buckminster Fuller's works From: Paul Strong Organization: University of Guelph Subject: Re: Calculus 102: A Humanistic Approach to Primitive Concepts Daniel Giaimo (rgiaimo@nospam.ix.netcom.com) wrote: : I happen to believe there is already way too much humanities training in : most colleges, and the math and physics is already so dumbed-down that an : average student with a moderate amount of perseverance, (a trait all too many : students lack), can get an A+ with little work. : No one has said that "multicultural youth", as you put it, are incapable of : learning mathematics except you. _No one_, regardless of ethnicity, has an : intuitive "in yer bones" understanding of mathematics. As Von Neumann once : said, "In mathematics, you don't understand things. You just get used to them." : Mathematics doesn't need more humanistic baby-talk to make it more : understandable. It needs more disciplined students who are ready to not : understand things, and to work through that lack of understanding through : perseverance and hard work. It also needs more math professors to demand that : kind of level of work by not grading on these ridiculous curves where a 70 can : get you an A+. What you wail about in academic math circles is precisely what those of us who teach humanties wail about. That is to say: there is way too much watered down pseudo-intellectual bullshit in humanties departments, just as there is too much watered down, curve-graded, mark-inflated bullshit going on in mathematics. Which is to say: there's a whole lotta crap going down in academe, confined to no particular department, and everyone would be a lot better off if all these disparate intellectual regions got their shit together. But it's not going to happen. Paul ========================================================================= Date: Sun, 19 Jul 1998 13:36:39 -0700 Reply-To: List for the discussion of Buckminster Fuller's works Sender: List for the discussion of Buckminster Fuller's works From: Brian Hutchings Subject: calculus? <> Brian Hutchings 19-JUL-1998 13:36 r001806@pen2.ci.santa-monica.ca.us it's quite amusing, Dan'l, that you'd insist, upon the wretchedly reductionist work of von Neumann as your factotum, as a caliber for grading in coursework, in spite of the near-hegemonic use of such things as Game Theory, in the depatrments o'math!... as you say, "comprehension sucketh" -- the true mark of an irrationalist or "positivist" !! thus quoth: said, "In mathematics, you don't understand things. You just get used to them." Mathematics doesn't need more humanistic baby-talk to make it more understandable. It needs more disciplined students who are ready to not understand things, and to work through that lack of understanding through perseverance and hard work. It also needs more math professors to demand th -- see "The End of History" chapter on Fukiyama's Imperial President: http://www.tarpley.net ========================================================================= Date: Sun, 19 Jul 1998 07:33:20 -0600 Reply-To: List for the discussion of Buckminster Fuller's works Sender: List for the discussion of Buckminster Fuller's works From: "John T. Lowry" Organization: Montana Communications Network Subject: Re: Calculus 102: A Humanistic Approach to Primitive Concepts Dear Paul S. and All: Amen! Yesterday I responded to a fellow who asked me about which academic departments are best for "flight physics." I responded, in part, "By and large, IMO, education has sunk to the level of a commodity business...I fairly disdainful...." Sad but true. John. John T. Lowry, PhD Flight Physics; Box 20919; Billings MT 59104 Voice: 406-248-2606 Paul Strong wrote in message <6os3pd$n8l$2@testinfo.uoguelph.ca>... >Daniel Giaimo (rgiaimo@nospam.ix.netcom.com) wrote: > >: I happen to believe there is already way too much humanities training in >: most colleges, and the math and physics is already so dumbed-down that an >: average student with a moderate amount of perseverance, (a trait all too many >: students lack), can get an A+ with little work. > > > >: No one has said that "multicultural youth", as you put it, are incapable of >: learning mathematics except you. _No one_, regardless of ethnicity, has an >: intuitive "in yer bones" understanding of mathematics. As Von Neumann once >: said, "In mathematics, you don't understand things. You just get used to them." >: Mathematics doesn't need more humanistic baby-talk to make it more >: understandable. It needs more disciplined students who are ready to not >: understand things, and to work through that lack of understanding through >: perseverance and hard work. It also needs more math professors to demand that >: kind of level of work by not grading on these ridiculous curves where a 70 can >: get you an A+. > >What you wail about in academic math circles is precisely what those of >us who teach humanties wail about. That is to say: there is way too much >watered down pseudo-intellectual bullshit in humanties departments, just >as there is too much watered down, curve-graded, mark-inflated bullshit >going on in mathematics. > >Which is to say: there's a whole lotta crap going down in academe, >confined to no particular department, and everyone would be a lot better >off if all these disparate intellectual regions got their shit together. >But it's not going to happen. > >Paul ========================================================================= Date: Mon, 20 Jul 1998 04:17:40 -0400 Reply-To: List for the discussion of Buckminster Fuller's works Sender: List for the discussion of Buckminster Fuller's works From: "3104702913@iname.com" <3104702913@INAME.COM> Subject: HERE IS THE PAGE YOU WERE ASKING ME FOR Hi Jamie here is the page you were looking for http://www.vivaerotica.com/jamie-abbasi/ call me if you had any question: Nazi 310-470-2913 - -------------------- 3104702913@iname.com sent you this message using WorldMerge, the fastest and easiest way to send personalized email messages to your customers, subscribers, leads or friends. For more information, visit http://www.coloradosoft.com 792214 ========================================================================= Date: Mon, 20 Jul 1998 08:16:00 GMT Reply-To: List for the discussion of Buckminster Fuller's works Sender: List for the discussion of Buckminster Fuller's works From: Kirby Urner Organization: 4D Solutions Subject: Re: Calculus 102: A Humanistic Approach to Primitive Concepts MIME-Version: 1.0 Content-Type: text/plain; charset=us-ascii Content-Transfer-Encoding: 7bit "John Shonder" wrote: > >Kirby Urner wrote in message <35acc494.122647960@news.teleport.com>... > >*snip* > >>This is just another layer or angle for my multicultural >>LAAP youth who lack intuitive "in yer bones" understanding >>of what the calculus is all about <> > >Are you saying students from Latin American and Asian-Pacific countries lack >the ability to learn calculus the traditional way? No. I'm saying this is just another layer or angle. The cultural makeup of my target audience is incidental. Kirby --------------------------------------------------------- Kirby T. Urner http://www.teleport.com/~pdx4d/kirby.html 4D Solutions http://www.teleport.com/~pdx4d/ [PGP OK] --------------------------------------------------------- ========================================================================= Date: Mon, 20 Jul 1998 08:17:33 GMT Reply-To: List for the discussion of Buckminster Fuller's works Sender: List for the discussion of Buckminster Fuller's works From: Kirby Urner Organization: 4D Solutions Subject: Re: Calculus 102: A Humanistic Approach to Primitive Concepts MIME-Version: 1.0 Content-Type: text/plain; charset=us-ascii Content-Transfer-Encoding: 7bit conover@tiac.net (Harry H Conover) wrote: >: Did even bother to explore the website before jumping on the >: backlash bandwagon? -- if so, then clear evidence that in >: your case more humanities training is indicated. > >Turning that around, there is clear evidence that in your >case more computer science training is indicated. This is >a Usenet netsgroup, which I read using a Unix newsreader >named tin running under a Unix shell account on my ISP.... I think "no" was the answer you were looking for. No need for the lecture re your UNIX newsreader blah blah. But if you need to justify, go right ahead. Kirby --------------------------------------------------------- Kirby T. Urner http://www.teleport.com/~pdx4d/kirby.html 4D Solutions http://www.teleport.com/~pdx4d/ [PGP OK] --------------------------------------------------------- ========================================================================= Date: Mon, 20 Jul 1998 08:46:22 GMT Reply-To: List for the discussion of Buckminster Fuller's works Sender: List for the discussion of Buckminster Fuller's works From: Kirby Urner Organization: 4D Solutions Subject: Re: Calculus 102: A Humanistic Approach to Primitive Concepts MIME-Version: 1.0 Content-Type: text/plain; charset=us-ascii Content-Transfer-Encoding: 7bit lrmead@orca.st.usm.edu (Larry Mead) wrote: >In other words, " To teach math to people who don't have skills using >simple symbols, use a lot of words and pictures instead." > You must have a clear idea of "simple symbol" versus "word" or "picture". To me, it's all ASCII, or Unicode. Lots of so-called "simple symbols" are just Greek letters, with time-honored traditions of using this one for that, this other one for something else. Just conventions, of the humanities type. No "mathematical" reason we use Greek symbols at all -- so kids deserve an historical overview, and then some cultural reinforcement around those geeky greek letters we intend to keep using (e.g. DELTA). >Duh-uh. > In your case, maybe stick to "simple symbols"... Kirby --------------------------------------------------------- Kirby T. Urner http://www.teleport.com/~pdx4d/kirby.html 4D Solutions http://www.teleport.com/~pdx4d/ [PGP OK] --------------------------------------------------------- ========================================================================= Date: Mon, 20 Jul 1998 08:20:47 GMT Reply-To: List for the discussion of Buckminster Fuller's works Sender: List for the discussion of Buckminster Fuller's works From: Kirby Urner Organization: 4D Solutions Subject: Re: Calculus 102: A Humanistic Approach to Primitive Concepts MIME-Version: 1.0 Content-Type: text/plain; charset=us-ascii Content-Transfer-Encoding: 7bit Robin Chapman wrote: >Can anyone understand this sentence? > I should explain Chapman's special discipline which is to not read my posts directly, but to circle vulture-like and swoop down on reponses to my posts. This is because he's a busy guy I think -- I forget. No, because I'm pretentious -- whatever. Maybe he's changed his practice by now anyway. Pretty quirky if you ask me. Kirby --------------------------------------------------------- Kirby T. Urner http://www.teleport.com/~pdx4d/kirby.html 4D Solutions http://www.teleport.com/~pdx4d/ [PGP OK] --------------------------------------------------------- ========================================================================= Date: Mon, 20 Jul 1998 08:41:50 GMT Reply-To: List for the discussion of Buckminster Fuller's works Sender: List for the discussion of Buckminster Fuller's works From: Kirby Urner Organization: 4D Solutions Subject: Re: Calculus 102: A Humanistic Approach to Primitive Concepts MIME-Version: 1.0 Content-Type: text/plain; charset=us-ascii Content-Transfer-Encoding: 7bit "Daniel Giaimo" wrote: > What website? > http://www.inetarena.com/~pdx4d/ocn/calculus2.html http://www.inetarena.com/~pdx4d/ocn/ mentioned in my opening (topic level) post... > > No one has said that "multicultural youth", as you put it, are incapable of >learning mathematics except you. I didn't say it either. "Multicultural" might include any mixed bag, Einstein and Gauss just more colored marbles. I apologize for making it sound like I was stooping down to talk to stoopid people -- not it at all. This is for kids ready to have more advanced comprehension of the "change" phenomenon (hyperlinks to relativity, good site on electronmagnetics, information theory etc.). >_No one_, regardless of ethnicity, has an intuitive "in yer bones" >understanding of mathematics. As Von Neumann once said, "In mathematics, >you don't understand things. You just get used to them." That's one school of thought. Mathematics is vast and some aspects feed the intuition more directly than others. I think my essay gives some handles kids might not have grasped previously, nor does my humanistic approach interfere with symbolic manipulation or formal proof presentations. I studied Calculus using Spivak (text) under Thurston at Princeton. In high school, my calculus teachers were Filipina (because I went to high school in the Philippines) and were excellent. >Mathematics doesn't need more humanistic baby-talk to make it more >understandable. This wasn't baby talk (I know, I know, the "choo choo" stuff grates -- chalk it up to the Doppler Effect (sounds deeper after it goes by)). >It needs more disciplined students who are ready to not >understand things, and to work through that lack of understanding through >perseverance and hard work. It also needs more math professors to demand that >kind of level of work by not grading on these ridiculous curves where a 70 can >get you an A+. > Part of my point re the LAAP youth is this is a volunteer afterschool program with no grade pressure. Also, this is all just brainstorming with an eye towards developing multimedia and other more sophisticated presentations. Mostly I'm writing for other math trainers working with kids outside the usual channels. >>I've already gotten a rave review for my essay from Gene Fowler, >>('Waking the Poet'), so I figure the audience I most want to >>reach is being well-served. > > You mean people who know nothing about mathematics nor care to learn? > Gene is a great programmer, writing his own XML editor these days. Has fed me quite a few geometry ideas. No slouch. Learns what he needs for the job at hand. Your prejudice is showing. > And your ridiculous humanistic ideas just expose you as a non-thinker. > Well, that's your opinion. I think my reinforcement of the frequency vs. amplitude modulation variables in relation to energy transfer (power = energy/time) were useful, and not everyone studies ancient Greek anymore, so emphasizing DELTA as a signifier for CHANGE is something no one should just assume -- need to wire up the associations (hypertext/humanities is all about doing that). The SIGMA -> Riemann Sum as a "smoothing" (as DELTA X approaches dx) is certainly not original with me, nor the connecting of DELTA x to "frame of film" (snapshot), i.e. differentiation as a process of capturing changes, integration as a running total "projection" of said changes. By using "action" (in the sense of film capturing) we're immediately in a multivariable context, seeing how lots of ratios (slopes) between variables might be "rule governed" -- expressed in terms of time, or in terms of other variables. I really don't think my point is controversial: we need a better, more culturally attuned, more savvy patter around the crypto-compressed symbolisms, to reconnect the symbols to the intuitions. I think mathematicians _do_ have a lot of intuitive feel for their subject in many cases, Von Neumann's quote notwithstanding. Courses in the calculus which leave kids bereft of an intuitive grasp, all symbolic manipulation abilities aside, have not done as complete a job of providing relevant insights as I think we might. What I'm offering is not a substitute but a supplement, and I think is indicative of how we in the humanities plan to NOT leave math teaching to the mathematicians entirely (and many good mathematicians are happy to see this awakening of peers on the other side of the C.P. Snow chasm -- in philosophy departments for example). Kirby --------------------------------------------------------- Kirby T. Urner http://www.teleport.com/~pdx4d/kirby.html 4D Solutions http://www.teleport.com/~pdx4d/ [PGP OK] --------------------------------------------------------- ========================================================================= Date: Mon, 20 Jul 1998 10:47:10 EDT Reply-To: List for the discussion of Buckminster Fuller's works Sender: List for the discussion of Buckminster Fuller's works From: Zac Elston Subject: Re: Calculus 102: A Humanistic Approach to Primitive Concepts Mime-Version: 1.0 Content-type: text/plain; charset=US-ASCII Content-transfer-encoding: 7bit In a message dated 98-07-20 08:31:54 EDT, you write: > > And your ridiculous humanistic ideas just expose you as a non-thinker. wow.. I'm so glad I dropped out of Aerospace to contemplate Sociology. The only forum I found that accepted new ideas and avenues of thinking was Humanities. In fact most of my problems in college was with CS and engineering professors who refused to look at anything that wasn't outlined in their text book. I quote from one CS professor "we will only be using PCs because I don't like Macs.....I don't like them because I don't understand them" Strange how I, the lonely hacker, was the only person in my class to get snatched up by a major corporation 2 years before I graduated. All my other engineering friends were still looking for a job a year after they graduated. Yes, my anecdote doesn't prove anything...but it sure influenced my life. If math is something to be used, not understood, then how will people ever learn about new ideas in math without examples or teachers willing to learn and show their students these new ideas? how can we ever break out of the mold? pretty limiting to me. I know I don't understand the math, but telling me I never will certainly wont inspire me to explore math either. Quoth Barbie " Math is hard" -zac ========================================================================= Date: Mon, 20 Jul 1998 12:24:38 GMT Reply-To: List for the discussion of Buckminster Fuller's works Sender: List for the discussion of Buckminster Fuller's works From: Larry Mead Organization: University of Southern Mississippi Subject: Re: Calculus 102: A Humanistic Approach to Primitive Concepts Kirby Urner (pdx4d@teleport.com) wrote: : lrmead@orca.st.usm.edu (Larry Mead) wrote: : >In other words, " To teach math to people who don't have skills using : >simple symbols, use a lot of words and pictures instead." : > : You must have a clear idea of "simple symbol" versus "word" or "picture". Of course - you don't? Mathematics is the only precise tool for handling information known to humankind. It behooves every intelligent person to learn to use this tool. Mathematics - symbol use - is learned by disciplined reasoning over time, rarely by flashes of color on a screen or by flowery speech. : To me, it's all ASCII, or Unicode. Lots of so-called "simple symbols" : are just Greek letters, with time-honored traditions of using this one There is nothing special about Greek letters that is different from English characters or any other. They each stand for a set of very precise words with *meaning* (often physical meaning). If you learn to understand the meaning, then you understand the symbol. Since, in fact, algebraic symbols just do stand for a string of words, how can you *not* learn to use algebra if your facility with words also is good? : for that, this other one for something else. Just conventions, of the : humanities type. Ah, that is the rub - the conventions are *not* of the humanities type. For example, in physics, the definitions of symbols are *operational* definitions (ie., the preciseness of which I spoke of above). : -- so kids deserve an historical overview, and then some cultural : reinforcement around those geeky greek letters we intend to keep using : (e.g. DELTA). And really good teachers will also *give* some history of the subject and the persons who created it. That also makes the subject come alive. At the college level for example, the Ph.D. means doctor of *philosophy* : meaning the history and development of one's subject and not just its technical aspects. Nevertheless, it does not help with the technical aspects of the subject which requires a necessary amount of concentrated thought in the silence of one's own room. [snide remark snipped] : Kirby -- Lawrence R. Mead Ph.D. (Lawrence.Mead@usm.edu) Eschew Obfuscation! Espouse Elucidation! www-dept.usm.edu/~physics/mead.html ========================================================================= Date: Mon, 20 Jul 1998 13:19:04 -0600 Reply-To: List for the discussion of Buckminster Fuller's works Sender: List for the discussion of Buckminster Fuller's works From: "Ken G. Brown" Subject: SOME DESIGN CONSIDERATIONS FOR GEODESIC SPHERICAL-DOME MINIMAL COST HOUSING Comments: To: GEODESIC@UBVM.cc.buffalo.edu Mime-Version: 1.0 Content-Type: text/plain; charset="iso-8859-1" Content-Transfer-Encoding: quoted-printable A paper written somewhere around 1971, transcribed by Ken G. Brown with permission from J.C. Bohlen, 980719. --------------------------------------------------------------- SOME DESIGN CONSIDERATIONS FOR GEODESIC SPHERICAL-DOME MINIMAL COST HOUSING J.C. Bohlen Research Scientist Department of the Environment Western Forest Products Laboratory Vancouver, B.C., Canada Abstract A concept of minimal-cost housing is presented which involves the use of geodesic spherical-domes fabricated and assembled with self-help labour. A unique low-cost wood-dowelled joint is used to connect the structural elements. An insulated wood shell and platform for a 16-foot diameter dome, arranged into a cluster of 5 assembled domes cost one-half of a conventional wood-frame house of equal floor space. Self-help labour further reduces the total cost to less than one-third. Introduction The conventionally built wood-frame house (5) is not within the economic reach of 20% of the Canadian people who are living below the official poverty line (2). It is hoped that this paper will suggest a practical minimal-cost structural alternative to current modes of wood-frame construction, with special attention to the Canadian climate. This suggests that structures for human habitation should be equipped with thermal insulation (4). Most of the population lives in an area where the annual total of degree-days for heating lies between 6,000 and 12,000. Thermal insulation also provides fuel savings which leads to lower operating costs and energy conservation. Optimum insulation values have been derived (1) which considers cost of insulation and cost of fuel. Provision is to be afforded within the structure to accommodate additional insulation for the more severe climatic regions with heating requirements for up to 23,000 degree-days. According to a United Nations study (9), by applying the principles of self-help to a house design, approximately 1/2 of the house cost may be saved. In Canada, knowledge of the use of simple wood-working tools is common throughout a wide range of the population. When directed towards housing, especially self-help housing, a wood structure is comparatively easy to alter in size or add to as the need arises, with a minimum of cost and work. A properly designed and constructed wood-frame house has a service life exceeding the life-span of it's owners. Thus, if self-help wood-frame construction is envisaged, the design should be directed towards attaining structural integrity with simplicity of construction. Any further cost reductions will be derived from material costs. This paper will deal only with structural frame considerations, thermal insulation, sheathing, cladding, and the platform upon which the structure is mounted. In 1965-1966, the National Research Council, Division of Building Research, undertook an experiment which was calculated to reduce the cost of materials in a conventionally designed wood-frame house (7). Since the study included a cost comparison with a "standard" wood-frame tract house built in Canada, it will be used as a basis for cost comparisons in this paper. An analysis of the detailed cost breakdown of the experimental house indicated less than 5% potential savings in material cost for the structural framework and platform. It was therefore decided in the present work to abandon conventional wood-frame design. Design of the Spherical Dome In 1954, R.B. Fuller obtained a patent (6) in the United States, which described among other things "..... A building framework of generally spherical form in which the main structural elements form a substantially uniform over-all pattern of great circle arcs intersecting in a three-way grid." Since that time many such geodesic domes have been built and the design has be proved both for ease of erection and structural strength. Many attempts have been made to employ geodesic principles to mass housing. Aside from lack of acceptance by tradition orientated prospective buyers, a major problem has been, and remains, in how to inexpensively weatherproof the outside of the structure. Large, internally sub-divided domes were ruled out as they require scaffolding to erect them. The problem of weatherproofing also mitigated against large domes as the radius is so great that a substantial portion of the top of the dome is essentially horizontal. The optimization of the dome size problem then resolved into providing the maximum usable floor area with the smallest dome diameter, at the minimum cost for materials. =46rom an architectural and space utilization point of view, small domes possess advantages over large domes: 1. Since each dome is a self-contained structural unit, a nucleus of enclosed space may be created to which other enclosed spaces may be added or deleted as required. 2. Small units may be assembled into a cluster of domes to form a larger structure, connected with passage ways or joined, affording the privacy of separate rooms. (Fig. 1) Geodesic domes evolve from various polyhedra, the edges of which are projected onto their circumscribing sphere, in such a way that the resulting projections lie approximately on great circle arcs (8). The edge projections are subdivided into linear elements which are chosen to yield a minimum number of different sized components, The degree of subdivision is selected to fulfill design requirements, which are usually architectural rather than structural. This dome is intended to utilize conventional building materials. Therefore, the geodesic structural elements were sized to accommodate them. Panel products such as plywood, insulating materials, etc. are most commonly available as modules of 48-inches. Therefore it is desirable to arrange the structural elements of the geodesic framework to use the optimum amount of material from a standard panel with the least amount of waste. The Icosahedron (a 20-sided polyhedron) does not divide properly to allow for maximum usable floor space unless a great number of odd-length structural elements are fabricated. This was not desirable in view of the simplicity required for the self-help principle. The Dodecahedron (a 12-sided polyhedron) presents the simplest solution, although the theoretical development is rather complex. This will be dealt with in another paper at some later date. Four different length members in varying quantities comprise the entire structural frame of a dodecahedron based dome design. Structural elements in a geodesic dome depend upon being interconnected for stability. When one member is taken from the network of structural elements, its removable introduces six degrees of translational freedom, thus incurring the need for additional structural material and labour for bracing. However, some of the elements have to be removed in order to afford physical access to the inside of the dome. The dodecahedron, once again yields locations of structural elements which afford access to the interior with minimum disturbance of the original configuration, (Fig. 2). A plane passed through the mid-point of a sphere results in minimum disruption of the elements. However this is not a satisfactory solution for maximum utilization of floor space, especially in small domes, where the small radius rapidly causes the dome surface to intrude upon the stand-up room. Fortunately, the dodecahedron geodesics permit the polyhedron to be conveniently pierced with a plane approximately at the six-tenths sphere diameter location. This allows the radius of curvature to reverse itself slightly, creating the head room which allows a person to stand much closer to the wall on only a slightly reduced total floor area. In consideration of the advantages of the dodecahedron geodesic element breakdown, it remains for a selection of a spherical-dome diameter to satisfy the design requirement. To minimize cutting waste from standard 4 x 8-foot panel products it was found that a nominal 16-foot diameter provided an optimum dome size. This proved to be adequate for architectural considerations as the floor area resulted in approximately 200 square feet, almost all of it accessible for a 6-foot person to stand erect. Floor area also satisfies minimum spatial requirements as outlined in the National Building Code of Canada. Design of Structural Elements Theoretically, 1 x 1-inch nominal spruce lumber could support the design live snow load of 30 psf. However, there are other considerations which make it desirable instead to use 2 x 4-inch sawn lumber. The longest piece of lumber required for the structural elements is 28-inches. These short lengths are available at very low prices. Further, 1 x 1 frame is too weak to stand on while the dome is being assembled, and it has insufficient depth upon which to apply permanent covering materials and insufficient thermal insulation. The larger elements withstand rougher handling during assembly and, most importantly, enable a simpler connector to be designed. Design of Structural Element Connections Previous experience with construction of geodesic domes (3), indicated a need for precise fabrication of the structural elements and their assembly. All suitable conventional fastening devices would cost more than the whole of the dome structural elements, therefore, a very simple, and economical pegged-strut was developed using no connector other than wooden doweling. (Fig. 3). The connecting hubs are made of 3/4-inch exterior grade plywood. The pegs, or dowels, are made of hardwood. The ends of the 2 x 4's are slotted on an angle to receive the predrilled hubs. The hubs are simply inserted into the sawn slots at the ends of the 2 x 4's and the dowels pushed into place. The holes in both the 2 x 4's and the hubs, are all predrilled to give the necessary precision and structural integrity. The hub and pegged strut system has been tested to failure at five times the design load of 375 pounds per strut. Failure is defined as the test load at which the proportional limit of the strut and peg and hub assembly is reached in simple axial compression. =46oundation Design and Assembly One of the basic reasons for using domes is their light weight and the fact that loads on the shell bear evenly along the whole perimeter of the dome. Consequently, very small design loads are imposed on the floor framing and the foundation. To minimize foundation costs a raised platform supported on posts is recommended. Here, the small dome philosophy of design demonstrates economy. Since the floor spans are short, very light weight joists may be used. To support a 40 psf live load, 2 x 6-inch joists are adequate. Or, if 2 x 4 studs are more commonly available an inverted "T"-beam may be fabricated from them. The joists connect to ten six-inch diameter posts which are buried in the ground. A center-post serves to divide the floor span so that 8-foot joists may be used. All joists are installed radially, like the spokes of a wheel, and intermediate nailing joists are installed on 2-foot centres, which gives the finished floor frame the appearance of a spider-web. (Fig. 4). After the foundation and floor framework have been erected, the bottom of the floor joists may be sheathed with insulating board, by nailing to the bottom of the joists. Where inverted "T"-beams are used, the insulating board is fitted between the radial joists and is supported by the "T"-flanges. The tops of the joists are covered with conventional flooring materials. This floor system may enable the space between the joists to be utilized as a return air plenum for a space-heating system. Prefabrication of Structural Elements The dome frame structural elements consist primarily of struts made from 2 x 4's and hubs made from 3/4-inch thick exterior grade plywood. There are three kinds of hubs, one pentagonal in shape and two hexagonal. The pentagon is coded with a spot of blue color. One hex is coded green, and another red. The four different strut lengths are color coded on each end according to their respective hub connections. Consequently, there will be a blue-green strut, a green-green strut, a green-red strut and a red-red strut. These are connected in a repeating pattern which is schematically shown, (Fig. 5). The smallest strut length is 23-inches, and the largest is 28-inches. Approximately 200 struts and 70 hubs are required to make one dome. After cutting them to length a drill jig is used to assist fabricating the struts. Each dome strut is machined to an identical end-shape regardless of its length. The hubs are cut to size and drilled with a simple marking template. Jig precision is designed to assure the specified dome diameter within a tolerance of =B11/4-inch. Dome Assembly Slots are cut in the subfloor over the 10 perimeter posts. Plywood hubs are dropped into the slots and the 2 x 4 structural members are assembled according to the colour coding which has been pre-applied to them. The dome can be assembled using the partially assembled framework itself as the scaffold. After assembly and alignment of the completed frame, the bottom hubs are securely nailed to the foundation posts. There are, of course, many possible solutions to cladding the dome frame. =46rom a structural point of view, none of the covering materials needs to b= e structural in nature, as the frame itself is completely stable. 3/8-inch sheathing grade plywood, aspenite, or particleboard made with exterior glue may be used, (Fig. 6). Door framing, window surrounds and flashing are applied to seal transition joints. Smoke pipe and vent pipe are installed and flashed. To seal the exterior surface, a layer of waterproof, moisture permeable building paper is applied over the dome surface and the joints sealed with roofers gum. The problem of providing for an outer cladding consists of two basic parts. One, to provide an inexpensive covering which will resist the elements and accommodate expansion, contraction, and movement of moisture. The other is an aesthetic problem, which may be approached from many differing aspects of personal choice. To date, the most suitable cladding material has proven to be shingles, either wood or asphalt, as shown in Figures 7 and 8. Thermal Insulation A design feature of the geodesic dome is that the structural elements form a geometric pattern which is aesthetically pleasing. The pegged-strut hub connection adds to this effect and gives the elements the look of half-timbered construction. It is the intention, therefore, to leave the structural elements exposed, and to "friction-fit" insulating board between them. With this technique it is a very simple matter to provide any amount of insulation required. Insulating boards made of Urethane foams are relatively inexpensive and have a vapour barrier cemented to them which can also serve as the finishing surface. 2-pound per cubic-foot density urethane insulation 1-inch thick will suit the requirement (4) for heating in areas where up to 8000 degree-days are encountered. For up to 12,000 degree-days, 1-1/2-inch of urethane is required. For 23,000 degree-days, 3 inch of insulation may be inserted between the structural elements. Further flexibility of this design is seen from the following example. Where a cluster of domes is used, there can be a variety of insulating patterns developed which depend strictly upon the use of each dome. For instance, in far northern climates it may be desirable to limit living space during the extremely cold months to one or two domes. The insulation from the unoccupied domes may be added by superimposing it over the insulation of the ones which are occupied, thus saving fuel. The enclosed volume of space is one-third less per square foot of living space in the dome than in conventional wood-frame construction. This results in reduced fuel costs. It is significant that the total insulated surface area of the 5 interconnected domes shown in Fig. 1 is approximately the same as the insulated surface area of the conventional wood-frame house of the same floor area (7). Cost Comparisons The costs for a conventional dwelling are those previously referred to (7), comprising a one-level house with a floor area of 1150 square feet and which is subdivided into a kitchen, bathroom, living-dining room, and three bedrooms. The cost comparison encompasses the complete shell of the house including interior partitions, wall coverings, platform materials, and framing; but does not include the foundation, or the sill upon which the platform is mounted. This brings the wood-framed house to the same stage of completion as a clustered assembly of 5 domes, with passage ways and/or joined as shown in Figure 1. The floor area of the 5 domes with platforms is approximately the same as that of the study house (7). The dome foundation posts are not included, nor is the floor insulation. The items considered comprise 28% of the total cost of a conventional wood-frame house, including labour. Thermal insulation in the domes is included for cost analysis as that amount of material being required to satisfy 8000 degree-day heating load, which corresponds to the area where the study house was built. The following Table shows the per square foot costs of the experimental wood-frame house which was built under NRC observation. As previously discussed this experimental house was only 5% less costly than the conventionally constructed house which was also studied (7). A comparison between the material costs of the experimental house and the dome indicates that the dome is 55% less expensive. Wood-Frame House (7) Peg-Strut NRC study (adjusted to Dome Cluster Item 1971 costs ($)per sq. ft.) ($)per sq. ft. Material Labour Material Labour __________________________________________________________________ Platform .44 .04 .20 - House Shell 2.25 1.29 1.00 - __________________________________________________________________ Total cost 2.69 1.33 1.20 - Self-Help Fabrication The structural elements, hubs, sheathing, and insulation may all be fabricated without the aid of any special power tools. Where a number of groups of clustered domes is anticipated, it might pay the community at large to invest in a table saw and a drill press, which are all the machine tools needed. The principles of self-help (9) involves a spread of the technology by having a prospective builder spend some time working with an experienced crew as a trainee, gradually developing the skills needed until the necessary competence is achieved. Summary and Conclusions The concept of minimal-cost housing is based upon the use of spherical domes fabricated and assembled with self-help labour. An insulated wood shell and platform for a 16-foot diameter dome, arranged for connection into a cluster of assembled domes to achieve the degree of floor space desired is presented. The shell and platform material cost is $1.20 per square foot, compared with $2.69 per square foot for a conventional wood-frame house and platform. This saving, coupled with anticipated labour cost savings of $1.33 per square foot will perhaps make feasible the provision of adequate housing space for some of the 20% of Canadians living below the poverty line (2). References 1. Beach, R.K. (1965) NRC-Div. Bldg. Res. Tech. Paper No. 187. Ottawa. 2. Canada Parliament Sen. (1971) Report: Poverty in Canada., Info. Canada. 3. Can. Forestry Svc (1971) Research News, Vol. 14, No. 2. Ottawa. 4. Can. Wood Council (1971) Thermal Insulation Bull. BCI 5.13, Ottawa. 5. Can. Wood Council (1960) Wood Frame Construction for Residential Bldgs. Wood Data Manual No. 1, Ottawa. 6. Fuller, R.B. (1954) U.S. Patent No. 2,682,235 June 1954. Wash. D.C. 7. Hansen, A.T. (1967) A cost study of two wood-frame bungalows. N.R.C. Div. Bldg. Res., Ottawa. 8. Scheel, H. (1969) 'The Canadian Architect', May 1969 pgs. 62-64. 9. UN-Dept. Econ. & Social Affairs (1964) Manual on self-help housing. N.Y. -------------------------------------------------------- =46ig. 1 - Pentagonal dome cluster schematic =46ig. 2 - View of erected structural elements without cladding =46ig. 3 - Close-up of hexagonal hub with struts attached =46ig. 4 - View of floor platform joist web =46ig. 5 - Diagram of strut geometry =46ig. 6 - View of partially erected dome =46ig. 7 - Close view of shingle cladding =46ig. 8 - View of completed dome ========================================================================= Date: Mon, 20 Jul 1998 16:52:24 GMT Reply-To: List for the discussion of Buckminster Fuller's works Sender: List for the discussion of Buckminster Fuller's works From: Kirby Urner Organization: 4D Solutions Subject: Re: Calculus 102: A Humanistic Approach to Primitive Concepts MIME-Version: 1.0 Content-Type: text/plain; charset=us-ascii Content-Transfer-Encoding: 7bit lrmead@orca.st.usm.edu (Larry Mead) wrote: >Kirby Urner (pdx4d@teleport.com) wrote: >: lrmead@orca.st.usm.edu (Larry Mead) wrote: > >: >In other words, " To teach math to people who don't have skills using >: >simple symbols, use a lot of words and pictures instead." >: > > >: You must have a clear idea of "simple symbol" versus "word" or "picture". > >Of course - you don't? Mathematics is the only precise tool for handling >information known to humankind. It behooves every intelligent person to >learn to use this tool. Computers use "words" (variable number of bits, depending on the operating system). "Simple symbol" is somewhat relative as to simplicity -- if Greek isn't a native alphabet for example. >Mathematics - symbol use - is learned by disciplined reasoning over time, >rarely by flashes of color on a screen or by flowery speech. > Visualization is an important tool, given short shrift there for awhile, but making a come back. Flowery speech -- well, it can be overdone I realize, but a more fluid and readable presentation would help phase in the concepts a lot of times. That's what I was attempting in my essay e.g. by showing how Commander Data is able to transmit a lot of energy in a short time via frequency modulation, whereas Whorf is more endowed in the brute force department (amplitude). Helpful to see where math came from at the time, historical context -- often times it was a front lines innovator making the new math (Ada), with academics following along behind indulging in their penchant for formalisms, neatness, and, yes, crypticism (there's this "math mystique" that stems from using all those crypto-compressed symbols which a lot of times is less about communicating content and more to do with putting on airs -- but of course the better mathematicians have less ego-involvement in "looking good" in front of peers, being already confidant in their abilities). >: To me, it's all ASCII, or Unicode. Lots of so-called "simple symbols" >: are just Greek letters, with time-honored traditions of using this one > >There is nothing special about Greek letters that is different from >English characters or any other. They each stand for a set of very precise >words with *meaning* (often physical meaning). If you learn to understand >the meaning, then you understand the symbol. Since, in fact, algebraic >symbols just do stand for a string of words, how can you *not* learn to >use algebra if your facility with words also is good? > Meaning comes across through usage patterns. You can change the meaning of something by using it differently. Metaphorically, we call this "altering the trajectory" of a signifier in semantic space. Mathematicians are always revectoring signifiers in this way: the word "dimension" for example, has not been static in its meaning since the early 1900s and continues to receive a lot of spin doctoring from the masters. >: for that, this other one for something else. Just conventions, of the >: humanities type. > >Ah, that is the rub - the conventions are *not* of the humanities type. >For example, in physics, the definitions of symbols are *operational* >definitions (ie., the preciseness of which I spoke of above). > I'd say "meaning coming through usage patterns" is a fine definition of "operational" -- we use symbols operationally in the humanities as well, in our computer codes especially (which tend to have less greek in them, given ASCII's cumbersome code page scheme -- maybe with Unicode we'll get a lot more computer languages using non-Roman, non-Greek character sets, e.g. Arabic or Cyrillic -- to be expected I think). >: -- so kids deserve an historical overview, and then some cultural >: reinforcement around those geeky greek letters we intend to keep using >: (e.g. DELTA). > >And really good teachers will also *give* some history of the subject and >the persons who created it. That also makes the subject come alive. At >the college level for example, the Ph.D. means doctor of *philosophy* : >meaning the history and development of one's subject and not just its >technical aspects. > Yes, part of what gives me hope, that "philosophy" has this strategic position embedded in a lot of "paper securities" (i.e. Ph.D. degrees) -- something I've posted about above. >Nevertheless, it does not help with the technical aspects of the >subject which requires a necessary amount of concentrated thought in >the silence of one's own room. >[snide remark snipped] > >: Kirby I'm not against concentrated thought in the silence of one's own room, outside on the grass or wherever. I don't really know how this got into it. Humanities readers need quiet time too -- concentration, the ability to focus the mind, and comprehension (often a result of concentration) are not exclusive capacities or requisite abilities in any one department or area of human endeavour or training. Kirby --------------------------------------------------------- Kirby T. Urner http://www.teleport.com/~pdx4d/kirby.html 4D Solutions http://www.teleport.com/~pdx4d/ [PGP OK] --------------------------------------------------------- ========================================================================= Date: Mon, 20 Jul 1998 22:04:55 +0200 Reply-To: List for the discussion of Buckminster Fuller's works Sender: List for the discussion of Buckminster Fuller's works From: tom aagdii Subject: land ownership In-Reply-To: MIME-Version: 1.0 Content-Type: TEXT/PLAIN; charset=US-ASCII what is it now, 20 of land in america owned by few companies. just trying the email again. tagdi ========================================================================= Date: Mon, 20 Jul 1998 17:17:09 GMT Reply-To: List for the discussion of Buckminster Fuller's works Sender: List for the discussion of Buckminster Fuller's works From: Kirby Urner Organization: 4D Solutions Subject: Re: Calculus 102: A Humanistic Approach to Primitive Concepts MIME-Version: 1.0 Content-Type: text/plain; charset=us-ascii Content-Transfer-Encoding: 7bit Robin Chapman wrote: > >Urner is fond of patronizing racial sterotypes. In an eariler thread he wrote > My thesis ("my" not exclusive of others using "my" for the same thesis), that the "race" concept stems from obsolete 1900s pseudoscience, is spelled out in detail at my website. "...a racist is someone who believes in races" (http://www.teleport.com/~pdx4d/terms.html#race). >> My rule of thumb is >> some starving kid in India has it figured out already, whatever >> it is, but we'll never know, because these kids have no access >> to peer-reviewed journals (guffaw). > >It is clear that in Urner's universe India is full of starving kids >full of "intuititive "in yer bones" understanding" and also every >"multicultural LAAP youth" is completley devoid of the same. > I consider myself a former (because no longer a youth) LAAP youth in many dimensions, given many formative years in the Philippines -- and my Filipina calculus teachers helped convey an "in yer bones" understanding of the subject. LAAP cultures more a part of my own heritage than Anglo, I'd be proud to declare (Oregon is on the Pacific Rim, after all). As to "starving kids in India" who have figured it out already, you asked me "why India?" at the time and I responded I was probably thinking of that Ramanujan dude (who was literally starving when trying to make headway as a mathematician, and facing lots of Anglo bias along the way). But in that context I was mostly playing up my sense that credit-hungry academics, conditioned to think being "special" (i.e. doing "stupid pet tricks" ala David Letterman Show) is what nets them food pellets, other accommodations, have developed a self-serving apparatus for giving one another credentials to the exclusion of those with just as much native smarts and capacity for insight, but who have little chance of "breaking in" owing to the stacked deck. So to equalize a little, when I see myself or others making claims to fame for having "discovered or invented" whatever, I apply my rule of thumb that someone out there starving (for lack of food pellets), in India or wherever, has already thought of this (whatever it is), but just never got the chance to share it with the world (because too busy starving to death). Basically, until kids have a more level playing field, I'm not willing to accredit any academic class or culture for being especially bright or worthy or chosen. When it comes to bias, it's a prejudice against Anglo culture that I most need to keep in check. As I write re Project Earthala: we won't repeat the mistake of the reactionaries -- Anglo culture is one culture among many and is certainly deserving of respect, but on an equal footing with others, e.g. the French or Laotian, but not as some imperial dominatrix able to direct the show, ala imperial Rome [http://members.xoom.com/Urner/afsc/earthala.html] I'm not an Anglophobe ('Austin Powers' a fine movie), but not an Anglophiliac either. Color me Celtic (with Pacific Rim shading). Kirby PS: of course given your special discipline of not reading my posts, it's doubtful any of this explanation makes a dent in all your preconceived characterizations of my positions, but I share it anyway, as perhaps others are curious. --------------------------------------------------------- Kirby T. Urner http://www.teleport.com/~pdx4d/kirby.html 4D Solutions http://www.teleport.com/~pdx4d/ [PGP OK] --------------------------------------------------------- ========================================================================= Date: Tue, 21 Jul 1998 03:20:49 GMT Reply-To: List for the discussion of Buckminster Fuller's works Sender: List for the discussion of Buckminster Fuller's works From: Kirby Urner Organization: 4D Solutions Subject: Re: Calculus 102: A Humanistic Approach to Primitive Concepts MIME-Version: 1.0 Content-Type: text/plain; charset=us-ascii Content-Transfer-Encoding: 7bit conover@tiac.net (Harry H Conover) wrote: >A nice goal, but a reduction of the matematics and physical >content of todays science to simple images sound rather like >the wishes of a child, rather than those of an intellectual >in any field of study. > > Harry C. > Actually Richard Feynman is one of my role models here -- always eager to distill the complex details to simple, yet accurate and precise, concepts and pictures. Cave paintings, if you will. I'll post another Calculus 102 essay below which perhaps will be a step closer to what you consider worthy of a child's intellect. We both have high standards I suspect -- but that doesn't mean the _same_ standards. Kirby --------------------------------------------------------- Kirby T. Urner http://www.teleport.com/~pdx4d/kirby.html 4D Solutions http://www.teleport.com/~pdx4d/ [PGP OK] --------------------------------------------------------- ========================================================================= Date: Tue, 21 Jul 1998 01:42:27 GMT Reply-To: List for the discussion of Buckminster Fuller's works Sender: List for the discussion of Buckminster Fuller's works From: Harry H Conover Organization: The Internet Access Company, Inc. Subject: Re: Calculus 102: A Humanistic Approach to Primitive Concepts Larry Mead (lrmead@orca.st.usm.edu) wrote: : : Nevertheless, it does not help with the technical aspects of the : subject which requires a necessary amount of concentrated thought in : the silence of one's own room. : Well stated. This is the key point that the humanities type [including Kirby] wish to ignore. Today's humanistic society desires instant gratification, they are repulsed by the fact that in the hard sciences such instant gratification does not exist, and cannot exist in any real depth. For me, the enigma with these people is simply this: They will spend years of effort mastering the implications of some long dead and likely (from a contemporary viewpoint) useless tongue or written language, while desiring that a mastery of today's much more productive language of science be reduces to a system of simple graphical images. A nice goal, but a reduction of the matematics and physical content of todays science to simple images sound rather like the wishes of a child, rather than those of an intellectual in any field of study. Harry C. ========================================================================= Date: Tue, 21 Jul 1998 16:45:36 +0200 Reply-To: List for the discussion of Buckminster Fuller's works Sender: List for the discussion of Buckminster Fuller's works From: tom aagdii Subject: Land ownership In-Reply-To: MIME-Version: 1.0 Content-Type: TEXT/PLAIN; charset=US-ASCII Content-Transfer-Encoding: QUOTED-PRINTABLE sorry about the mistakes in my last email. sometimes i think it is the software that breaking my message. what i wanted to say is that few companies own 20% of the land in America. i have the number stached somewhere, i shall send confirmation. the queen of england owns land of total value of 1.7 billion =A3, she own all the sea coast shelf also. the church of england total land returns is also in that range, about 1 billion =A3. i am using good indexing of all information from now on. at this moment i am just trying the email, i have to do this so fast because i have to pay 1.5 pounds for 1/2 hour. forgive me for not giving refrence this time. of course this information might not be relvant, but i think it is good to archieve all the intricate behind the seen realities. tagdi ========================================================================= Date: Tue, 21 Jul 1998 13:02:39 -0500 Reply-To: spammers.eat.used.kitty.litter.coolbear@earthlink.net Sender: List for the discussion of Buckminster Fuller's works From: Jonathan Thompson Subject: Re: Land ownership In-Reply-To: MIME-Version: 1.0 Content-Type: text/plain; charset="iso-8859-1" Content-Transfer-Encoding: 8bit Tom If it costs you for time/minute, I strongly suggest that you type your replies offline, so that you only pay for sending and receiving. This would also make it easy to send it through a spelling and grammar checker, if you wish. This would allow you to expand with more complete, easily understood details that you wish to explain. It would also save you money. Remove the comment about kitty litter to reply! spammers.eat.used.kitty.litter.coolbear@earthlink.net > -----Original Message----- > From: List for the discussion of Buckminster Fuller's works > [mailto:GEODESIC@LISTSERV.ACSU.BUFFALO.EDU]On Behalf Of tom aagdii > Sent: Tuesday, July 21, 1998 9:46 AM > To: GEODESIC@LISTSERV.ACSU.BUFFALO.EDU > Subject: Land ownership > > > sorry about the mistakes in my last email. sometimes i think it is > the software that breaking my message. > > what i wanted to say is that few companies own 20% of the land > in America. i have the number stached somewhere, i shall send > confirmation. > > the queen of england owns land of total value of 1.7 billion £, > she own all the sea coast shelf also. > the church of england total land returns is also in that range, > about 1 billion £. > > i am using good indexing of all information from now on. > at this moment i am just trying the email, i have to do this > so fast because i have to pay 1.5 pounds for 1/2 hour. > forgive me for not giving refrence this time. > > of course this information might not be relvant, but i think > it is good to archieve all the intricate behind the seen > realities. > > tagdi > ========================================================================= Date: Tue, 21 Jul 1998 14:13:21 GMT Reply-To: List for the discussion of Buckminster Fuller's works Sender: List for the discussion of Buckminster Fuller's works From: Larry Mead Organization: University of Southern Mississippi Subject: Re: Calculus 102: A Humanistic Approach to Primitive Concepts Kirby Urner (pdx4d@teleport.com) wrote: : conover@tiac.net (Harry H Conover) wrote: : >A nice goal, but a reduction of the matematics and physical : >content of todays science to simple images sound rather like : >the wishes of a child, rather than those of an intellectual : >in any field of study. : > : > Harry C. : > : Actually Richard Feynman is one of my role models here -- : always eager to distill the complex details to simple, : yet accurate and precise, concepts and pictures. Cave : paintings, if you will. Feynman is one of my favorites for this ability too. Keep in mind though that he could do this *because* he understood the technical and symbolic aspects of these complex details in a depth that few of us ever achieve. His "good" explanations were rooted in his technical mastery of mathematics and arguments based upon it; they did not arise full blown from any independent pictorial "understanding". -- Lawrence R. Mead Ph.D. (Lawrence.Mead@usm.edu) Eschew Obfuscation! Espouse Elucidation! www-dept.usm.edu/~physics/mead.html ========================================================================= Date: Tue, 21 Jul 1998 14:08:08 GMT Reply-To: List for the discussion of Buckminster Fuller's works Sender: List for the discussion of Buckminster Fuller's works From: Larry Mead Organization: University of Southern Mississippi Subject: Re: Calculus 102: A Humanistic Approach to Primitive Concepts Kirby Urner (pdx4d@teleport.com) wrote: : lrmead@orca.st.usm.edu (Larry Mead) wrote: : >Kirby Urner (pdx4d@teleport.com) wrote: : >: lrmead@orca.st.usm.edu (Larry Mead) wrote: : > : >: >In other words, " To teach math to people who don't have skills using : >: >simple symbols, use a lot of words and pictures instead." : >: > : > : >: You must have a clear idea of "simple symbol" versus "word" or "picture". : > : >Of course - you don't? Mathematics is the only precise tool for handling : >information known to humankind. It behooves every intelligent person to : >learn to use this tool. : Computers use "words" (variable number of bits, depending on the : operating system). "Simple symbol" is somewhat relative as to : simplicity -- if Greek isn't a native alphabet for example. Why is that relevant? You mean one never learns any symbol use not in one's native language? Hogwash. : >Mathematics - symbol use - is learned by disciplined reasoning over time, : >rarely by flashes of color on a screen or by flowery speech. : > : Visualization is an important tool, given short shrift there for awhile, : but making a come back. [snip] Visualization was always there in science - where did it go in humanities? : >: To me, it's all ASCII, or Unicode. Lots of so-called "simple symbols" : >: are just Greek letters, with time-honored traditions of using this one : Meaning comes across through usage patterns. You can change the meaning : of something by using it differently. Metaphorically, we call this : "altering the trajectory" of a signifier in semantic space. Mathematicians : are always revectoring signifiers in this way: the word "dimension" for : example, has not been static in its meaning since the early 1900s and : continues to receive a lot of spin doctoring from the masters. A definition is just that: a designation of *convenience* . That such a convenience changes over long periods of time is expected. In physics, the definitions of units are revised every so often to take into account our changing abilites to make measurements. Why relevant? : >: for that, this other one for something else. Just conventions, of the : >: humanities type. : > : >Ah, that is the rub - the conventions are *not* of the humanities type. : >For example, in physics, the definitions of symbols are *operational* : >definitions (ie., the preciseness of which I spoke of above). : I'd say "meaning coming through usage patterns" is a fine definition of : "operational" -- we use symbols operationally in the humanities as well, Ah, but that is just the *opposite* of an operational definition: that is of the form, "Do this *experiment* and the result will be *by definition* the thing to be defined." Operational definitions tell one - by physical experiment - how to find something. That way no one can misunderstand the definition and it is universal. For example, momentum (sorry I have to use some symbols here) is - by definition - the product of an objects velocity and its mass. Thus, to find the momentum of a volkswagen one finds how fast it is going using any convenient measuring apparatus, and measures its mass (now or previously, doesn't matter). The momemtum of the vehicle is - by operational definition - the product mv, and in the direction of travel. : >And really good teachers will also *give* some history of the subject and : >the persons who created it. That also makes the subject come alive. At : >the college level for example, the Ph.D. means doctor of *philosophy* : : >meaning the history and development of one's subject and not just its : >technical aspects. : Yes, part of what gives me hope, that "philosophy" has this strategic : position embedded in a lot of "paper securities" (i.e. Ph.D. degrees) : -- something I've posted about above. Well, one can always hope ;-) : >Nevertheless, it does not help with the technical aspects of the : >subject which requires a necessary amount of concentrated thought in : >the silence of one's own room. : > : >: Kirby : I'm not against concentrated thought in the silence of one's own room, : outside on the grass or wherever. I don't really know how this got : into it. Humanities readers need quiet time too -- concentration, : the ability to focus the mind, and comprehension (often a result of : concentration) are not exclusive capacities or requisite abilities : in any one department or area of human endeavour or training. : Kirby I won't disagree there. -- Lawrence R. Mead Ph.D. (Lawrence.Mead@usm.edu) Eschew Obfuscation! Espouse Elucidation! www-dept.usm.edu/~physics/mead.html ========================================================================= Date: Tue, 21 Jul 1998 16:12:06 GMT Reply-To: List for the discussion of Buckminster Fuller's works Sender: List for the discussion of Buckminster Fuller's works From: Kirby Urner Organization: 4D Solutions Subject: Re: Calculus 102: A Humanistic Approach to Primitive Concepts MIME-Version: 1.0 Content-Type: text/plain; charset=us-ascii Content-Transfer-Encoding: 7bit lrmead@orca.st.usm.edu (Larry Mead) wrote: >: Computers use "words" (variable number of bits, depending on the >: operating system). "Simple symbol" is somewhat relative as to >: simplicity -- if Greek isn't a native alphabet for example. > >Why is that relevant? You mean one never learns any symbol use not in >one's native language? Hogwash. > Relevant because you were saying "simple" and I'm saying we should recognize it takes work to accommodate alien charactersets in one's thinking -- both humanities and math face this same challenge. > >Visualization was always there in science - where did it go in humanities? > We call it "the visual arts" -- the computer has become in important tool in this department (cite Ken Snelson's recent visualizations of the atom, early SGI renditions of tensegrity sculptures). >A definition is just that: a designation of *convenience* . That such >a convenience changes over long periods of time is expected. In physics, >the definitions of units are revised every so often to take into account >our changing abilites to make measurements. Why relevant? > Again relevant because same state of affairs pertains in both math and the humanities (fields of precessionally interacting wordmeaning trajectories). >: I'd say "meaning coming through usage patterns" is a fine definition of >: "operational" -- we use symbols operationally in the humanities as well, > >Ah, but that is just the *opposite* of an operational definition: that is >of the form, "Do this *experiment* and the result will be *by definition* >the thing to be defined." Operational definitions tell one - by physical >experiment - how to find something. Mathematics prides itself on not being dependent on physical experiment, but distilled from logical rule-based thinking. If one wishes to find out whether a mathematical concept has physical application, then experiment comes into it. Of course in the real world, lots of people are going back and forth between conceptualization and experiment, refining concepts -- an operational setting, out of which definitions are progressively honed, sometimes with trial and error playing a big role. >the definition and it is universal. For example, momentum (sorry I >have to use some symbols here) is - by definition - the product of an >objects velocity and its mass. Thus, to find the momentum of a volkswagen >one finds how fast it is going using any convenient measuring apparatus, >and measures its mass (now or previously, doesn't matter). The momemtum >of the vehicle is - by operational definition - the product mv, and in >the direction of travel. > Yes. And for what interval (f) is our Volkswagon moving with momentum mv and through what distance (d)? If v is constant (no acceleration), then f and d determine each other. mvd is a unit of "action" (as is Planck's Constant h) and mvdf (where f = 1/t i.e. a time slice) is in units of energy i.e. mvd/t = mvv (energy is a quantity relating to the ability to make change i.e. accomplish work). Also, mvf or mv/t is ma (a=acceleration) with F=ma and mad (Fd) another expression for energy. That's why my notion of "film frames" as intervals (f = frequency) is cool, because it links in hf (an expression for energy, linear with frequency) while introducing the physics concept of "action" (mvd). Lights, camera, action! "Differentiation" and "integration" linked to camera and projector respectively, with "smooth motion" coming with "high frequency" (of frames per time, giving the sense of "continuity" or "flow"). You'll see these associations getting made in my cave paintings. Philosophically speaking, our experience of change (mv vectors in size/time intervals -- hf energy quanta) is phenomenological, whereas distilled cgs units (e.g. "distance" and "time") are operationally extracted definitions related to measuring equipment. When Einstein showed how distance and time covary with viewpoint (reference frame), while energy is conserved regardless, he was showing how "change" is more the reality than either "time" or "distance" taken alone (since in "change" we have time and size inextricably melded together). Kirby --------------------------------------------------------- Kirby T. Urner http://www.teleport.com/~pdx4d/kirby.html 4D Solutions http://www.teleport.com/~pdx4d/ [PGP OK] --------------------------------------------------------- ========================================================================= Date: Tue, 21 Jul 1998 16:52:25 -0600 Reply-To: List for the discussion of Buckminster Fuller's works Sender: List for the discussion of Buckminster Fuller's works From: "Ken G. Brown" Subject: UNIVERSAL REQUIREMENTS OF A DWELLING ADVANTAGE Comments: To: GEODESIC@UBVM.cc.buffalo.edu Mime-Version: 1.0 Content-Type: text/plain; charset="us-ascii" From: Inventory of World Resources Human Trends and Needs Document 2 pp. 142-156 Fuller Projects Southern Illinois University Carbondale, Illinois Transcribed by Curtis L. Palmer , formatted copy available by request to Curtis or . UNIVERSAL REQUIREMENTS OF A DWELLING ADVANTAGE Teleologic Schedule by Buckminster Fuller Check list of the Universal Design Requirements of a Scientific Dwelling Facility,- as a component function of a new world encompassing, service industry,- predesigned, Rather than haphazardly evolved,- and thus avoiding a succession of short circuited and overloaded burnouts of premature, and incompetent attempts to exploit the ultimate and most important phase of industrialization, to wit, the direct application of highest potential of scientific advantage toward advancement of world living standards- to be accomplished by inauguration of a comprehensive anticipatory technology scientifically informed of the probable variables and possible randoms- this new volition to succeed the era of 'survival', - that is survival-despite,- despite preponderant submission to ignorance, - ignorance of future probabilities and general behaviour of nature- which heretofore 'survival', tolerated lethal opportunism, wherein the progressive deteriorations bred emergencies which called upon scientific ability to perform last minute miracles but only as a curative dispensation of morbid inertia. The universal design requirements of a scientific dwelling facility are that it accomplish comprehensive advantage for man over all primitive factors of energetic nature. That factors may be broadly classified in four parts as follows: I. Essentially RANDOM and SUBJECTIVE phenomena A. Exterior variables- factors of destructive or useful potential; of nakedly intolerable magnitudes, inescapably impinging IA Structural, mechanical or chemical interception and control of externally impinging factors, either by rejection, reflection, deflection Through shunting, channelling, impounding, modulating and / or retiming of volumetric flows of variable external factors of nakedly - intolerable magnitudes 1. Immunization against aperiodic, energietic interferences, - externally impinging at intolerable magnitudes and heretofore classified as cataclysmic, = because exceeding the practical stress abiliites of as yet available technology - However - (new era essence). Since accomplishment of higher physio-chemical stress abilities in, for instance, supersonic flight and snorkle submarine, the stress abiliites of technology in general now far exceed the predictable stresses of the hitherto cataclysmic structural interferences - the 180 m.p.h. velocity of Antarctic hurricane or Pacific typhoon is now a relatively minor aeronautical velocity - of - interaction of designed structures. External impingements are classified in order of frequency of probable occurrence and relative magnitudes. a. Cataclysmic - Improbably annual, possibly 'never', and least frequent, but of highest stress when occurring 1. earthquake 2. tornado 3. hurricane 4. typhoon 5. avalanche 6. landslide 7. volcanic eruption 8. bombardment 9. forest fire 10. tidal wave 11. plague 12. radio activity 13. lethal gases 14. Bacteriological Warfare b. Dangerous - probably annual, of borderline 'disaster' magnitudes 1. gale 2. local fire 3. flood 4. pestilence 5. lightning 6. selfishness (self-preoccupation pursued until self loses its way and self - generates fear and spontaneous random surging, i.e. panic, the plural of which is mob outburst in unpremeditated wave synchronizations of the individually random components) a. vandals b. marauders c. meddlers d. politics e. fanaticism f. commercialism g. materialism c. Inclement Of high seasonal frequency and of low orders of stress or of naked intolerability 1. fumes 2. hail 3. rain 4. snow 5. dust 6. electrolysis 7. oxidation 8. heat 9. cold 10. epidemic 11. vermin 12. insects 13. fungi 14. minor random missiles 2. Rejection, or deflection for delayed or immediate use as a. energy, admitted into direct work as, for instance, radiation or electronic reaction, or b. indirectly into work as, for instance, impounded wind (aeronautical) or water (hydraulic) power 1. piped - for direct use 2. wired - for direct use 3. valved - for direct or delayed use 4. stored - in cistern, tank or battery for delayed use 5. stored - in thermal bank or compost bins, etc. B. Interior variables- factors of destructive or useful potential; of nakedly intolerable magnitudes, inescapably impinging IB Dynamic control of internally impinging factors 1. Interception of and dispellment of the momentum trends of ignorance, - through incorporation of experience informing natural design replacements, realized in physical principles. 2. Interception and neutralization of bacteria by isolation of , - or by direct elimination 3. Elimination of physical fatique a. human robotism and drudgery by provision of adequate mechanics of technical advantage 4. Elimination of psychological fatique (repression) by a. removal of accident hazard through mechanical adequacy (don't proofing) b. removal of arbitrary cellular limitations to permit free interaction of living functions c. provision for selective privacy by push-button sound, sight and smell barriers surrounding any interior space 5. The elimination of emotional fatigue a. factors stimulating nerve reactions to be automatically controlled in 'neutral' until voluntarily brought into play by the occupant through: 6. provision of mechanics for wide range in selection of means and degrees of sensible realization of the prosaic or harmonic phenomenon a. visual b. aural c. tactile d. olfactoral, i.e. taste and smell C. Exterior constants of relative inertia forgotten through persistent obviosity and randomly re-encountered IC Control by anticipatory design over exterior constants of inertia forgotten through persistent obviosity and only randomly re-encountered 1. Constants of environment, i.e. the mud forgotten between rains, odorous winds from remote sources, snowdrifting 2. Control devices installed for seasonal duration only requiring inordinate time investments 3. Chemical accumulations 4. Biological accumulations a. vegetation, composts, weed b. insect, animal residues, nestings, general growth changes 5. Surprise emergencies of environmental complex uniqued to locality, i.e. possible water, oil, gas springs and seepage II. Essentially ROUTINE and SUBJECTIVE phenomena - internal to dwelling- predictably periodic, rhythmic A. Inescapable functions of the organic processes, internal to dwelling and external to man. IIA Provision for (unselfconscious) (spontaneous) mechanical performance of inevitable organic routines of the dwelling and its occupants with minimum of invested attention or effort 1. Fueling of house (external metabolism) 2. Realignment of house 3. Scavenging of house B. A. Inescapable functions of the organic processes, internal to dwelling and internal to man. IIB Provision for (unselfconscious) (spontaneous) mechanical performance of inevitable organic routines of the dwelling and its occupants with minimum of invested attention or effort 1. Fueling of occupants (internal metabolism) 2. Realignment of occupants (sleep) by allowed muscular, nerve and cellular realignment accomplished by designed elimination of known restrictive factors. 3. Scavenging of occupants a. internal, i.e. intestinal, etc. b. external, i.e. bathing or pore cleansing c. mental, i.e. elimination by empirical dynamics d. circulatory: external, - atmospheric control internal, - as respiratory functions. C. Interior constants of relative inertia forgotten through persistent obviosity, and regularly rediscovered, e.g. furniture to be lifted with each house-cleaning IIC Control by anticipatory design over interior constants of relative inertia forgotten by fatigue cloture of feedback sensibilities and routinely re-encountered - (such as heavy furniture to be moved about daily for cleanliness operations, storages to be overhauled to obtain the tentatively retained devices of possible or infrequent use) 1. By provision of adequate occupational - specialty storage means 2. By home employment of travel equipment 3. by dimensional reduction (e.g. of collections of large data to microfilm) III. Essentially RANDOM and OBJECTIVE phenomena- internal to dwelling- initiative, spontaneously intermittent- teleologic A. Investment of earned increments of lifetime for free will regeneration of the advantage of life over a priori environment. Realization of man's potentials as an individual IIIA Provision of ready mechanical means, complementing or implementing, all development requirements of the individual's potential growth phenomena, - allowing the facile, scientifically efficient, no-energy-or-time-loss, - spontaneous development of self disciplined education, by means of 1. Conning, i.e. selectively stimulated awareness of the momentary interactions of universal progressions accomplished by means of facile references to vital data on a. history b. news c. forecasts calls for a conning facility combining book and periodical library, radio, television facilities, systematically arranged incoming reports on: 1. current supply and demand conditions 2. currrent dynamic conditions - weather - earthquakes - latest scientific research findings 3. social dynamics - surfacing of commonweal problems of comprehensive readjustment to new potentials anc concomitant obsolescence factors 4. latest technical reference in: a. texts b. movie documentation c. television university (soon evoluting to increasing importance and reliability as the autonomous dwelling facility becomes widely available) 2. Adequate mechanics of personal articualation (prosoaic or harmonic) for the spontaneous investment of the imagination - gestating intellectual - increments of experience, - (teleology) which trend ever to satisfy the evolving needs - prosaic or harmonic - routine or plus. This category of original articulations also includes the necessity or crystallization of universal progress a. instruments are tools of communication 1. direct 2. indirect 3. aural 4. visual 5. tactile a. music, writing, drawing, measuring instruments b. wood, metal and chemical working tools c. typewriter d. wire - tape - and - disc - all - purpose - recoreder - radio - phonograph e. easel f. photographic equimpent - taking, developing, printing, projection 3. Recreation - appropriate equipment to full physical development 4. Procreation B. Implemented and insulated spontaneity of feedback acceleration- continuity of the self amplifying individual IIIB Insulation, or isolation, of the instrumented initiatives Private diaries, tape recordings, films, instrumentally recorded data as yet incomplete, undigested, ungestated as complete teleologic regeneration C. Instrumentation of 'home' magnitude physical realizations of man's potential as a continuous- man, i.e. a team of individuals overlapping and weaving around individual birth - deaths and separate generations, a Total Man who never sleeps, dies, nor forgets. IIIC Home Magnitude means of displaying, exposing, experimenting and measuring of 'target' or 'trend to target' or 'trend following' assumptions - of - realization - initiative - and - articulation. - i.e. 'vital navigation ' or 'teleology', i.e. personal and social and cosmic feedback control. The comprehensive 'frames' - relative to which display, exposure, experiments, measurement and progressive dynamic trend assumptions may be referenced is FOURFOLD * IV. Essentially INCISIVE and routine OBJECTIVE phenomena- external to dwelling- initiating a sustainable complex continuity = design realization of all men's joint potential- teleologic A priori Design Realization Assumptions Asking not why, whither, nor whence man-life? but assuming the accumulated experience evidences that biological phenomena in general and man-life in particular function in universe as the anti-entropic, - the anti-random, - the simple and complex organic, - the systematically convergent phases of the comprehensive cycling of omni energy transformations and therefore the realization that man-life's extension into cosmic measurement already billions folds the sensory limits of integral faculties presages a further successful amplification of the man-life function in universe and therefore that the regenerative ability of intellect in extension, acceleration, and expansion of the extra corporeal cosmic- functioning-stature of the man-life in universe is realizable in comprehensive design initiative relayed through industrialization and therefore the function of comprehensive design initiative relayed through industrialization and therefore the function of comprehensive design is most naturally and effectively preoccupied with omni-abetment of the realization in full of the potentials of the 'individual' complex - an organic atomic nebula identified superficially as man - man potential includes regeneratively improving potentials of sequential derivative orders of increasing advantage of the organic over the (random-entropic) chaos growths. 'Individual' man's highest potential may be realized in terms of full interaction of all men's potentials - ergo man's universal function trends to amplify first the pull potential of the individual, - but inherently multiplicative man - life. Therefore on first priority in design consideration is the full realization of individual potential in order to reach the second derivative, - full realization for all individuals. Keys to design realization are the anthropological measurements, of the limiting factors of corporeal man, beyond which extra-corporeal articulation of the integral faculties may be accomplished by extension in principle through atomic-complex trains, and energetic transformations to cosmic stature advantage. Universal conditions of design realization commence with the static and dynamic dimensions of man and his basic behavior involvements of which there exists a wealth of data. The whole program of realization is to be considered in the following order which breaks into two primary categories or phases: (1) the initial work to be undertaken by the individual prior to his engagement of the aid of associates and (2) original and initial work to be undertaken by the first group of associates. These two phases may be subdivided as follows: A. Investment of earned increments of technical advantage of the science- industry complex in design realization of the complex dwelling facility service IVA Research and development by initiating individual (prior to inauguration of design action and development action involving full-time employment of others). Inauguration of a general work pattern as a natural pattern coinciding with best scientific procedure to wit: Preliminary Initiation of diary and notebook Initiation of photographic documentation Initiation of tactical conferences PHASE I, INDIVIDUAL 1. Comprehensive library study of accrued developments within the pertinent arts1* a. past b. contemporary 2. Listing therefrom of authorities available for further information a. local, personal contact b. remote, correspondence 3. Pursuant to information thus gained, calling at suggested local laboratories a. university b. industry c. setting up of informative tests for first-hand knowledge in own laboratory 4. First phase of design assumption a. consideration of novel complex interaction unique to project b. preferred apparatus from competitive field c. design of appropriate flowsheets 5. Flowsheets submitted to: a. those competitive specialists who have proved helpful in step b and c b. industrial producers of similar equipment and assemblies c. make informative tests for closure of gaps supporting assumed theory 6. Submit specifications and drawings of general assembly and unique component parts for informative bids by manufacturers a. second redesign of flowsheet based on available and suggested apparatus, price information, etc. 7. Prepare report consisting of diary of above supported by photographic documentation and collected literature - with trial balance conclusions of indicated economic advantage (which, if positive, will inaugurate Phase II) B. Implementation and insulation of synergetic feedback of higher order accruing to spontaneous group realizations of newly evolving potential IVB Design and development undertaking - involving plural authorship phase and Specialization of full -time associates Consideration of Relationship of prototype to industrial complex by constant review of principles of solution initially selected as appropriate to assumptions Adoption of assumptions for realization in design of pertinent principles and latest technology afforded 1. Comprehensive survey of whole sequence of operations from original ;undertaking to consumer synchronization. Realization strategy #1 by individual (Phase I) - Realization strategy #2 by associates (Phase II) a. Physical tests in principle of the design assumptions' unique inclusions not evidenced in available data b. General assembly drawings (schematic) providing primary assembly drawing schedule reference c. General assembly assumption, small scale models and mockup full size d. primary assembly, sub-assembly and parts calculations (stress) e. Trial balance of probable parts weights and direct manufacturing costs (approximately three times material costs; includes labor, supervision and inspection) and forecast of overall cost magnitudes, and curve plotting, - at various rates of production, rationed to direct costs per part and ' all other costs, - i.e. 'overhead', tool and plant 'amortization', 'contingencies', 'profit' f. 'Freezing; of general assembly and its reference drawing g. drawing for first full size production prototype commences in general assembly, primary assembly, sub-assembly and parts h. Budget of calculating and drawing time is set with tactical deadlines for each i. Parts drawing and full size lofting and offset patterns j. Prototype parts production on 'soft tools' commences k. Sub-assembly and primary assemblies with 'obvious' corrections and 'necessary' replacements (not 'improvements' or 'desirables' which must be deferred until second prototype is undertaken after all-comprehensive physical tests have been applied) l. m Photography of all parts and assemblies n. Full assembly completed and inspected - cost appraised with estimates of possible 'improvement' savings to be effected o. static load tests p. Operational tests q. Assembly and disassembly tests r. Photography of all phases s. Packaging and shipping tests t. Estimates of savings to be effected by special powered field tools u. Opinion testing v. Final production 'clean-up' prototype placed in formal calculation and drawing with engineering budgeted with deadlines w. Parts cost scheduled by class 'A' tools and time x. Production tool layout fixed y. Production tools ordered z. Production dates set a'. Lofting and offsets produced of full-size = test 'masters' and templates b' Fabrication of special jigs and fixtures c'.. Production materials ordered d' Production tool-jig-fixture tune-up e'.. Parts and assembly testing f'. Filed operation scheduling g' Field tools ordered h'. Distribution strategy in terms of initial logistic limitations i'.. Field tests with special tools j'. Field tools ordered or placed in special design and fabrication k'. Test target area selected for first production l'. Production commences m First field assemblies with power tools n''. Maintenance service instituted and complaints: alleviated, analyzed, change orders of parts instituted o'. Plans for 'new yearly model improvement run through all or previous steps - for original production p'. Cycle repeated 2. Production and distribution velocity assumptions 3. Plotting the assumed progressive mass-production curves to determine basic velocities of new industry 4. Tensioning by crystalline, pneumatic, hydraulic, magnetic means 5. Compressioning by crystalline, pneumatic, hydraulic, magnetic means 6. Consideration of manufacturer's basic production forms, - relative to proposed design components for determination of minimum steps, minimum tools, and minimum waste realization 7. Establishment of priority hierarchies of effort 8. Time and energy and cost budgeting 9. Assumption of industry responsibility for field practices, not only in mechanical and structural, but in economic design 10. Designing for specific longevity of design appropriate to anticipated cycles of progressive obsolescence and replacement ability as ascertained from comprehensive economic trend curves 11. Designing with 'view to efficient screening of component chemicals for recirculated employment in later designs' 12. maxima and minima stated and realized performance requirements per unit of invested energy and experience and capital advantage of tools and structures employed and devised 13. Logistics assumptions compacted shipping considerations as original design requirement in 14. Consideration of tool techniques 15. Consideration of material's availability 16. Consideration of materials ration per total design 17. Elimination of special operator technique forming 18. Elimination of novel special soft tool designing 19. Numbers of: 20. Numbers of forming operations 21. Number of manufacturing tools by types 22. Schedule of forming operations included on parts drawings 23. Decimal fraction man hours per operation 24. Designed - in over-all one - man - man ability at every stage of operation 25. Schedule of design routines and disciplines 26. Establish a 'parts inventory of 'active and obsolete drawings - from beginning 27. Establish a 'parts' budget of 'required' designs of 'parts' for assemblies and major assembly and general assembly and molds 28. Drawing dimension standards 29. Establish a numbering system of controlled parts 30. Establish purchasing techniques, jig and fixture, lofting techniques C. Instrumentation of industrial or institute / university magnitude realization of man's potential as a continuous - man. i.e. a team of individuals overlapping and weaving around individual birth - deaths and separate generations, a Total Man who never sleeps, dies, nor forgets. IVC Industrial Magnitude means of etc. This section repeats all content of IIIC except at Industrial magnitude instead of at Home magnitude. PUBLIC RELATIONS To run concurrently with all phases of IVB 1. Education of public Rule I: Never show half finished work a. General magnitude of product, production , distribution. But no particulars that will compromise latitude of scientific design and production philosophy of IVB b. Publicize the 'facts', i.e. the number of steps before 'consumer realization' c. Understate all advantage d. Never seek publicity e. Have prepared releases for publisher requests when 'facts' ripe Note: That I and II above are subjective and defensive and exclusive and that III and IV are objective and offensive and inclusive. Note: That I defines the outer ramparts and II the inner defenses while III represents the inner initiative - taking and IV the full grown outer offensive - conquest - contact. Note: That this arrangement is geometrically teleologic, i.e. omni-directionally convergent - divergent - propogative. ========================================================================= Date: Wed, 22 Jul 1998 03:29:11 -0700 Reply-To: List for the discussion of Buckminster Fuller's works Sender: List for the discussion of Buckminster Fuller's works From: Brian Hutchings Subject: Calculus 102 (the torrid effort; 5 semesters-worth of the 2nd sem <> Brian Hutchings 22-JUL-1998 3:29 r001806@pen2.ci.santa-monica.ca.us you seem to imply, Harry, that there is no worth to the study of Greek classics or, say, the work of Nicholas of Cusa in the original Latin -- although the main works are now available in English, two; there's cerainly a *lot* more to read, than in Esperanto! thus quoth: For me, the enigma with these people is simply this: They will spend years of effort mastering the implications of some long dead and likely (from a contemporary viewpoint) useless tongue or written language, while desiring that a mastery of today's much more productive language of science be reduces to a system of simple graphical images. -- "The End of History". "Who?" "Sir George's officially unofficial hagiographer, Francis Fukuyama; see http://www.tarpley.net!" "Oh, gee, thanks, Beavis." ========================================================================= Date: Wed, 22 Jul 1998 13:03:13 -0700 Reply-To: List for the discussion of Buckminster Fuller's works Sender: List for the discussion of Buckminster Fuller's works From: Kirby Urner Subject: Re: MidEast Comments: To: Maxine Nunn , Ilisec@aol.com Comments: cc: synergetics-l@teleport.com In-Reply-To: <199807220725.CAA32752@earlham.edu> Mime-Version: 1.0 Content-Type: text/plain; charset="us-ascii" > Yesterday, Gush Shalom - the Peace Bloc - tried to redress the > balance and took the initiative of "Marking the Green Line". The > purpose was to convey its position that after thirty-one years > the 1967 border, known as "The Green Line", remains Israel's > internationally-recognised boundary, and that it is on the basis > of this border that peace can be conceived between Israel and > Palestine. Thanks for the forward, Maxine. Personally speaking, I'm skeptical that emphasizing the green line international boundary is constructive peace activism. As I see it, ethnic enclaves interpenetrate too much for vast land tract demarcation (political jurisdiction solution) to work -- same problem as in Bosnia (Kosovo etc.). Effective infrastructure planning needs to be bioregional, with an eye towards generic solutions regardless of ethnic identity (water, sewer, transportation and communications systems don't know about religio-political divisions). I think of New York City (enclaved like crazy, but with one subway system running under it all). I think of Disney World. In some ways, corporations (many with resources beyond what nation-states now control) serve as a model of how humans can organize, both locally and globally, without respect to some "vast land tract" territorial demarcation system inherited from kingdoms and empires long gone. Corporations have historical ties to sea cultures (liability- limiting for landlubbers, to allow paper securities underwriting of high risk, high seas venturing ala East India Tea) and partly for this reason look more like Phoenicia did: a port facility here, a training facility there -- but no "vast contiguous land tract" holdings as per political nation-states, because "home" is the open water, and no one but the most pretentious try to claim private ownership of the oceans, where pirates freely roam and nature reigns supreme. Israel and Palestine envisioned more as corporate entities with shared infrastructure would make the Middle East appear more like Greater LA in our imaginations. The problem is not to make "nations" co-exist, but to design/implement ecosystem-economies which work for people, regardless of their ethnic or religious differences. Israeli settlements right next to Palestinian ones should be no more of a problem than a Sheraton next to a Hilton, a Hertz next to an Avis. If Palestine and Israel both want Jerusalem for a headquarters, fine. London serves as home base for any number of such entities. It's the nation-state as institution which is too stupid to fit the real world of the computerized, satellite-linked late 20th century, given its silly rules about one capital per country, never shared etc. To think Jerusalem is too small to serve as a base of operations for more than one organizational headquarters is to indulge in idle fantasy (something politicians are good at, given how easy it is to peddle such fantasies to gullible constituents via the commericial media -- there's no business like show business). I'm not saying that political boundaries will disappear overnight, but I prefer to leave it to politicians to care about them. From my point of view, we have planet Earth and a lot of people needing services (which means we need to train them in the requisite skills in a hurry). Beliefs about political jurisdictions certainly inform peoples' actions (encourages them band into armed gangs behind warlords for example, to waste time/energy on a tremendous scale, while killing off profitable enterprising in the civilian sector -- a vicious circle). My own experience, however, is that many CEOs challenged to think globally and long term on a daily basis (in the interests of their global shareholders), are finding this politically-minded jigsaw-puzzle overlay-view of Earthian affairs is an increasingly irrelevant way of intelligently organizing all the incoming global data. Like, it's all Phoenicia folks (or call it Spaceship Earth). Get over it. Get a life. Background: http://www.teleport.com/~pdx4d/bosnia.html ===== FYI, previous exchange (off-list): Date: Tue, 21 Jul 1998 10:49:11 -0700 To: Ilisec@AOL.COM From: Kirby Urner Subject: Re: bad news from Hebron Cc: [long list] >A Hebron spokesman issued the following statement: >Gangs of Arab youth continue to attack Hebron's children, both boys and >girls. The Arabs are equipped with metal chains and bars. We demand that >Israeli police and security forces take all action necessary to stop these >attacks and to bring the Arabs responsible to justice. > Of course it isn't necessary to always divide into Arabs and Israelis. Hebron spokesman might have said: Gangs of youth continue to attack Hebron's children, both boys and girls. The gangs are equipped with metal chains and bars. We demand that police and security forces take all action necessary to stop these attacks and to bring the youth responsible to justice. Of course a lot of people on both sides think in terms of an Arab/Israeli polarity. But from my distance (out here on the Pacific Rim), it's easier to think of the Middle East as greater LA -- a place with a serious gang problem, lots of thuggery (including in high office). Ethnicity is a factor of course, but nationality really isn't so much (LA is USA-contained). What we've got in Greater Israel (or Greater Palestine -- I don't really care what we call it) are 'hoods like around Ramallah (been there) and Hebron, some well-to-do, others more squalid (which is really more the root problem than religious differences for a lot of people, and more a challenge for architects, planners and engineers than for politicians without relevant skills and suffering from over-polarized imaginations). Kirby ===== From: Ilisec@aol.com Date: Tue, 21 Jul 1998 16:08:41 EDT To: pdx4d@teleport.com Subject: Re: bad news from Hebron thank you for your perspective. We need to hear it much more often! Ilise Cohen ===== ========================================================================= Date: Wed, 22 Jul 1998 13:10:21 GMT Reply-To: List for the discussion of Buckminster Fuller's works Sender: List for the discussion of Buckminster Fuller's works From: Larry Mead Organization: University of Southern Mississippi Subject: Re: Calculus 102: A Humanistic Approach to Primitive Concepts Kirby Urner (pdx4d@teleport.com) wrote: : lrmead@orca.st.usm.edu (Larry Mead) wrote: [snip] : Again relevant because same state of affairs pertains in both math : and the humanities (fields of precessionally interacting wordmeaning : trajectories). [\bigsnip] Well, I was following you up to here ( and even enjoying the commentary) when . Scientists like myself who consider themselves good teachers as well, pride ourselves in their ability to use simple language to express complex ideas. Now, I am at home with a lot of multisyllabic verbiage, but " fields of precessionally interacting wordmeaning trajectories" is causing lots of problems. A trajectory is the path taken in space by a point ( or point mass). I cannot imagine how it is that meanings of words interact, can precess (rotate about the angular momentum vector), though how they can constitute a "field" is better. Do you care to elaborate, or are we just not going to make any progress here? -- Lawrence R. Mead Ph.D. (Lawrence.Mead@usm.edu) Eschew Obfuscation! Espouse Elucidation! www-dept.usm.edu/~physics/mead.html ========================================================================= Date: Wed, 22 Jul 1998 21:20:23 -0700 Reply-To: List for the discussion of Buckminster Fuller's works Sender: List for the discussion of Buckminster Fuller's works From: Brian Hutchings Subject: Calculus 102 <> Brian Hutchings 22-JUL-1998 21:20 r001806@pen2.ci.santa-monica.ca.us hah, and people have whined about *my* verballistical tendencies.... really, Kirbo was at least trying to metaphorialize (like, EDITorializing, if you will); in any case, Bucky has used the notion of cycling trajectories, or what-he-say, as in one's daily routine (say, riding some "fossil'fueled" conveyance to "work" ... see, one of his books is _Utopia or Oblivion_, which i think was meant in the "XOR" sense !-) personally, following Bucky, aslo, I'd *never* (at least formally) use the notion of a "point" or a "point-mass" a-trajectorying, because a) the meaning probably predates the ballistics, and b) a point is (at minimum) a subvisible tetragon (like, a twinkling star .-)... true, it will "have" an idealized center o'gravity, so, I *would* use it in a formal sense, there. thus quoth: verbiage, but " fields of precessionally interacting wordmeaning trajectories" is causing lots of problems. A trajectory is the path taken in space by a point ( or point mass). I cannot imagine how it is that meanings of words interact, can precess (rotate about the angular momentum vector), though how they can constitute a "field" is better. Do you care to elaborate, or are we just not going to make any progress here? -- Lawrence R. Mead Ph.D. (Lawrence.Mead@usm.edu) ========================================================================= Date: Wed, 22 Jul 1998 07:50:47 PST Reply-To: List for the discussion of Buckminster Fuller's works Sender: List for the discussion of Buckminster Fuller's works From: 094398 Organization: ;lsdkf Subject: "Pam Lee & Bret Michaels Sex Video Available Now ! HOLY SHIT BATMAN!!!!!!!! http://www.pamporn.com - ANNOUNCING YET ANOTHER- PAMELA ANDERSON HARDCORE SEX TAPE!!!!!!!! -Pamela Anderson & Bret Michaels Sex Tape- UN-FUCKING BELIEVABLE Could it be true? YES! 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So get your credit card ready and order today. http://www.pamporn.com GNXCXSEZIHEFHTVENVPBRFZMWORVBRONYFKTDHKH ========================================================================= Date: Wed, 22 Jul 1998 22:45:26 -0700 Reply-To: List for the discussion of Buckminster Fuller's works Sender: List for the discussion of Buckminster Fuller's works From: Brian Hutchings Subject: Re: Mideast <> Brian Hutchings 22-JUL-1998 22:45 r001806@pen2.ci.santa-monica.ca.us "I think of Disney World", in deed. while I am not averse to some of your "histoire speculatif" a la Bucky, your charicature of the role of the nation-state is inapt, as in your usage of "Greater Israel"; Greater MyCouhtryTisO'Thee is the usual phrase used by the chauvinists and ethnicals, the Zionists in the former case. beings steeped in Buckythink, or stooped unto it, is not substitute for "universal history" (a-hem !-) ========================================================================= Date: Wed, 22 Jul 1998 22:54:17 -0700 Reply-To: List for the discussion of Buckminster Fuller's works Sender: List for the discussion of Buckminster Fuller's works From: Kirby Urner Subject: Re: Mideast In-Reply-To: <199807230545.WAA30728@pen2.ci.santa-monica.ca.us> Mime-Version: 1.0 Content-Type: text/plain; charset="us-ascii" This wasn't history but futurism -- the willful tuning out of the political overlay as obscuring of more relevant underlying ecosystems, more properly the subject of design science and our world game brainstorming. Myse of "Greater Israel" was intentional (I know the connotations) but with the caveat we might as well call it "Greater Palestine" -- because we simply don't care, really. More: Lots of people take their nation-states very seriously and never question their integrity as human contrivances designed to solve certain problems. This will continue to be the case. But some of us do not see this theater as quality drama, and question the right of political pundits to monopolize the world stage with their sage lines and proposed scenarios, would like a greater mix and variety, especially with a focus on possible near futures that would be too interesting and intelligent and worth living in to make war seem such an attractive alternative. If history a few years from now is going to have a lot less interest in nations and nationalism, then being a hero or martyr for this or that nation maybe won't seem so attractive to the young impressionables anxious to go out in a blaze of glory, taking as many of the enemy with them as possible etc. Not a channel that's going to get high ratings. Not a show we're going to waste much time on in future. Maybe time to learn some new roles and get out of the guns and coffins routine. Get this: a lot of us kids don't see your nations on our maps, and we don't care to learn about them as political entities. We do not care for boundaries and wonder why you do. Not an apathetic 'not caring' or ignorant laziness but a willful, intentional, focused not-tuning-in, not recognizing, as an exercise of personal freedom to not have history ram itself down our throats. Again, this is just a thread, a bias, which is needed, in my estimation, to balance a seriously off-balance focus on nation-states as now and forever more. [http://www.teleport.com/~pdx4d/bosnia.html] > beings steeped in Buckythink, or stooped unto it, > is not substitute for "universal history" (a-hem !-) > > ========================================================================= Date: Thu, 23 Jul 1998 00:54:12 GMT Reply-To: List for the discussion of Buckminster Fuller's works Sender: List for the discussion of Buckminster Fuller's works From: urnerk@MY-DEJANEWS.COM Organization: 4D Solutions Subject: Re: Calculus 102: A Humanistic Approach to Primitive Concepts > Well, I was following you up to here ( and even enjoying the commentary) > when . Scientists like myself who consider themselves good > teachers as well, pride ourselves in their ability to use simple language > to express complex ideas. Now, I am at home with a lot of multisyllabic > verbiage, but " fields of precessionally interacting wordmeaning > trajectories" is causing lots of problems. A trajectory is the path taken > in space by a point ( or point mass). I cannot imagine how it is that > meanings of words interact, can precess (rotate about the angular momentum > vector), though how they can constitute a "field" is better. > Do you care to elaborate, or are we just not going to make any progress > here? > That words interact is clear -- change the meaning of "democrat" and you've got a new spin on "President Clinton" and so on and so forth. Imagining words with trajectories in semantic space helps dislodge another picture: that meanings are objects, such that name->object relationships "anchor" words (language on the one hand, not-language on the other). Better to see objects as semantic elements in their own right, likewise with trajectories in semantic space (a giant camel on a billboard hyperlinks to an image of cigarettes -- that's language for ya!). As for "precession", I'm using that to characterize a relationship that isn't just some simple "I tug, you come closer" (which is more the way gravity works when two objects are in critical proximity -- they "fall in" together). When I tug on a spinning top, it yields by tilting at 90 degrees to my pull vector. Likewise I'm suggesting that our semantic field is characterized by such non-180 degree behaviors in response to tension (pull) or compression (push). >From one of my other web essays: Separately islanded systems in a tensive medium precess one another. A spinning system does not have to yield ground at 90 degrees by simply "falling in" as when meteors give up the ghost and crash into the Earth's atmosphere, heating to umpteen degrees, evaporating to become atmosphere. Large spinning axials, when tugged at, tend to yield in some sideways direction. A gyroscope tilts in a plane perpendicular to the line of force. This sidewise yielding is what humans need to learn about when they set out to operationally produce wealth in their local energy harvesting units. Simple tugging does not necessarily yield simple results. All systems are interprecessing. No straight lines. Everything is affected by everything else. Things are normally in motion, accelerating, always. [http://www.inetarena.com/~pdx4d/synergetica/invisible4.html] If you think this kind of thinking is highly metaphoric, then I'd say you're right. But metaphorical doesn't necessarily imply imprecise. We're doing philosophy here, more than physics -- probably what makes this uncomfortable. If you want some visuals to go with the chatter, you might check: http://members.xoom.com/Urner/working3.html Kirby 4D Solutions -----== Posted via Deja News, The Leader in Internet Discussion ==----- http://www.dejanews.com/rg_mkgrp.xp Create Your Own Free Member Forum ========================================================================= Date: Thu, 23 Jul 1998 00:44:31 -0700 Reply-To: List for the discussion of Buckminster Fuller's works Sender: List for the discussion of Buckminster Fuller's works From: Brian Hutchings Subject: Re: the nation-joke <> Brian Hutchings 23-JUL-1998 0:44 r001806@pen2.ci.santa-monica.ca.us it is impossible to provide justice through a lot of sloganeering, the immensity of the PR biz notwithstanding, Kirby (surf *that*, dude .-)... when I use the phrase, universal history, I have a sinking feeling that I am treading water beyond the alledgedly Phoenician extent of Geodesic-L, for you & certainly for a far-cry lot of the usership of this list (in this probable backwater of proverbially unmilitary intelligence [*]), many of whom are happily busy on their "dome on a range" -- or some other *flat*, fat scenario of isolate livingry. "livingry", a nice, desolate Buckyism, although of inherently dual-usage! out of a primary ignorance, however widespread (and mostly shared by myself; but I can still slogan, like a Sho-Gun, or a son-of-a-gun), you insist upon a "nation" that is nothing more than an empire, however-so localized, or "balkanized". like the Phoenecian Empire; eh? I suppose it has some thing to do with the problem, that "my fearless leader" [**] conscientiously objects to you christian, or jesuitical sect -- but I haven't read your George Fox link! "This is an International Veeking Crossing" (beware the open water .-) -- kill the Beast (but only if you're going to eat it) !! http://www.tarpley.net ========================================================================= Date: Thu, 23 Jul 1998 08:38:37 -0700 Reply-To: List for the discussion of Buckminster Fuller's works Sender: List for the discussion of Buckminster Fuller's works From: Kirby Urner Subject: Re: the nation-joke In-Reply-To: <199807230744.AAA31330@pen2.ci.santa-monica.ca.us> Mime-Version: 1.0 Content-Type: text/plain; charset="us-ascii" > I suppose it has some thing to do with the problem, that > "my fearless leader" [**] conscientiously objects to you christian, or > jesuitical sect -- but I haven't read your George Fox link! > > "This is an International Veeking Crossing" > (beware the open water .-) > Hey, more lucid than usual Breeeeean. Of course we buckynauts go Phoenician -> Veeking -> Venetian, which leads us into backwaters of technoinvective at Tarpley's site. Had to wonder if the Fuller School would make the hit list in a hurry, given villification all things Venetian, especially as informative of latter day Anglo imperialism: There is a cancer growing on world history - the cancer of oligarchism. Between the year 1200 AD and about 1600 AD, the world center of gravity for the forces of oligarchism was the oligarchy of Venice. Towards the end of that time, the Venetian oligarchy decided for various reasons to transfer its families, fortunes, and characteristic outlook to a new base of operations, which turned out to be the British isles. The old program of a worldwide new Roman Empire with its capital in Venice was replaced by the new program of a worldwide new Roman Empire with its capital in London - what eventually came to be known as the British Empire. [http://www.tarpley.net/nosouls.htm] Tarpley's narrative parallels Bucky's in a lot of ways because both are tracking maritime cultural threads. I enjoy Tarpley's scholarship and have written to the guy asking if maybe the Fuller School was "too Venetian" (paraphrase). Probably. But from my point of view, GRUNCH is a positively reoriented successor to LAWCAP (in the "thinking globally" arena), not just "more of the same" -- meaning better living standards and less nationalism. It's a consistent viewpoint with its own philosophy. No point whining that I sound too much like a buckynaut. This _is_ GEODESIC after all, and I _am_ one of those Jesuitical Quakers or whatever we are. Which doesn't make me an Anglophiliac (much as I'm willing to respect Anglos, on equal footing with the rest). Color me Celtic, with shades of Pacific Rim. Blessed be, Kirby 4D Solutions ========================================================================= Date: Thu, 23 Jul 1998 12:45:55 GMT Reply-To: List for the discussion of Buckminster Fuller's works Sender: List for the discussion of Buckminster Fuller's works From: Larry Mead Organization: University of Southern Mississippi Subject: Re: Calculus 102: A Humanistic Approach to Primitive Concepts [snip] I followed *some* of that. : If you think this kind of thinking is highly metaphoric, then I'd : say you're right. But metaphorical doesn't necessarily imply : imprecise. We're doing philosophy here, more than physics -- But here, I must protest. Metaphoric *always* means imprecise. It is only that which is assigned number which *is* precise, and that is one reason why it is difficult for me to follow your theses. Let me reiterate once again: in philosophy one can do whatever one wants as you don't have to get anything *right* . That is, there is no universe which checks your answers 8-). -- Lawrence R. Mead Ph.D. (Lawrence.Mead@usm.edu) Eschew Obfuscation! Espouse Elucidation! www-dept.usm.edu/~physics/mead.html ========================================================================= Date: Thu, 23 Jul 1998 16:58:37 GMT Reply-To: List for the discussion of Buckminster Fuller's works Sender: List for the discussion of Buckminster Fuller's works From: Kirby Urner Organization: 4D Solutions Subject: Re: Calculus 102: A Humanistic Approach to Primitive Concepts MIME-Version: 1.0 Content-Type: text/plain; charset=us-ascii Content-Transfer-Encoding: 7bit lrmead@orca.st.usm.edu (Larry Mead) wrote: >Let me reiterate once again: in philosophy one can do whatever one wants >as you don't have to get anything *right* . That is, there is no >universe which checks your answers 8-). I think this is a prejudice. A CEO for a large corporation has a "business philosophy". Numbers, statistical analyses, computations and projections go across her desk, provide reality checks and feedback, but a lot of the management decisions and recommendations flow from intuitions and philosophical considerations which cannot be reduced to mere "business rules" in some basement computer. And the business world tends to be punishing, unforgiving. If your philosophy is insufficiently robust, out of sync, not attuned, then your business may well go under, leaving countless workers floundering and in need of a new job (with the CEO back on the street, looking for a mail room entre). True, no professor of physics is sitting by your side to correct your papers, putting "true or false" next to every "answer" -- but that doesn't mean "there is no Universe". Math-science types like to complain that philosophy is insufficiently strict or rigorous, but their disciplines don't offer anything to replace the hard core, just offer vitamin supplements, helpful tools, better mouse-traps. The humanities still has to supply the more comprehensive trainings by default. Kirby --------------------------------------------------------- Kirby T. Urner http://www.teleport.com/~pdx4d/kirby.html 4D Solutions http://www.teleport.com/~pdx4d/ [PGP OK] --------------------------------------------------------- ========================================================================= Date: Thu, 23 Jul 1998 13:29:46 -0400 Reply-To: List for the discussion of Buckminster Fuller's works Sender: List for the discussion of Buckminster Fuller's works From: Jim Hunter Organization: Johns Hopkins University Applied Physics Laboratory Subject: Re: Calculus 102: A Humanistic Approach to Primitive Concepts Mime-Version: 1.0 Content-Type: text/plain; charset=us-ascii Content-Transfer-Encoding: 7bit Kirby Urner wrote: > > lrmead@orca.st.usm.edu (Larry Mead) wrote: > > >Let me reiterate once again: in philosophy one can do whatever one wants > >as you don't have to get anything *right* . That is, there is no > >universe which checks your answers 8-). > > I think this is a prejudice. > > A CEO for a large corporation has a "business philosophy". Numbers, > statistical analyses, computations and projections go across her desk, > provide reality checks and feedback, but a lot of the management > decisions and recommendations flow from intuitions and philosophical > considerations which cannot be reduced to mere "business rules" in > some basement computer. And the business world tends to be punishing, > unforgiving. If your philosophy is insufficiently robust, out of > sync, not attuned, then your business may well go under, leaving > countless workers floundering and in need of a new job (with the > CEO back on the street, looking for a mail room entre). Unfortunately for the buisness environment, Peter's Principle is alive and thriving. The less you actually know about anything physical or mathematical gets you a pat on the back and a raise. --- Jim ========================================================================= Date: Fri, 24 Jul 1998 03:28:34 GMT Reply-To: List for the discussion of Buckminster Fuller's works Sender: List for the discussion of Buckminster Fuller's works From: Harry H Conover Organization: The Internet Access Company, Inc. Subject: Re: Calculus 102: A Humanistic Approach to Primitive Concepts Jim Hunter (jim.hunter@REMOVE_TO_EMAIL.jhuapl.edu) wrote: : : Unfortunately for the buisness environment, Peter's Principle : is alive and thriving. The less you actually know about anything : physical or mathematical gets you a pat on the back and a : raise. : Ain't that God's honest truth! Of course the real problem is that those that do rise to their level of incompetence get control, and since they can never rise any higher stay, and stay, and stay.... This is the curse of the large corporation...and accounts for their need to acquire rather than innovate. Harry C. ========================================================================= Date: Thu, 23 Jul 1998 22:35:21 -0400 Reply-To: List for the discussion of Buckminster Fuller's works Sender: List for the discussion of Buckminster Fuller's works From: Todd S Reynolds Organization: The University of Toledo Subject: concrete shell Hello , I have been thinking about building a home using one of the steel span building kits available,( American steel , Pioneer Steel) , then spraying the outside with the yellow polystyrene that I have seen on This Old House and then covering that with either Shotcrete of similar coating. My question is , Does this sound reasonable? I have seen the Monolithic domes and this would be similar except I would use a steel shell form instead of an inflated bag. Any feedback would be great. -- treynol@pop3.utoledo.edu ========================================================================= Date: Fri, 24 Jul 1998 03:04:14 -0700 Reply-To: List for the discussion of Buckminster Fuller's works Sender: List for the discussion of Buckminster Fuller's works From: Brian Hutchings Subject: concrete shell MESSAGE from ="List 24-JUL-1998 2:52 Hello , I have been thinking about building a home using one of the steel span building kits available,( American steel , Pioneer Steel) , then spraying the outside with the yellow polystyrene that I have seen on This Old House and then covering that with either Shotcrete of similar coating. My question is , Does this sound reasonable? I have seen the Monolithic domes and this would be similar except I would use a steel shell form instead of an inflated bag. Any feedback would be great. -- treynol@pop3.utoledo.edu - - - - - <> Brian Hutchings 24-JUL-1998 3:04 r001806@pen2.ci.santa-monica.ca.us what is a "steel pan building kit" ?? -- sex & drugs & president -- http://www.tarpley.net ========================================================================= Date: Fri, 24 Jul 1998 08:35:59 GMT Reply-To: List for the discussion of Buckminster Fuller's works Sender: List for the discussion of Buckminster Fuller's works From: Kirby Urner Organization: 4D Solutions Subject: Re: Calculus 102: A Humanistic Approach to Primitive Concepts MIME-Version: 1.0 Content-Type: text/plain; charset=us-ascii Content-Transfer-Encoding: 7bit conover@tiac.net (Harry H Conover) wrote: >This is the curse of the large corporation...and accounts for their >need to acquire rather than innovate. > > Harry C. > Such complacent and scornful sneers from the peanut gallery. CEOs really need smart cookies without math phobia on board. Here in the Silicon Forest, we aim to provide a highly skilled, competent workforce. My humanistic mathematics is one ingredient in making that happen. This is not a "for dummies" curriculum -- probably what accounts for it's poor reception in this group. Kirby --------------------------------------------------------- Kirby T. Urner http://www.teleport.com/~pdx4d/kirby.html 4D Solutions http://www.teleport.com/~pdx4d/ [PGP OK] --------------------------------------------------------- ========================================================================= Date: Fri, 24 Jul 1998 04:53:13 -0700 Reply-To: List for the discussion of Buckminster Fuller's works Sender: List for the discussion of Buckminster Fuller's works From: Brian Hutchings Subject: Re: Mideast <> Brian Hutchings 24-JUL-1998 4:53 r001806@pen2.ci.santa-monica.ca.us the contrast between a jesuit and a christian was a tweak, dude; they have always been like that, since Ignatius, to their continuing promoti of "libtheo" in Iberoamerica (see our translation of Schiller's short work, "The Jesuit Government of Paraguay", based upon a contremporary expose; they did similarly creepy, syncretical & wicked work with the Mohawks, in Canada, to attack the English colonies -- they didn't scalp anyone, til then). how the Quakers rate on the scale, now, as a whole, I don't know the future, either! I think of Disney World. on the Matterhorn, I feel good, exhilerated; I think of Tinkerbell and fireworks in summer (I lived in "Analheim" for exactly a summer, and Tinkerbell managed to dodge those rockets, *every* God-am night); then, I think of It's a Small World -- THEN I loose my lunch. ah, Trekkies; they are *rather* juvenile. thus quoth: of us kids don't see your nations on our maps, and we don't care to learn about them as political entities. anyway, I really agree, that "development is the name of peace"; we said it, the Pope said it, every one *says* it, but few realize the role of the nation in *deploying* it, and maintiaining the in (most of the media is utterly flamboozled by the "trade is freedom" ideology, inducting Adam Smith into the Founding Parental Units, when he was just a Chair at the U.of Edinburgh, funded by the East India Co.; he condoned the plowing-in of cereals, for the planting of poppies, to be sold in China [_The Wealth of Nations_, published *en masse* in'76 by Penguin, Ltd.; think, "Batman" and Gotham/NYC's pantheon of arch-criminals .-] oh, yes; certainly, Bucky's Transcendentalist "speerchul" forebears were Vene maybe not in the sense that he thought of the latter, but I don't see that he gave the PhoeVeekIans a pretty gloss, considering his characterization of the pirates of the latter-day Empire (or, Commonwealth), like SIR Francis Drake (but She hasn't knighted her own fundmanager, Soros "the golem", yet. of course, I also thought that "GRoss UNiverse Cash Heist" was the bad guys, and I had a whole *box* o'that paperback !-) in deed, "London serves as home base for many" terrorist organizations, such as most of the ones that are so-called Islamic Fundamentalists, like the satanist GIA in Algeria; you can fax them your credit-card#, at their London-area safe-house, if you want to help. like Lawd Avebury sait in Parliament, "one man's terrorist is another man's freedom-fighter", or a whole family's.... of course, Jerusalem already *is* a holy HQ for many sects of 3 religions, that I know of; it is only "breeteesh zioneests" like Bibi, who want to blow it all to Hell. -- Of Human Slimeage -- http://www.tarpley,net ========================================================================= Date: Fri, 24 Jul 1998 08:32:24 GMT Reply-To: List for the discussion of Buckminster Fuller's works Sender: List for the discussion of Buckminster Fuller's works From: fchristo@MY-DEJANEWS.COM Organization: Deja News - The Leader in Internet Discussion Subject: Re: Calculus 102: A Humanistic Approach to Primitive Concepts In article <35b767eb.70309312@news.teleport.com>, pdx4d@teleport.com (Kirby Urner) wrote: > lrmead@orca.st.usm.edu (Larry Mead) wrote: > > >Let me reiterate once again: in philosophy one can do whatever one wants > >as you don't have to get anything *right* . That is, there is no > >universe which checks your answers 8-). > > I think this is a prejudice. ..snip!.. > True, no professor of physics is sitting by your side to correct > your papers, putting "true or false" next to every "answer" -- > but that doesn't mean "there is no Universe". Math-science types > like to complain that philosophy is insufficiently strict or > rigorous, but their disciplines don't offer anything to replace > the hard core, just offer vitamin supplements, helpful tools, > better mouse-traps. The humanities still has to supply the > more comprehensive trainings by default. I think I agree with you here, Kirby, but your example of "business philosophy" [not quoted above] makes me think you are using the word "philosophy" in the sense of "an acquired set of beliefs or morals". It is not hard to see why that would evoke such a violent reaction from Larry. Larry seems to think that philosophy is an anything-goes forum where any loonie idea will receive serious attention, provided one couches it in a sufficiently obscure fashion. I guess this is probably a common complaint from technical people who are ignorant of the literature, but it's quite far from the truth. I probably would have agreed with you once in college, but then I took a class on the philosophy of language. I was a CS major, and I took it partly because I'm interested in language and linguistics, partly to fulfill some credit requirements, and partly, I admit, because I was expecting an easy A. But I was pleasantly surprised (until I saw my grades :) to learn that philosophy is a very rigorous discipline. Of course philosophers don't go around quantifying metaphysical properties to support their hypotheses, for the obvious reason that it is not a science. Nor do they justify theories with proof calculi, because philosophy is not (just) mathematics (although you would be surprised how well-versed philosophers are in formal logic). But rigor, I think, is not just about quantifying data or writing squiggly symbols on a piece of paper, or typing them into a computer program; that is just _formality_. Rather, _rigor_ is about making the logical steps between pieces of evidence convincing enough that one's conclusions are warranted and ultimately inescapable. In mathematics, it is mostly possible to make these steps not just convincing, but perfectly explicit. In science, one can make them convincing by eliminating enough other plausible explanations that the probability of alternate theories becomes vanishingly small. A good philosopher is indeed rigorous in just this sense, except that the greater portion of a philosophical argument is typically informal. There is a trap that one may fall into when working daily in the technical community. The trap is to believe that the object of your study is the formal symbols you are manipulating, rather than that the symbols are indeed just that---symbols that signify, among other things, some process or pattern of interest. (And model theory, more generally computer science, is exactly the study of the relationship between those two.) But we are reminded again and again, that "formality is there to help us." That aphorism should also recall to us that formality is a tool which facilitates sound arguments, rather than merely encapsulating the arguments themselves. What really brought this idea home for me was a lecture by the late Carl Sagan that I attended the same year I took the philosophy class. I think it is all too easy for us to jibe the "soft" sciences (the name itself is almost derogatory), making snide remarks to the effect that they are "easy" because _any_ crackpot idea is fair game. One of the things from Sagan's speech that stood out for me that night was the notion that soft sciences and---although I don't think he meant to include them, but I also think it applies more generally---non-technical subjects are not "easier" than technical ones, but rather _harder_ precisely because they lack the formal tools that allow us to express ideas so clearly and concisely in science and math. Or better: non-technical fields are still in the process of finding out how best to apply those tools. You can see this in psychology, which has developed from a largely qualitative field based on Freud's abstract notion of child development and dream interpretation, to a more quantitative field driven by statistics theory. When you are missing the formal tools, you need to be extra careful that your argument is sound, and that your conclusions are warranted. Philosophers need to be more critical than scientists, and they have to have more discerning minds. I think, frankly, that at least the philosophy of language is quite good on this score. In fact, I think that if you check the literature, you will find that many of the philosophers in this area were also mathematicians. Tarski and Frege are two examples. Together they laid the foundations for modern mathematical logic, and I think that Frege actually developed the predicate calculus to talk about the philosophy of language, rather than the other way around. It is true that much of the philosophical literature is very abstract. But I think that the task of philosophy is not just to make claims that are subject to formal or scientific verification, but also to raise questions that might ultimately be answered in other fields. Many philosophical issues have no right or wrong resolution, and what's wrong with that? True/false is just the simplest way of evaluating an idea, suitable for those that you might want to encode in a computer and walk away from, but philosophical issues are more complex, more personal and more human. By the way, physics probably spun off from philosophy and, in fact, one could argue that all the sciences that have existed from before the 20th century probably originated in this way. (Scientists used to be called "natural philosophers.") So it would be wrong to say that philosophy hasn't done anything for the world. Some of the ideas I studied in that class, in fact, have found practical applications in computer science in the design of natural language generators and parsers. I guess I should qualify all this by saying that most (but not all) of my contact with philosophy has been in the area of language philosophy, which I admit is probably the most rigorous branch, precisely because of the availability of formal tools and the vast influence of Frege. --FC -----== Posted via Deja News, The Leader in Internet Discussion ==----- http://www.dejanews.com/rg_mkgrp.xp Create Your Own Free Member Forum ========================================================================= Date: Fri, 24 Jul 1998 05:45:04 GMT Reply-To: List for the discussion of Buckminster Fuller's works Sender: List for the discussion of Buckminster Fuller's works From: Doug Milliken Organization: Buffalo Free-Net Subject: Re: SOME DESIGN CONSIDERATIONS FOR GEODESIC SPHERICAL-DOME MINIMAL COST HOUSING In-Reply-To: Content-Type: TEXT/PLAIN; charset=US-ASCII Mime-Version: 1.0 emailed, and posted on bit.listserv.geodesic On Mon, 20 Jul 1998, Ken G. Brown wrote: > A paper written somewhere around 1971, transcribed by Ken G. Brown > with permission from J.C. Bohlen, 980719. > --------------------------------------------------------------- > SOME DESIGN CONSIDERATIONS FOR GEODESIC SPHERICAL-DOME MINIMAL COST HOUSING Is there any chance that you could get the figures scanned and put up on a web site somewhere? Also, are there details/drawings of the actual pieces, cut-angles etc? -- Doug -------------------------------------------------------- > Fig. 1 - Pentagonal dome cluster schematic > Fig. 2 - View of erected structural elements without cladding > Fig. 3 - Close-up of hexagonal hub with struts attached > Fig. 4 - View of floor platform joist web > Fig. 5 - Diagram of strut geometry > Fig. 6 - View of partially erected dome > Fig. 7 - Close view of shingle cladding > Fig. 8 - View of completed dome ========================================================================= Date: Fri, 24 Jul 1998 08:31:36 GMT Reply-To: List for the discussion of Buckminster Fuller's works Sender: List for the discussion of Buckminster Fuller's works From: Kirby Urner Organization: 4D Solutions Subject: Re: Calculus 102: A Humanistic Approach to Primitive Concepts MIME-Version: 1.0 Content-Type: text/plain; charset=us-ascii Content-Transfer-Encoding: 7bit Jim Hunter wrote: > Unfortunately for the buisness environment, Peter's Principle > is alive and thriving. The less you actually know about anything > physical or mathematical gets you a pat on the back and a > raise. > > --- > Jim Not in your case. Don't bother sending a resume. Kirby --------------------------------------------------------- Kirby T. Urner http://www.teleport.com/~pdx4d/kirby.html 4D Solutions http://www.teleport.com/~pdx4d/ [PGP OK] --------------------------------------------------------- ========================================================================= Date: Fri, 24 Jul 1998 13:17:32 GMT Reply-To: List for the discussion of Buckminster Fuller's works Sender: List for the discussion of Buckminster Fuller's works From: Larry Mead Organization: University of Southern Mississippi Subject: Re: Calculus 102: A Humanistic Approach to Primitive Concepts Kirby Urner (pdx4d@teleport.com) wrote: : lrmead@orca.st.usm.edu (Larry Mead) wrote: : >Let me reiterate once again: in philosophy one can do whatever one wants : >as you don't have to get anything *right* . That is, there is no : >universe which checks your answers 8-). : I think this is a prejudice. [business analogy snipped] Needless to say, I do not. : True, no professor of physics is sitting by your side to correct : your papers, putting "true or false" next to every "answer" -- : but that doesn't mean "there is no Universe". Math-science types : like to complain that philosophy is insufficiently strict or : rigorous, but their disciplines don't offer anything to replace This last (naive) statement seems to show that you simply do not yet fully understand how science operates and how numbers give precision wheras all other information does not. It will be very difficult to communicate further. Let me suggest that some of the questions you want answered may not lie within the purvue of science ("why are we here?" "who created the universe?" , "What is the correct way to behave?"). Nonetheless, philosophy, while good at *stating* these questions, has absolutely no means of answering any of them until it somehow becomes quantitative and operational. Same with business (that is getting there quickly thanks to mathematical economists and physicists working in probability theory, etc.), sociology, psychology and many other "ologies". While over time they have found lots of questions to ask, and certainly not to minimize either the importance or the depth of those questions, they as yet do not have the quantitative tools to supply the answers. -- Lawrence R. Mead Ph.D. (Lawrence.Mead@usm.edu) Eschew Obfuscation! Espouse Elucidation! www-dept.usm.edu/~physics/mead.html ========================================================================= Date: Fri, 24 Jul 1998 10:42:10 -0700 Reply-To: List for the discussion of Buckminster Fuller's works Sender: List for the discussion of Buckminster Fuller's works From: Kirby Urner Subject: Re: Mideast In-Reply-To: <199807241153.EAA06873@pen2.ci.santa-monica.ca.us> Mime-Version: 1.0 Content-Type: text/plain; charset="us-ascii" > I also thought that "GRoss UNiverse Cash Heist" was the bad guys, and > I had a whole *box* o'that paperback !-) I think you've learned to think in terms of "good and bad" a little too well, example set by fearless leader. Not that these words will be going out of style (nor nations disappearing, in the eyes of many beholders), but twas Fuller's discipline to "rise above" moralizing for a more "beyond good and evil" narrative (see opening sentence of Critical Path): IT IS THE AUTHOR'S working assumption that the words good and bad are meaningless. Behind the "cast of characters" (e.g. "giants" at one extreme) you tend to get "metals" in Fuller's alchemical narrative -- harder to be paranoid when the archetypals are so elemental (like, don't take it all so personally, enjoy the ride, play your part -- maybe this is why Bucky and "love machine" Erhard seemed to get along so well (compatible gadgets)). I had Walter Kaufmann for a teacher at Princeton so heard a positive spin (with caveats) re Nietzsche e.g. learned that "blonde beast" had nothing whatever to do with German racial superiority (Nietzsche wrote a lot of technoinvective aimed at Germans plus his "contra Wagner" piece -- that beast was mythopoetic lion, a spiritual metaphor, not code for "Aryan"). But in Tarpley we find Nietzsche cast with the other baddies, in part because he apparently vacationed in Venice once or twice: Friedrich Nietzsche loved Venice, returned there incessantly, and dedicated certain poems to the city, which can today still be used in lieu of a powerful emetic. Venice was an inspiration for Lord Byron, for Thomas Mann, and so on. Like, tsk tsk re loving Venice. And the lumping of Neitzsche with Wagner, despite the "Contra Wagner" essay, and picking up the time-worn stereotype of Neitzsche as proto-fascist (blonde beast meme) -- this, to me, is perhaps slapdash and sloppy scholarship. Neitzsche's sister put the racial spin on his work posthumously. Something of a nut case. Lazy scholarship goes along: The cancer, so to speak, had already had ample time for metastasis--into Geneva, Amsterdam, London, Edinburgh, and elsewhere. Thus, although the sovereign political power of Venice had been extinguished, its characteristic method lived on, helping to incubate what the twentieth century knows as fascism, first as a breeding ground for the protofascist cultural productions of Wagner and Nietzsche, later through fascist politicians like Gabriele D'Annunzio and Benito Mussolini.... [http://www.tarpley.net/venconsp.htm] Already wrote to Tarpley about all this, one scholar to another. Wondering if you have anything of your own to add. Kirby PS: If you want to make waves, write that "Fuller as Nietzsche's Overman" essay (embraced life, and "beyond good and evil", echoes of Nietzsche in "Twilight of...", Norman O. Brown connection: synergetics as polymorphic, if not perverse) -- and spend the rest of your life dodging incoming. ========================================================================= Date: Fri, 24 Jul 1998 10:44:04 -0700 Reply-To: List for the discussion of Buckminster Fuller's works Sender: List for the discussion of Buckminster Fuller's works From: Kirby Urner Subject: Response to "Dome Days" essay (anthologized) In-Reply-To: <6p9gqo$urj$1@nnrp1.dejanews.com> Mime-Version: 1.0 Content-Type: text/plain; charset="us-ascii" ARCHIVE COPY Date: Sun, 07 Jun 1998 17:32:44 -0700 To: Alex Soojung-Kim Pang From: Kirby Urner Subject: Re: 'Dome Days' (essay by Alex Soojung-Kim Pang) MEMORANDUM June 7, 1998 FR: Kirby Urner TO: Alex Soojung-Kim Pang RE: Your essay Howdy Alex -- Just read your 'Dome Days: Buckminster Fuller in the Cold War' in 'Cultural Babbage : Technology, Time and Invention' edited by Francis Spufford & Jenny Uglow (Faber & Faber, 1996). I learned quite a bit about those Cold War trade fair exhibits from your research -- more about what was actually going inside the domes. That "model nuclear family" with actors doing their schtick amidst lots of homey conveniences sounds somewhat twilight zone -- all that repetitious, scripted behavior would give an eerie, robotic flavor to this American dream come true; USA capitalism as a form of "frozen family" to go with all those frozen foods. I see you mention James Fitzgibbon on pg. 179. I got a long distance phone call a couple years ago from some guy hitting my website at random (searching on "Brenholtz" -- my step-daughter's last name), who claimed Fuller and Fitzgibbon had to fake a photo of a dome being lifted by helicopter in order to get the Marine Corps to try it -- to show it had already been done (reassuring). At least I think it was Fitzgibbon -- I've never been able to confirm this little anecdote. I'm somewhat puzzled to see your analysis terminates in the 1970s, with our 'Domebook' kids and their CommuniDome (which has some appeal -- I'd want to see the kitchen and menu). Given the book's copyright date of 1996, one wonders what happened next. Certainly Fuller didn't just disappear into the haze of hippidom, as your closing sentence implies. Perhaps you wrote this essay quite some time ago and never had a chance to bring it up to date. Also, I think you're too quick to write off Fuller's books as "peculiarities to all but the most loyal of his admirers". Even if true, these books are where Fuller does a lot of work to impart his own "spin" to the domes, other artifacts (which, as you rightly point out, are semantic-symbolic, have vectors within many cultures, not just the Cold War USA's). You impart a spin of your own (domes as agents of dispersal) but then muzzle Fuller, in favor of a few carefully chosen excerpts from his memoranda, to rub in and bring out that Cold Warrior sheen. That's certainly your prerogative, as a critical thinker, to offer context and interpretation. But then your curt dismissal of the books as "peculiar", and the absense of any charting of his trajectory since the Vietnam chapter, seems a bit too convenient, steals from the scholarly tone of your essay and makes it more a propaganda piece itself. But perhaps that was your ironic intent -- to effectively demonstrate the endless malleability of cultural memes in the hands of a skilled writer. PS: if the book goes to a next edition, maybe someone can change the "thirty" to "twenty" in your descriptions of the spherical icosahedron (variably frequenced). ========================================================================= Date: Fri, 24 Jul 1998 13:23:32 GMT Reply-To: List for the discussion of Buckminster Fuller's works Sender: List for the discussion of Buckminster Fuller's works From: Larry Mead Organization: University of Southern Mississippi Subject: Re: Calculus 102: A Humanistic Approach to Primitive Concepts fchristo@my-dejanews.com wrote: : In article <35b767eb.70309312@news.teleport.com>, : pdx4d@teleport.com (Kirby Urner) wrote: : > lrmead@orca.st.usm.edu (Larry Mead) wrote: : I think I agree with you here, Kirby, but your example of "business : philosophy" [not quoted above] makes me think you are using the word : "philosophy" in the sense of "an acquired set of beliefs or morals". It is : not hard to see why that would evoke such a violent reaction from Larry. : Larry seems to think that philosophy is an anything-goes forum where any : loonie idea will receive serious attention, provided one couches it in a : sufficiently obscure fashion. I guess this is probably a common complaint : from technical people who are ignorant of the literature, but it's quite far : from the truth. [\bigsnip] Actually, that is not at all what he believes. Rather, only that pure logic without quantitative analysis is too imprecise, and that there is therefore no way to *check* (by experiementation and measurement) whether or not any philosophical answer is correct or not. In no way (some of my friends are professional philosophers btw) do I think that such persons use less than rigorous rules of logic. -- Lawrence R. Mead Ph.D. (Lawrence.Mead@usm.edu) Eschew Obfuscation! Espouse Elucidation! www-dept.usm.edu/~physics/mead.html ========================================================================= Date: Fri, 24 Jul 1998 17:13:11 GMT Reply-To: List for the discussion of Buckminster Fuller's works Sender: List for the discussion of Buckminster Fuller's works From: "Brian M. Scott" Organization: Cleveland State University Subject: Re: Calculus 102: A Humanistic Approach to Primitive Concepts On Fri, 24 Jul 1998 08:35:59 GMT, pdx4d@teleport.com (Kirby Urner) wrote: > My humanistic mathematics >is one ingredient in making that happen. This is not a >"for dummies" curriculum -- probably what accounts for >it's poor reception in this group. No, the salesman and his evangelistic fervour account for a good part of the poor reception. Misuse of the term 'humanistic' doesn't help, either, especially with those of us with strong interests in the humanities. Brian M. Scott ========================================================================= Date: Fri, 24 Jul 1998 18:52:54 GMT Reply-To: List for the discussion of Buckminster Fuller's works Sender: List for the discussion of Buckminster Fuller's works From: Harry H Conover Organization: The Internet Access Company, Inc. Subject: Re: Calculus 102: A Humanistic Approach to Primitive Concepts Kirby Urner (pdx4d@teleport.com) wrote: : conover@tiac.net (Harry H Conover) wrote: : : >This is the curse of the large corporation...and accounts for their : >need to acquire rather than innovate. : > : > Harry C. : > : : Such complacent and scornful sneers from the peanut gallery. : CEOs really need smart cookies without math phobia on board. I agree. The problem introduces itself at a layer or two down the hierarchy, where those who have risen to their level of incompetence protect their job security by refusing to employ anymore with stronger qualifications than their own. If you haven't personally seen this effect in action, you've either led a very sheltered life or remained isolated from the real world in the sheltered ivory towers of academia -- perhaps both. : Here in the Silicon Forest, we aim to provide a highly : skilled, competent workforce. More power to you in this case. This will be a revolutionary change to the West Coast status quo employment situation, where the workforce, except those in senior positions, are currently regarded and treated as trained, mindless drones. : My humanistic mathematics : is one ingredient in making that happen. So you claim. Still, it is not clear that your "humanistic mathematics" has the potential to make anything happen beyond stroking your personal ego. : This is not a : "for dummies" curriculum -- probably what accounts for : it's poor reception in this group. Actually, I believe that your poor reception by this group has more to do with the fact that most readers here, unlike your targeted victims, are very comfortable in the use of conventional mathematics. Try pitching your nonsense in a less sophisticated newsgroup. Harry C. ========================================================================= Date: Fri, 24 Jul 1998 19:22:11 GMT Reply-To: List for the discussion of Buckminster Fuller's works Sender: List for the discussion of Buckminster Fuller's works From: lazariuk@MY-DEJANEWS.COM Organization: Deja News - The Leader in Internet Discussion Subject: Re: Calculus 102: A Humanistic Approach to Primitive Concepts In article <6pa1hc$826$1@thorn.cc.usm.edu>, lrmead@orca.st.usm.edu (Larry Mead) wrote: > Let me suggest that some of the questions you want > answered may not lie within the purvue of science ("why are we here?" > "who created the universe?" , "What is the correct way to behave?"). > Nonetheless, philosophy, while good at *stating* these questions, has > absolutely no means of answering any of them until it somehow becomes > quantitative and operational. Let me suggest that mathematics will become more relevant when those teaching it see that those questions are within the purview of science. At least to the extent that they appreciate the mystery. JAck -----== Posted via Deja News, The Leader in Internet Discussion ==----- http://www.dejanews.com/rg_mkgrp.xp Create Your Own Free Member Forum ========================================================================= Date: Fri, 24 Jul 1998 19:02:05 GMT Reply-To: List for the discussion of Buckminster Fuller's works Sender: List for the discussion of Buckminster Fuller's works From: jack@DIGIMAX.COM Organization: Deja News - The Leader in Internet Discussion Subject: Re: Calculus 102: A Humanistic Approach to Primitive Concepts In article <6pa1hc$826$1@thorn.cc.usm.edu>, lrmead@orca.st.usm.edu (Larry Mead) wrote: > This last (naive) statement seems to show that you simply do not yet > fully understand how science operates and how numbers give precision > wheras all other information does not. It will be very difficult to > communicate further. As an interested observer in this discussion I do hope it does continue further. It would be my opinion from what I have read of Kirby that he does understand how science operates and how numbers give precision. Some of what you and Kirby write leads me to ponder that there may be a concern that to the degree that we place a value on precision to that same degree we ignor the totality of our understanding of life that cannot be communicated precisely. Kirby seems to be attempting to be more comprehensive than you and that he wants math to be in unision with those, as you say it, unanswerable questions. Jack As far as the laws of mathematics refer to reality, they are not certain, as far as they are certain, they do not refer to reality. -- Albert Einstein -----== Posted via Deja News, The Leader in Internet Discussion ==----- http://www.dejanews.com/rg_mkgrp.xp Create Your Own Free Member Forum ========================================================================= Date: Fri, 24 Jul 1998 18:44:54 GMT Reply-To: List for the discussion of Buckminster Fuller's works Sender: List for the discussion of Buckminster Fuller's works From: Kirby Urner Organization: 4D Solutions Subject: Re: Calculus 102: A Humanistic Approach to Primitive Concepts MIME-Version: 1.0 Content-Type: text/plain; charset=us-ascii Content-Transfer-Encoding: 7bit scott@math.csuohio.edu (Brian M. Scott) wrote: >No, the salesman and his evangelistic fervour account for a good part >of the poor reception. Misuse of the term 'humanistic' doesn't help, >either, especially with those of us with strong interests in the >humanities. > >Brian M. Scott Not uniformly poor, I should add. Your attitude is already well-documented so I'm not sure why you keep reiterating without adding any new content of your own. Do you have a substantive contribution to make, or is your mission to simply carp about mine? Seems a pretty lazy-assed approach. Free country though -- not many rules against wasting a lot of time (including within the Ivory Tower -- slackers everywhere!). Kirby --------------------------------------------------------- Kirby T. Urner http://www.teleport.com/~pdx4d/kirby.html 4D Solutions http://www.teleport.com/~pdx4d/ [PGP OK] --------------------------------------------------------- ========================================================================= Date: Fri, 24 Jul 1998 18:57:19 GMT Reply-To: List for the discussion of Buckminster Fuller's works Sender: List for the discussion of Buckminster Fuller's works From: Kirby Urner Organization: 4D Solutions Subject: Re: Calculus 102: A Humanistic Approach to Primitive Concepts MIME-Version: 1.0 Content-Type: text/plain; charset=us-ascii Content-Transfer-Encoding: 7bit lrmead@orca.st.usm.edu (Larry Mead) wrote: >This last (naive) statement seems to show that you simply do not yet >fully understand how science operates and how numbers give precision >wheras all other information does not. Your (patronizing) statement seems to show that you are on the verge of edifying us with your philosophical viewpoint re the relationship between logic and history (principles and reality, numbers and energy) -- but then you stop. >While over time they have found lots of questions to ask, and certainly >not to minimize either the importance or the depth of those questions, >they as yet do not have the quantitative tools to supply the answers. My point is "they" have to make lots of decisions, right now, today. Not idle star-gazing, running a large enterprise, using quantitive tools such as we have them (economics and astrology have a lot in common, still). There's no waiting for "ologies" to get their act together (no time), no luxury of twiddling our thumbs while waiting for unfulfilled promises of AI to materialize (Hal, where are you? -- it's almost 2001). I don't necessarily accept you as an authority or teacher as to what is science, how it operates BTW -- you seem to arrogate that role, but in this NG I assume a more egalitarian environment: we each pick and choose whom we can learn from. Ph.D. means "doctor of philosophy" and its worth, like any paper security, can be way over-inflated, especially when our philo degree holders are so often slackers who haven't bothered to update themselves re even 20th century developments in the field (given overspecialization and compartmentation, who's to make them? -- cross-disciplinary peer review is at low ebb these days, with few in any department willing to call others on their B.S. (I won't call you on yours if you don't call me on mine is the oft unspoken agreement)). Kirby --------------------------------------------------------- Kirby T. Urner http://www.teleport.com/~pdx4d/kirby.html 4D Solutions http://www.teleport.com/~pdx4d/ [PGP OK] --------------------------------------------------------- ========================================================================= Date: Fri, 24 Jul 1998 23:24:51 GMT Reply-To: List for the discussion of Buckminster Fuller's works Sender: List for the discussion of Buckminster Fuller's works From: "Brian M. Scott" Organization: Cleveland State University Subject: Re: Calculus 102: A Humanistic Approach to Primitive Concepts On Fri, 24 Jul 1998 19:22:11 GMT, lazariuk@my-dejanews.com wrote: >In article <6pa1hc$826$1@thorn.cc.usm.edu>, > lrmead@orca.st.usm.edu (Larry Mead) wrote: >> Let me suggest that some of the questions you want >> answered may not lie within the purvue of science ("why are we here?" >> "who created the universe?" , "What is the correct way to behave?"). >> Nonetheless, philosophy, while good at *stating* these questions, has >> absolutely no means of answering any of them until it somehow becomes >> quantitative and operational. >Let me suggest that mathematics will become more relevant Relevant to what? It's hard to think of a facet of life to which mathematics is *not* relevant. > when those teaching >it see that those questions are within the purview of science. Can you demonstrate that they are? No one else seems to have made a very credible go at it yet. > At least to >the extent that they appreciate the mystery. That has nothing to do with whether the questions are within the purview of science. Brian M. Scott ========================================================================= Date: Sat, 25 Jul 1998 00:32:01 GMT Reply-To: List for the discussion of Buckminster Fuller's works Sender: List for the discussion of Buckminster Fuller's works From: urnerk@MY-DEJANEWS.COM Organization: Deja News - The Leader in Internet Discussion Subject: Re: Calculus 102: A Humanistic Approach to Primitive Concepts > > So you claim. Still, it is not clear that your "humanistic > mathematics" has the potential to make anything happen beyond > stroking your personal ego. > As opposed to my impersonal ego? > Actually, I believe that your poor reception by this group has > more to do with the fact that most readers here, unlike > your targeted victims, are very comfortable in the use of > conventional mathematics. > Yes, it's been most obvious from the beginning that this is your point of view. Smug complacency re some level of attainment re conventional mathematics is par for the course. But unconventional mathematics (e.g. what I pitch) is greeted with knee-jerk hostility. > Try pitching your nonsense in a less sophisticated newsgroup. > > Harry C. > You call it nonsense, but after admitting you haven't even bothered to check out what you're passing judgement upon. Too proud of your UNIX newsreader and its apparent inability to talk to your web browser (LINUX world not quite so dark ages is it?). Kirby PS: and rest assured, I do peddle my "nonsense" elsewhere, although I'll not pass blanket judgement on the "sophistication" of anonymous accessors of public domain filings. Here's a recent posting to a math-oriented listserv, FYI: ========== For those of you who liked my "An Intro to Math", I've got more re the calculus implementing my computer language approach. Got a positive review on sci.math (below). For the full text, see website original at: http://www.inetarena.com/~pdx4d/ocn/calculus1.html NOTE: calculus2.html (same website) is proving far more controversial however, given it claims to be a contribution to "humanistic math" -- brings up a lot of prejudices math folks have vs. any humanities approach as inevitably "dumbing down" (not the way I see it; just another angle on the same content, useful for sparking intuitions in people who may have found more crypto-compressed symbolism inaccessible -- this text helps 'em get oriented). Kirby ====== In sci.math, "John T. Lowry" wrote (7-21-98): Dear Kirby and All: Your numerical introduction to calculus makes some good points and is accessible to some who wouldn't otherwise come to the table. Especially if you have a similarly good introduction to the function concept. John. -- John T. Lowry, PhD Flight Physics; Box 20919; Billings MT 59104 Voice: 406-248-2606 Kirby Urner wrote in message <35b70d0e.27672989@news.teleport.com>... > > >[from Oregon Curriculum Network website > http://www.inetarena.com/~pdx4d/ocn] > >========= > > The Calculus: Differentiation and Integration > > by Kirby Urner > Originally posted: December 23, 1997 > Last modified: February 15, 1998 > >If I have a series of numbers, a can write the differences >between them on the line below: > >1 4 9 16 25 36 49 64 > \ / \ / \ / \ / \ / \ / \ / > 3 5 7 9 11 13 15 > ====== -----== Posted via Deja News, The Leader in Internet Discussion ==----- http://www.dejanews.com/rg_mkgrp.xp Create Your Own Free Member Forum ========================================================================= Date: Sat, 25 Jul 1998 04:04:58 GMT Reply-To: List for the discussion of Buckminster Fuller's works Sender: List for the discussion of Buckminster Fuller's works From: "Brian M. Scott" Organization: Cleveland State University Subject: Re: Calculus 102: A Humanistic Approach to Primitive Concepts On Fri, 24 Jul 1998 18:44:54 GMT, pdx4d@teleport.com (Kirby Urner) wrote: >scott@math.csuohio.edu (Brian M. Scott) wrote: >>No, the salesman and his evangelistic fervour account for a good part >>of the poor reception. Misuse of the term 'humanistic' doesn't help, >>either, especially with those of us with strong interests in the >>humanities. >Not uniformly poor, I should add. >Your attitude is already well-documented so I'm not sure why you >keep reiterating without adding any new content of your own. Pointing out the misuse of 'humanism' isn't new content? Perhaps I missed a post. (And your argument here is a dangerously two-edged sword.) > Do >you have a substantive contribution to make, or is your mission >to simply carp about mine? The real question is what substantive contribution *you* have to make that would justify the messianic trumpetings. Brian M. Scott ========================================================================= Date: Sat, 25 Jul 1998 04:28:12 GMT Reply-To: List for the discussion of Buckminster Fuller's works Sender: List for the discussion of Buckminster Fuller's works From: "Brian M. Scott" Organization: Cleveland State University Subject: Re: Calculus 102: A Humanistic Approach to Primitive Concepts On Sat, 25 Jul 1998 00:32:01 GMT, urnerk@my-dejanews.com wrote: >But unconventional mathematics (e.g. what I pitch) is greeted >with knee-jerk hostility. I have seen little if any hostility toward the mathematics itself. I have seen a good deal of hostility toward the exaggerated claims made for it, the accompanying derogation of perfectly useful mathematics and terminology, and the flack's jargon - hardly humanistic! - in which you habitually express yourself. I might also add to the list the blatant appeal to prejudice that is especially noticeable at the end of the calculus2.html page. Brian M. Scott ========================================================================= Date: Sat, 25 Jul 1998 10:34:23 GMT Reply-To: List for the discussion of Buckminster Fuller's works Sender: List for the discussion of Buckminster Fuller's works From: Kirby Urner Organization: 4D Solutions Subject: Re: Calculus 102: A Humanistic Approach to Primitive Concepts MIME-Version: 1.0 Content-Type: text/plain; charset=us-ascii Content-Transfer-Encoding: 7bit scott@math.csuohio.edu (Brian M. Scott) wrote: >Pointing out the misuse of 'humanism' isn't new content? Perhaps I >missed a post. (And your argument here is a dangerously two-edged >sword.) > It was "humanistic" in the topic header (still is). You assert I'm misusing but then fail to elaborate as to how or where. You seem to think mere assertion, minus any substantiation, is tantamount to "content". Not in my book. All I'm getting is Brian Scott doesn't like my stuff (duh). I'd be happy to get the details, but from your posts so far, I really don't. Like, what's your problem, guy? > >The real question is what substantive contribution *you* have to make >that would justify the messianic trumpetings. > >Brian M. Scott What messianic trumpetings? It's so easy to toss out these pejorative cliches but minus quotes, analysis of specific claims, it comes across as shallow projecting (to me -- maybe others consider your critique "deep"). I'm curious about what your viewpoint is, just don't feel you've done much work to elucidate it. I think my stuff might be useful and enlightening to some people, yes, otherwise I wouldn't go to the trouble. But that doesn't put me in a special category I wouldn't say. Why does _anyone_ take the time to write lengthy essays and post them on the web and/or in newsgroups and/or in print media or wherever. To say I'm egoistic is tautologous -- I'm a guy with something to share, and like so what? Kirby --------------------------------------------------------- Kirby T. Urner http://www.teleport.com/~pdx4d/kirby.html 4D Solutions http://www.teleport.com/~pdx4d/ [PGP OK] --------------------------------------------------------- ========================================================================= Date: Sat, 25 Jul 1998 11:56:50 GMT Reply-To: List for the discussion of Buckminster Fuller's works Sender: List for the discussion of Buckminster Fuller's works From: Kirby Urner Organization: 4D Solutions Subject: Re: Calculus 102: A Humanistic Approach to Primitive Concepts MIME-Version: 1.0 Content-Type: text/plain; charset=us-ascii Content-Transfer-Encoding: 7bit scott@math.csuohio.edu (Brian M. Scott) wrote: >I have seen little if any hostility toward the mathematics itself. I >have seen a good deal of hostility toward the exaggerated claims made >for it, the accompanying derogation of perfectly useful mathematics >and terminology, and the flack's jargon - hardly humanistic! - in >which you habitually express yourself. I might also add to the list >the blatant appeal to prejudice that is especially noticeable at the >end of the calculus2.html page. > >Brian M. Scott Maybe you're of the Chapman school that it's best to not read the replies when sparring with an opponent in a newsgroup? Kind of like trying to play chess but without letting yourself in on the other guy's moves. I already posted above that I don't see quadrays as providing anyone with salvation, use them as a "philosophers' toy" (my wording) to engage in rather specialized investigations into low-level concepts such as "dimension" and "linear independence" -- but not with an eye towards undermining or pushing out older Cartesian language games (which I play myself, and will continue to do so). The polemics against "hypercross dogmatics" don't have much to do with the n-tuple (n,n,n...) vectors (not problematic), nor with the methods for operating on them (extrapolated from Cartesian 3D, with metaphors to suit), but with the attendent metaphysics, which I treat as a cultural phenomenon separable from the mathematics. You've argued that I "demonize" an inner circle that doesn't exist and I've replied that "demons" are clever in my cosmology, and what I'm polemical against is closer to silly superstition (something most science-minded are only too happy to attack -- just not when the skeptical inquirer flag is planted too close to home, in their own back yard). My claim is that too many try to have it both ways: bash superstition on the one hand, but encourage laypersons to channel latent spirituality through this "higher dimensions" chatter on the other, which hyperdimensional talk academics are all too inclined to parley into some kind of awe for their supposed priest-like abilities to "visualize in any number of dimensions". In contrast, I think trying to push "four orthogonals, all mutually perpendicular" is pathetic, is not demanded by the underlying mathematics, is to transmute nonsense and the accompanying confusion into establishment-sanctioned hocus pocus (still snake oil, but a brand the righteous schoolmen are only to happy to have you buy). You may (a) deny such a cultural phenomenon exists (but I supply many exhibits of what I'm talking about at my hypercross.html) or (b) tell me I just don't understand mathematics well enough to be in a position to mount such criticisms. Maybe (b) is the case, but so far I haven't seen anyone on sci.math rushing to defend the 4-orthogonals hypercross as a necessary device. And it's also true that I find quadrays useful for countering hypercross dogmatists: having a consistent 4-tuple NeoCartesian apparatus which works well in so-called "3-space" is just unsettling enough to raise some doubt in the minds of those layperson-followers that "dimension talk" is really all that well-founded or thought through (and I suspect I have an ally in Georg Cantor on this point -- something I'd be happy to explore further, given the high degree of mathematical literacy I presume must exist in our readership). But this thread isn't even about my anti-hypercrosser thesis. I posted that essay separately (after wading through CubeWorld) and have gotten no replies to date. This topic is about an approach to calculus which encourages students to start with "change", to capture "change" on film, and to wire concepts re integration, differentiation, action, energy, power, and frequency to that conceptual framework. A lot is done to impart some basic physics and tools for thinking about "matter in motion" without diving into the crypto-compressed notations right off the bat -- which notations are cultural, could have been otherwise (i.e. are based in convention and accident of history), and aren't necessarily the "crystal core of precision" we so celebrate (aka the holy grail of science) so much as reflective of such in the hands of those with finely attuned intuitions. But then I've seen posts here saying "you can't really comprehend math, just learn to fly blind on instruments" (paraphrasing that Von Neumann quote). Well, I beg to differ, sorry. I happen to think the calculus is based in intuitions, and these can be communicated, mind-to-mind, without indulging in a lot of squiggles (those can come later, when it comes time to program our computers), squiggles we need not inflict right from the get go on kids with no previous exposure to ancient Greek (at least lets build up some associations around the DELTA first -- as a signifier of the generic "change" concept). Two quantities covary a little during a time-slice (change happens). That's all you need for a ratio, and that suggests a slope, a rate, action in time (energy). You can have any number of these covariants and you'll find that some "action packed" sequences (of frames) get more work done than others, because of the path taken vis-a-vis the gradient (directional within a field). "Work" is also relative, implies a direction of "anti- entropy" or "a fight against noise" (not to be confused with "chaos" which may simply be a very high degree of complexity -- information rich). grad cross F is curl, grad dot F is div -- one a field of vectors, one a field of scalars (where F is maybe momentum vectors). Curl connects to screws (Archimedes) and dot to surface area. Put a Riemann Sum symbol in front and you're sum-totaling a lot of these quantities (but often we dot a curl vector with dN, normal vector, to make it a scalar, otherwise what's to sum?). But why start here? Better to "get it in yer bones" first, and _then_ wade into the geeky greek stuff -- a lot of which has been automated by now anyway, and, as mathematician Keith Devlin puts it, math is about a lot more than turning out cheap imitations of thirty dollar calculators (or ten thousand dollar computers for that matter). Kirby PS: what "blatant appeal to prejudice?" I say we shouldn't diss Whorf just because he's well-endowed in the brute strength department compared to Data, who has the ability to rewire a circuit at high speed (more precision work, than heavy lifting). Both capabilities may need to be coupled with judgement and courage. I'm saying we need to respect both Whorf and Data for who they are -- not what I'd call a "blatant appeal to prejudice" would you? --------------------------------------------------------- Kirby T. Urner http://www.teleport.com/~pdx4d/kirby.html 4D Solutions http://www.teleport.com/~pdx4d/ [PGP OK] --------------------------------------------------------- ========================================================================= Date: Sat, 25 Jul 1998 14:05:33 -0700 Reply-To: List for the discussion of Buckminster Fuller's works Sender: List for the discussion of Buckminster Fuller's works From: Brian Hutchings Subject: Re: SOME DESIGN CONSIDERATIONS FOR GEODESIC SPHERICAL-DOME MESSAGE from ="List 24-JUL-1998 18:15 emailed, and posted on bit.listserv.geodesic On Mon, 20 Jul 1998, Ken G. Brown wrote: > A paper written somewhere around 1971, transcribed by Ken G. Brown > with permission from J.C. Bohlen, 980719. > --------------------------------------------------------------- > SOME DESIGN CONSIDERATIONS FOR GEODESIC SPHERICAL-DOME MINIMAL COST HOUSING Is there any chance that you could get the figures scanned and put up on a web site somewhere? Also, are there details/drawings of the actual pieces, cut-angles etc? -- Doug -------------------------------------------------------- > Fig. 1 - Pentagonal dome cluster schematic > Fig. 2 - View of erected structural elements without cladding > Fig. 3 - Close-up of hexagonal hub with struts attached > Fig. 4 - View of floor platform joist web > Fig. 5 - Diagram of strut geometry > Fig. 6 - View of partially erected dome > Fig. 7 - Close view of shingle cladding > Fig. 8 - View of completed dome - - - - - <> Brian Hutchings 25-JUL-1998 14:05 r001806@pen2.ci.santa-monica.ca.us I am assuming that the author-builder meant, *pentagonal* dodecahedral structure, in which case his complaint about "geodesics" is somewhat off, if you look at the parameters for the "2 freq.alternate" (or what ever, at 5/8 of a dome, or such) icosahedral dome, in *Geodesic Math and How To Use It_ by Pugh or Kenner (i gets mixed "up", folkses .-)... however, I did like the use of dowels, if not schematically shown; what's the Japanese word for that stuff? ========================================================================= Date: Sat, 25 Jul 1998 15:17:57 -0700 Reply-To: List for the discussion of Buckminster Fuller's works Sender: List for the discussion of Buckminster Fuller's works From: Brian Hutchings Subject: Re: Calculus 102: A Humanistic Approach to Primitive Concepts <> Brian Hutchings 25-JUL-1998 15:17 r001806@pen2.ci.santa-monica.ca.us Sagan really flipped-out with "Contact", if the requirement for ET-assistance was not just a metaphor or goad (then-again, he was a protoge of the original doc.Strangelove, Leo Szilard). I am not sure, if you are promoting the "two cultures", FC. uh, "FC"; since when did they give the Unabomer a terminal?... well, since you're "here", why don't you tell us, what that really stands-for -- family circle? [note: I can't see any "from" field on this set-up. NB: I didn't *see* the movie, but I read reviews of it; I love to hate Hollyweird !-] as for your assertion, linguistic philosophy is so rigorous, then, Why is Chomsky such a jerk?... ha-ha, rhetorical question: it (apparently) is because he's a Fabian Socialist!... seriously, in things "scientifically methodical", you have to go to the Socratic dialog, of which "dialectical materialism" is such a tepid shadow, in part because of Marx et al's obiesance to British imperialism, and the self-same's definition of capitalism, as per Adam Smith's antirepublican tract, as "trade is freedom" -- and Adam was a Founder o'th'USoA; I buh-LEAF !! -- eat the Beast (pass the Tobasco (tm)) !! http://www.tarpley.net ========================================================================= Date: Sat, 25 Jul 1998 15:54:16 -0700 Reply-To: List for the discussion of Buckminster Fuller's works Sender: List for the discussion of Buckminster Fuller's works From: Brian Hutchings Subject: Re: the mideast (as we Occidentally call it) <> Brian Hutchings 25-JUL-1998 15:54 r001806@pen2.ci.santa-monica.ca.us oh, just recalled my clip of yours; le'me put it in this way, to paraphrase Lawd Avebury: one man's good is another man's bad! IT IS THE AUTHOR'S working assumption that the words good and bad are meaningless. as if such a definition is really required (a-hem !-) -- one man's double-plus-ungood: http://ww.tarpley.net -- esp.the book on the left! ========================================================================= Date: Sat, 25 Jul 1998 15:20:36 -0400 Reply-To: List for the discussion of Buckminster Fuller's works Sender: List for the discussion of Buckminster Fuller's works From: Jeff Erickson Organization: Center for Geometric Computing, Duke University Subject: Re: Calculus 102: A Humanistic Approach to Primitive Concepts Mime-Version: 1.0 Content-Type: text/plain; charset=us-ascii Content-Transfer-Encoding: 7bit Harry H Conover wrote: > > ...those who have risen to their level of incompetence protect > their job security by refusing to employ anymore with stronger > qualifications than their own. > > If you haven't personally seen this effect in action, you've either > led a very sheltered life or remained isolated from the real world > in the sheltered ivory towers of academia -- perhaps both. Er... You must not work "in the sheltered ivory towers of academia". Peter's Principle is just as relevant here as it is out there in the "real" world. Even in math departments. -- Jeff ========================================================================= Date: Sat, 25 Jul 1998 16:57:29 -0700 Reply-To: List for the discussion of Buckminster Fuller's works Sender: List for the discussion of Buckminster Fuller's works From: Kirby Urner Subject: Re: the mideast (as we Occidentally call it) In-Reply-To: <199807252254.PAA16976@pen2.ci.santa-monica.ca.us> Mime-Version: 1.0 Content-Type: text/plain; charset="us-ascii" At 03:54 PM 7/25/98 -0700, you wrote: ><> Brian Hutchings 25-JUL-1998 15:54 > r001806@pen2.ci.santa-monica.ca.us > > oh, just recalled my clip of yours; What clip of whose? > le'me put it in this way, to paraphrase Lawd Avebury: But what this way? > one man's good is another man's bad! > > IT IS THE AUTHOR'S working assumption that the words good > and bad are meaningless. > > as if such a definition is really required (a-hem !-) > Guess you had nothing to add re Tarpley on Nietzsche. He and I both bus boys at Princeton turns out (threw away a *lot* of perfectly good food, taken but not eaten by the upper crust -- oh the horror, the horror). Kirby ========================================================================= Date: Sat, 25 Jul 1998 16:54:51 -0700 Reply-To: List for the discussion of Buckminster Fuller's works Sender: List for the discussion of Buckminster Fuller's works From: Kirby Urner Subject: Re: Calculus 102: A Humanistic Approach to Primitive Concepts In-Reply-To: <199807252217.PAA16802@pen2.ci.santa-monica.ca.us> Mime-Version: 1.0 Content-Type: text/plain; charset="us-ascii" At 03:17 PM 7/25/98 -0700, you wrote: ><> Brian Hutchings 25-JUL-1998 15:17 > r001806@pen2.ci.santa-monica.ca.us > > Sagan really flipped-out with "Contact", if Seems you've lapsed back into babble -- enjoyed the brief moments with a more lucid "Charlie" ('Flowers for Algernon'). Kirby ========================================================================= Date: Sat, 25 Jul 1998 17:48:08 -0700 Reply-To: List for the discussion of Buckminster Fuller's works Sender: List for the discussion of Buckminster Fuller's works From: Brian Hutchings Subject: Re: the mideast (as we Occidentally call it) MESSAGE from ="List 25-JUL-1998 17:40 At 03:54 PM 7/25/98 -0700, you wrote: ><> Brian Hutchings 25-JUL-1998 15:54 > r001806@pen2.ci.santa-monica.ca.us > > oh, just recalled my clip of yours; What clip of whose? > le'me put it in this way, to paraphrase Lawd Avebury: But what this way? > one man's good is another man's bad! > > IT IS THE AUTHOR'S working assumption that the words good > and bad are meaningless. > > as if such a definition is really required (a-hem !-) > Guess you had nothing to add re Tarpley on Nietzsche. He and I both bus boys at Princeton turns out (threw away a *lot* of perfectly good food, taken but not eaten by the upper crust -- oh the horror, the horror). Kirby - - - - - <> Brian Hutchings 25-JUL-1998 17:48 r001806@pen2.ci.santa-monica.ca.us I *did* have some thing to say, about 5' worth, but it seems that it was swallowed by my faulty connection, via school. ========================================================================= Date: Sat, 25 Jul 1998 17:50:31 -0700 Reply-To: List for the discussion of Buckminster Fuller's works Sender: List for the discussion of Buckminster Fuller's works From: Brian Hutchings Subject: Re: Calculus 102: A Humanistic Approach to Primitive Concepts MESSAGE from ="List 25-JUL-1998 17:40 At 03:17 PM 7/25/98 -0700, you wrote: ><> Brian Hutchings 25-JUL-1998 15:17 > r001806@pen2.ci.santa-monica.ca.us > > Sagan really flipped-out with "Contact", if Seems you've lapsed back into babble -- enjoyed the brief moments with a more lucid "Charlie" ('Flowers for Algernon'). Kirby - - - - - <> Brian Hutchings 25-JUL-1998 17:50 r001806@pen2.ci.santa-monica.ca.us ** yours, Kirbomatic. -- we came *this close* to "The End of History" -- http://www.tarpley.net oops; I meant, "**" that! ========================================================================= Date: Sat, 25 Jul 1998 18:03:00 -0700 Reply-To: List for the discussion of Buckminster Fuller's works Sender: List for the discussion of Buckminster Fuller's works From: Brian Hutchings Subject: Re: the mideast (as we Occidentally call it) MESSAGE from ="List 25-JUL-1998 17:40 <> Brian Hutchings 25-JUL-1998 15:54 r001806@pen2.ci.santa-monica.ca.us oh, just recalled my clip of yours; le'me put it in this way, to paraphrase Lawd Avebury: one man's good is another man's bad! IT IS THE AUTHOR'S working assumption that the words good and bad are meaningless. as if such a definition is really required (a-hem !-) -- one man's double-plus-ungood: http://ww.tarpley.net -- esp.the book on the left! - - - - - <> Brian Hutchings 25-JUL-1998 18:02 r001806@pen2.ci.santa-monica.ca.us last night, or the night before ("speerchul nite" on KPFK's show of Roy o'Hollywood, after midnight on weekdays except Friday), I heard Shin-zen Young dyscussing generical "tantra", meaning a "text" or body of doctrine; in referring to the *sexual* tantra, he suggested that, if [however vastly unlimited or multiply-connected or what ever] orgasm is such a spiritual transcend for one, one ought to (at least) prick oneself, to see if one can remain as *equanamous* with pain. now, that is not to say, in spite of an orgyroomfull o'sadomasochists, that One man's torture is another man's enlightenment; is it? ========================================================================= Date: Sat, 25 Jul 1998 22:12:14 GMT Reply-To: List for the discussion of Buckminster Fuller's works Sender: List for the discussion of Buckminster Fuller's works From: lazariuk@MY-DEJANEWS.COM Organization: Deja News - The Leader in Internet Discussion Subject: Re: Calculus 102: A Humanistic Approach to Primitive Concepts In article <35b916b5.24036715@news.csuohio.edu>, scott@math.csuohio.edu (Brian M. Scott) wrote: > On Fri, 24 Jul 1998 19:22:11 GMT, lazariuk@my-dejanews.com wrote: > >Let me suggest that mathematics will become more relevant > > Relevant to what? It's hard to think of a facet of life to which > mathematics is *not* relevant. Not relevant to what but rather relevant to who. As in the people being taught and I am not meaning relevant in an objective sense but more in a subjective sense. My son seems to learn in a very comprehensive and ejoyable way that which to him seems to be relevant even if only socially relevant amoung his peers. > > when those teaching > >it see that those questions are within the purview of science. > > Can you demonstrate that they are? No one else seems to have made a > very credible go at it yet. Forgive what may be my ignorance as I am not well school educated but I was under the assumption that people were doing science because they wanted to understand more about why we are here and where we are headed and what is the proper course of behavior. At least that is what some have told me. How would one demonstrate what questions are within the purview of science except by showing what motivates people to do science? How can anyone do that? > > At least to > >the extent that they appreciate the mystery. > > That has nothing to do with whether the questions are within the > purview of science. Brian, if it not our sense or rather our experience of mystery, that determines what is within the purview of science - then what is? And if you reply with a comprehensive range of what you may consider practical goals or pressing necessities do you not feel the word science large enough to *also* include the questions posed? Jack -----== Posted via Deja News, The Leader in Internet Discussion ==----- http://www.dejanews.com/rg_mkgrp.xp Create Your Own Free Member Forum ========================================================================= Date: Sun, 26 Jul 1998 00:19:16 GMT Reply-To: List for the discussion of Buckminster Fuller's works Sender: List for the discussion of Buckminster Fuller's works From: Kirby Urner Organization: 4D Solutions Subject: Re: An Overview of the Quadray Coordinate System MIME-Version: 1.0 Content-Type: text/plain; charset=us-ascii Content-Transfer-Encoding: 7bit pdx4d@teleport.com (Kirby Urner) wrote: > > > AN OVERVIEW OF THE QUADRAY COORDINATE SYSTEM > by Kirby Urner > 4D Solutions > July 9, 1998 > > >NeoCartesian Coordinates > Since posting this essay July 9 1998, the following exchange: === Date: Wed, 22 Jul 1998 14:11:30 -1000 From: "D. Lloyd Jarmusch" X-To: pdx4d@teleport.com Subject: Quadrays and Nuclear Fusion I was astonished to find your web pages on the quadray system. A month or so ago I had no idea that anyone besides myself had ever conceived the system, much less developed it to the point you have. Your work is brilliant and well presented, and you are to be congratulated for your contributions to the advancement of knowledge. I developed the system myself, independently, back in 1981, and at the time I also called it the quadray system (lately I had been calling it a quadraxial Cartesian system, I notice you call it a NeoCartesian system). I was somewhat surprised that our systems are so similar, right down to the notation for coordinates and the fact that every point has a unique address where at least one of the coordinates is zero and all the others are non negative. In retrospect I should not have been surprised since the system is so natural that it was inevitable that others would come up with it as well. I though you might be interested to know that when I conceived the system myself in 1981 I immediately thought that, since it seemed more "natural" than the rectangular Cartesian system it would be useful in solving some of the problems that physics is struggling to solve using the rectangular system. The first problem of physics I thought to address was the confinement of plasmas in nuclear fusion. It seemed to me that the quadray system revealed a fundamental aspect of nature, that is that space is what I call "four-directional". It seemed to me that the problem of magnetic confinement might be better addressed if physicists were to concentrate on confining the movement of the plasma in any of the four directions, thus forming the plasma into a tetrahedral shape. The problem of magnetic confinement is very complex, and I was merely a freshman studying philosophy, and none of the physicists I talked to were interested in my new coordinate system, so I gave up the problem after a short while. Suddenly in 1993 it occurred to me that fusion might be achieved by colliding beams of hydrogen from the four directions indicated by the quadray system. I investigated the problem of fusion again and became convinced that my design for a nuclear fusion reactor had merit and ought to be developed further. I set out to patent and fund the reactor, and after several years of effort I am finally getting the patent. I just paid the issue fee for the patent last week. I have been trying to develop support for the concept that space is four-directional, especially in the usenet newsgroup sci.physics.fusion. A reader of the group emailed me a paper by you about the quadray system. I was very pleased to read the paper and to visit your excellent webpages on the subject. I cannot express to you how happy I am that you have developed the system so well, and have presented it in such a beautiful and well thought-out format. I will refer to your webpages often. Thank you so much for your surperb work. Aloha, D. Lloyd Jarmusch P.O. Box 677 Kilauea, Hawaii 96754 ======= Date: Wed, 22 Jul 1998 17:45:14 -0700 To: "D. Lloyd Jarmusch" From: Kirby Urner Subject: Re: Quadrays and Nuclear Fusion Thanks for your email re quadrays sir! The essential ideas came to my awareness thanks to David Chako, who shared them on Synergetics-L, a listserv re Bucky Fuller's philosophical geometry which I administer. In the 'For further reading' section of http://www.teleport.com/~pdx4d/quadrays.html you'll find a hyperlink to a verbatim excerpt from the Syn-L archives showing where David first introduced his idea (along with some of our initial feedback) ["Genesis on Synergetics-L"]. Josef Hasslberger was likewise entertaining similar notions, minus a formalized notation, and you'll find my link to his web-page on the concept at quadcolors.html (a collaborative work based on his ideas regarding quadrays and color). He calls them Tetra Space Co-ordinates. My contribution to the literature involved coming up with a distance formula and formalizing an XYZ<->quadrays conversion convention (quadxyz.html) that makes this apparatus especially useful for converging with Fuller's synergetics (the main focus of my website, 'Synergetics on the Web'). I also developed source code for outputting polyhedra saved in quadray coordinates, to Povray for ray tracing (some of the renderings need to be redone -- aspect ratio off, giving a slightly 'quashed' appearance). FoxPro Advisor, a computer magazine, has recently solicited an article on my use of VFP to do this kind of geometry work (a novel usage from the point of view of your average bread and butter xBase programmer). I give you all this by way of background and orientation vis-a-vis my viewpoint. That you came up with this same apparatus independently in 1981 (when I was just beginning to get interested in Fuller) is very interesting to me and no doubt your long term consideration of this system in tandem with physics challenges will open up some new vistas, at least from our point of view on Synergetics-L. I should also mention that David Chako has called them 'tetrays' and further elaborated the system, using the equivalence of all (n,n,n,n) from a spatial point of view to introduce a temporal index. His coordinate system increases with frequency through time and vectors come out as probability calculations (ala Pascal's triangle/ tetrahedron) relating to pathways from the origin to a terminus. But I leave the details for him to explain -- I don't pretend competence vis-a-vis his 'tetray' apparatus. As you note, I'm basically using quadrays as a close analog of XYZ, call it NeoCartesian for this reason, and use it in philosophical circles to do Wittgensteinian-type investigations of low-level math concepts e.g. "dimension" and "linear independence" (quadphil.html). Aloha, Kirby PS: with your permission, I'd like to forward your email, and this response, to Synergetics-L for sharing/archiving. I'd also like to save this exchange from a hyperlink at quadrays.html to better include your trajectory and give us a jumping-off point for future developments (both colla- borative and solo). Thanks again for getting in touch. As I'm sure you know, it's not unusual for ideas to occur to lots of folks, unbeknownst to one another -- usually indicative of something in the wind (zeitgeist and all that). === Date: Wed, 22 Jul 1998 16:06:10 -1000 From: "D. Lloyd Jarmusch" To: Kirby Urner Subject: Re: Quadrays and Nuclear Fusion Kirby Urner wrote: > Thanks for your email re quadrays sir! You are more than welcome. Thank you for the additional info in your last email. > > > ... with your permission, I'd like to forward your email, > and this response, to Synergetics-L for sharing/archiving. > I'd also like to save this exchange from a hyperlink at > quadrays.html to better include your trajectory and give > us a jumping-off point for future developments I would be flattered to have you forward my email or post it where ever you like. Thank you and aloha for now, D. Lloyd Jarmusch ===== Date: Wed, 22 Jul 1998 22:04:05 -0700 To: "D. Lloyd Jarmusch" From: Kirby Urner Subject: Re: Quadrays and Nuclear Fusion Cc: synergetics-l@teleport.com >I would be flattered to have you forward my email or post it where ever >you like. > >Thank you and aloha for now, > >D. Lloyd Jarmusch > Our email exchange (sharing genesis of quadrays in our respective scenarios) is now linked from the 'For Further Reading' section of 'An Introduction to Quadrays' (www.teleport.com/~pdx4d/quadrays.html). Lets keep in touch. Your intuition that "space is four-directional" is likewise what Bucky Fuller was communicating when saying space is "four dimensional" (cite www.teleport.com/~pdx4d/terms.html#4d). Ciao, Kirby 4D Solutions --------------------------------------------------------- Kirby T. Urner http://www.teleport.com/~pdx4d/kirby.html 4D Solutions http://www.teleport.com/~pdx4d/ [PGP OK] --------------------------------------------------------- ========================================================================= Date: Sun, 26 Jul 1998 07:03:50 GMT Reply-To: List for the discussion of Buckminster Fuller's works Sender: List for the discussion of Buckminster Fuller's works From: "Brian M. Scott" Organization: Cleveland State University Subject: Re: Calculus 102: A Humanistic Approach to Primitive Concepts On Sat, 25 Jul 1998 22:12:14 GMT, lazariuk@my-dejanews.com wrote: > scott@math.csuohio.edu (Brian M. Scott) wrote: >> On Fri, 24 Jul 1998 19:22:11 GMT, lazariuk@my-dejanews.com wrote: >> > when those teaching >> >it see that those questions are within the purview of science. >> Can you demonstrate that they are? No one else seems to have made a >> very credible go at it yet. >Forgive what may be my ignorance as I am not well school educated No need to apologize. > but I was >under the assumption that people were doing science because they wanted to >understand more about why we are here and where we are headed and what is the >proper course of behavior. At least that is what some have told me. I imagine that some scientists have such motivations. In my experience, though, curiosity about how the universe works is more common. >How would one demonstrate what questions are within the purview of science >except by showing what motivates people to do science? How can anyone do that? I don't think that what *motivates* people to do science necessarily tells us much about what problems science can tackle. After all, one's motivation might not amount to much more than 'I'm good at it, and I need to eat'! One would do better to consider what kinds of questions are best addressed by the methods of science. Science is in general much better at answering 'How?' than 'For what purpose?' >> > At least to >> >the extent that they appreciate the mystery. >> That has nothing to do with whether the questions are within the >> purview of science. >Brian, if it not our sense or rather our experience of mystery, that >determines what is within the purview of science - then what is? This question honestly makes no sense to me. I'm certainly not claiming that scientists have no sense of wonder or mystery; quite the contrary, in my experience. It may even extend to these particular questions, but I can't for the life of me see what that has to do with the scope of science. For me, oversimplifying a bit, science is a particular approach to studying what we commonly call the real world, and the nature of that approach largely determines the kinds of questions that fall within the scope of science. Others, including no doubt some scientists, might disagree, but I see no way to bring your questions into the fold. 'Why are we here?' seems to me completely unanswerable for the foreseeable future; moreover, I can't think of a plausible answer that would have any effect on the way I conduct my life, so I find the question very uninteresting. Finding the proper course of behavior in general is a matter for philosophy, or ethics, or religion; all science can do is supply information regarding what choices are actually available and what their consequences are. > And if you >reply with a comprehensive range of what you may consider practical goals or >pressing necessities do you not feel the word science large enough to *also* >include the questions posed? My conception of science goes far beyond practical goals and pressing necessities; indeed, my own interests by and large have little to do with either. But I still don't think that your questions are capable of scientific study. Brian M. Scott ========================================================================= Date: Sun, 26 Jul 1998 03:53:25 GMT Reply-To: List for the discussion of Buckminster Fuller's works Sender: List for the discussion of Buckminster Fuller's works From: "Brian M. Scott" Organization: Cleveland State University Subject: Re: Calculus 102: A Humanistic Approach to Primitive Concepts On Sat, 25 Jul 1998 11:56:50 GMT, pdx4d@teleport.com (Kirby Urner) wrote: >scott@math.csuohio.edu (Brian M. Scott) wrote: >>I have seen little if any hostility toward the mathematics itself. I >>have seen a good deal of hostility toward the exaggerated claims made >>for it, the accompanying derogation of perfectly useful mathematics >>and terminology, and the flack's jargon - hardly humanistic! - in >>which you habitually express yourself. I might also add to the list >>the blatant appeal to prejudice that is especially noticeable at the >>end of the calculus2.html page. >I already posted above that I don't see quadrays as providing >anyone with salvation, use them as a "philosophers' toy" (my >wording) to engage in rather specialized investigations into >low-level concepts such as "dimension" and "linear independence" >-- but not with an eye towards undermining or pushing out >older Cartesian language games (which I play myself, and will >continue to do so). Yes, occasionally you remember the audience for which you're writing. I pay more attention to the message that you send in your less guarded moments and to other audiences, which is that the traditional language is bad and needs to be superseded. >You've argued that I "demonize" an inner circle that doesn't >exist and I've replied that "demons" are clever in my cosmology, How *you* use the term is irrelevant; you apparently understood my meaning. >and what I'm polemical against is closer to silly superstition ... that is virtually non-existent amonst serious mathematicians. >My claim is that too many try to have it both ways: bash >superstition on the one hand, but encourage laypersons to >channel latent spirituality through this "higher dimensions" >chatter on the other, which hyperdimensional talk academics >are all too inclined to parley into some kind of awe for >their supposed priest-like abilities to "visualize in any >number of dimensions". Your claim is horseshit - and that's putting it politely. See below. >In contrast, I think trying to push "four orthogonals, all >mutually perpendicular" is pathetic, is not demanded by the >underlying mathematics, is to transmute nonsense and the >accompanying confusion into establishment-sanctioned hocus >pocus (still snake oil, but a brand the righteous schoolmen >are only to happy to have you buy). To say that four lines in R^4 are mutually orthogonal is perfectly meaningful and certainly not nonsense. If you have a problem with it, it's because you're still naively trying to give it a physical meaning in everyday physical space. Worse, you're imagining that most mathematicians do the same. Elsewhere you write: 'The ego's best defense is to project itself as powerless, a victimized, innocent bystander to the holocaust. The circle is vicious: a self-righteous, abused "little me" is a painful thing to be, begetting a stronger need for comforting palliatives and escapist blockbuster fantasies.' Physician, heal thyself. >You may (a) deny such a cultural phenomenon exists (but I >supply many exhibits of what I'm talking about at my >hypercross.html) No, you don't. You mention Abbott's _Flatland_, and you provide links to several pages where various people associate some notion(s) of dimension with various more or less religious concepts, in contexts ranging from science fiction through what appears to be some form of spiritualism to quantum mechanics. You provide evidence that the word 'dimension' is a convenient handle for people who don't know much about its mathematical uses; you provide NO evidence for your oft-repeated claim that any significant number of mathematicians claim to be able to visualize more than three spatial dimensions or encourage others to believe in such 'supposed priest-like abilities'. > or (b) tell me I just don't understand >mathematics well enough to be in a position to mount >such criticisms. >Maybe (b) is the case, but so far I haven't seen anyone on >sci.math rushing to defend the 4-orthogonals hypercross as a >necessary device. And it's also true that I find quadrays >useful for countering hypercross dogmatists: having a >consistent 4-tuple NeoCartesian apparatus which works well >in so-called "3-space" is just unsettling enough to raise >some doubt in the minds of those layperson-followers that >"dimension talk" is really all that well-founded or thought >through Do you know enough mathematics to be aware of the fact that there are many different notions of dimension? If so, you must also be aware that for R^n all of the important ones coincide: the dimension of R^n is n. Any doubts that you raise are unjustified, and raising them is therefore a disservice. The rough-and-ready notion of dimension as a degree of freedom, on the other hand, *is* a useful notion. If you wanted to do something useful with your essentially barycentric coordinates, you'd point out that although four of them are used to specify a point, there are really only three degrees of freedom. This is particularly evident after you've normalized them. >But then I've seen posts here saying "you can't really >comprehend math, just learn to fly blind on instruments" >(paraphrasing that Von Neumann quote). Well, I beg to >differ, sorry. So do I. > I happen to think the calculus is based >in intuitions, and these can be communicated, mind-to-mind, >without indulging in a lot of squiggles (those can come >later, when it comes time to program our computers), >squiggles we need not inflict right from the get go on >kids with no previous exposure to ancient Greek (at least >lets build up some associations around the DELTA first >-- as a signifier of the generic "change" concept). Some can, some can't. Some of the intuitions can't be communicated until you have the vocabulary (including symbols) to express them. And Greek has nothing to do with it. >Two quantities covary a little during a time-slice >(change happens). This (mis)use of 'co-vary' is a perfect example of what sets teeth on edge. What's wrong with saying that two quantities change over time, and the change in one is related (somehow) to the change in the other? When you say that x and y co-vary, I expect dy/dx to be positive. > That's all you need for a ratio, and >that suggests a slope, a rate, action in time (energy). *If* this were true, teaching calculus would be a snap. Unfortunately, it's not: if you're lucky it suggests a rate, but it certainly doesn't suggest a slope. >"Work" is also relative, implies a direction of "anti- >entropy" or "a fight against noise" Not true. >PS: what "blatant appeal to prejudice?" I say we shouldn't >diss Whorf just because he's well-endowed in the brute >strength department compared to Data, who has the ability >to rewire a circuit at high speed (more precision work, >than heavy lifting). Both capabilities may need to be >coupled with judgement and courage. I'm saying we need >to respect both Whorf and Data for who they are -- not >what I'd call a "blatant appeal to prejudice" would you? Have you looked at the language that you actually used? If it isn't a blatant appeal to anti-intellectual prejudice, you must have the biggest tin ear this side of Oz. I quote: 'The stories are not all about technogeeks circumventing strong players (in other dimensions) using various dweeby cyphers that "the knuckleheads" can't grok. On the contrary, many stories are about ordinary folk with no "special training" or academic degrees networking to revector energy (aka finances) in ways that keep the technogeeks from blowing everything sky high because they feel "misunderstood" or "resent the unintelligent" or whatever sick and twisted form of misanthropy feeds their mad scientist fantasies of making others pay.' You will perhaps respond that this is intended as a caricature. Perhaps it is, but if so, the fact's not obvious; moreover, the view expressed is not obviously inconsistent with your rhetoric here. Brian M. Scott ========================================================================= Date: Mon, 27 Jul 1998 02:07:10 GMT Reply-To: List for the discussion of Buckminster Fuller's works Sender: List for the discussion of Buckminster Fuller's works From: Kirby Urner Organization: 4D Solutions Subject: Re: Calculus 102: A Humanistic Approach to Primitive Concepts MIME-Version: 1.0 Content-Type: text/plain; charset=us-ascii Content-Transfer-Encoding: 7bit scott@math.csuohio.edu (Brian M. Scott) wrote: >Yes, occasionally you remember the audience for which you're writing. >I pay more attention to the message that you send in your less guarded >moments and to other audiences, which is that the traditional language >is bad and needs to be superseded. > I think we should do more with sphere-packing in K-12, which is more 60-degree focussed, cutting into the 90-degree intensive XYZ time-share if necessary. Too few kids know that S = 10 ff + 2 or that rhombic dodecahedra of volume 6 (relative to the unit volume tetrahedron) fill space etc. These are not "secret teachings" I share in my less guarded moments, but clearly spelled out curricula, complete with outlines, essays and graphics, at my Oregon Curriculum Network and other websites. >>You've argued that I "demonize" an inner circle that doesn't >>exist and I've replied that "demons" are clever in my cosmology, > >How *you* use the term is irrelevant; you apparently understood my >meaning. > What, I'm a second class user of my own language? > >Your claim is horseshit - and that's putting it politely. See below. > Yawn. School yard invective is no substitute for intelligent communication. >To say that four lines in R^4 are mutually orthogonal is perfectly >meaningful and certainly not nonsense. If you have a problem with it, >it's because you're still naively trying to give it a physical meaning >in everyday physical space. Worse, you're imagining that most >mathematicians do the same. > It's meaningful as a tautology, sure. You label as "naive" those who think "orthogonal" means something "physical" in "physical space". That's arrogant on your part -- as if people had no right to expect anything physical. Mabye little kids just need to accept this "dimension talk" without question, but once we're adults, we maybe don't "fear the rod" (aka the hypercross) quite so much. >Elsewhere you write: 'The ego's best defense is to project itself as >powerless, a victimized, innocent bystander to the holocaust. The >circle is vicious: a self-righteous, abused "little me" is a painful >thing to be, begetting a stronger need for comforting palliatives and >escapist blockbuster fantasies.' Physician, heal thyself. > You should have put the "Physician, heal thyself" in quotes as well, as I've used that too. Or least I have "Heal Thyself" next to a (rather poorly sketched) caduceus (symbol associated with the healing arts) at my Philosophers' Network site (down for the moment, while Xoom upgrades its hardware). I appreciate your providing us with a quote by the way. Now maybe we're getting someplace. Do I sound like a powerless, victimized innocent bystander to you? True, I duck out to see a movie now and then. Must be an ego in there somewhere, no question. >>You may (a) deny such a cultural phenomenon exists (but I >>supply many exhibits of what I'm talking about at my >>hypercross.html) > >No, you don't. You mention Abbott's _Flatland_, and you provide links >to several pages where various people associate some notion(s) of >dimension with various more or less religious concepts, in contexts >ranging from science fiction through what appears to be some form of >spiritualism to quantum mechanics. Exactly. That's the cultural phenomenon I'm talking about. >You provide evidence that the word 'dimension' is a convenient handle >for people who don't know much about its mathematical uses; you provide >NO evidence for your oft-repeated claim that any significant number of >mathematicians claim to be able to visualize more than three spatial >dimensions or encourage others to believe in such 'supposed priest-like >abilities'. "As for analogous figures in four or more dimensions, we can never fully comprehend them by direct observation. In attempting to do so, however, we seem to peep through a chink in the wall of our physical limitations, into a new world of dazzling beauty." -- H.S.M Coxeter, 'Regular Polytopes', Preface to 1st Edition I don't disagree about the beauty and elegance of the decompressed n-tuple data structures, e.g. the stuff on Plate II or Plate IV. But I don't buy that the reason I can't visualize 4 mutual orthogonals has anything to do with my "physical limitations" or that Coxeter's peep hole is owing to any greater ability to visualize a nonsensical proposition (which isn't to say I don't credit him with far greater abilities than mine as a geometer -- I most certainly do). > >Do you know enough mathematics to be aware of the fact that there are >many different notions of dimension? Sure, I say prefrequency quadrays are 4D for example. And a physical model involving energy in some form (e.g. quadrays apparatus made of metal or wood or plastic) is 4D+ (more than 4D -- because of the "frequency added" making the generic template special-case, or "mortal" -- mathematical term meaning "with a beginning, middle and end in the time dimension"). >If so, you must also be aware >that for R^n all of the important ones coincide: the dimension of R^n >is n. I usually am interested in discrete spaces, point populations. I may use n-tuple addressing, but I don't posit continuity, infinitely close proximity, nor the infinite vastness of my coordinated sets. Definite sets and multiple possible indexing schemes accessing the same points: this is the computer world in which I operate (professionally and for money). For all I care (professionally speaking), we don't even have "real numbers" (hence no R^n either). We have terminals (any floating point storable) and algorithmics (PI is an icon for an iterative loop, a program, not a "real number" because it has no finite storable form -- except as an executable). This is definitional, low-level -- but still mathematical. Seems like sometimes mathematicians give lip service to how consistency and precision are the hallmarks of their game-playing, but then turn up their noses if someone comes along with a consistent and precise symbol game that just doesn't happen to be the same as theirs. As if Universe had room for only one consistent "dimension talk" (e.g. the R^n stuff). Your math is just one of many. As Ian Stewart put it recently (in a talk here in Portland), he can easily imagine himself walking into a room in future, and knowing that math is going on all around him, but not having the least idea of how it operates -- until maybe Keith Devlin comes along and "makes the invisible visible", i.e. maybe renders this future more intelligible to the old timers. I note that a discrete set of points addressed as (x,y,z) in Cartesian style, or (a,b,c,d) in NeoCartesian style, may also be addressed purely sequentially, i.e. that the number of coordinates bears no intrinsic relationship to either (a) degrees of freedom or (b) the number of dimensions. I don't claim to be the first to make this observation -- didn't Cantor? >Any doubts that you raise are unjustified, and raising them is >therefore a disservice. I disagree. This is healthy give and take and to try suppressing it out of hand because "a disservice" is to sound like a dogmatist. >The rough-and-ready notion of dimension as a >degree of freedom, on the other hand, *is* a useful notion. If you >wanted to do something useful with your essentially barycentric >coordinates, ...not essentially barycentric, I disagree... Recently got email from a guy in Hawaii, a scientist, who thought up quadrays in 1981, even called them that and used the same notation (posted our correspondence yesterday in this newsgroup) . Pretty cool! Had never heard of him before (I got my quadrays stuff from David Chako, came up with some innovations that some starving kid in India has probably already thought of, long ago). >you'd point out that although four of them are used to >specify a point, there are really only three degrees of freedom. This depends on definitions. I say my degrees of freedom are (a) to expand/contract (b) to rotate about an axis and (c) to turn inside-out. You might add "translation" but my system is anchored, not all that free to move away from the origin. If this sounds a bit like an excerpt from the that "Chinese Encyclopedia" in Foucault (quoting from Borges as I recall) in 'The Order of Things' that's somewhat intentional. >This is particularly evident after you've normalized them. > I can add pairs of quadrays to get 6 pairs of orthogonal vectors emanating from the origin in an XYZ "jack" apparatus -- is this what you mean by "normalized"? Remember, in your game 'vector reversal' (application of the '-' sign) is lumped under scalar multiplication. But in my game I say a change in orientation (in this case by 180 degrees) is a different kind of operation than grow/shrink with no change in direction (see quadphil.html). For this reason, I don't see '-' vectors as "less basic" than '+' vectors in XYZ. Positive mirrors Negative and vice versa, but both should be on equal footing -- the XYZ game seems unbalanced because of its positive bias. My students think so too. >>But then I've seen posts here saying "you can't really >>comprehend math, just learn to fly blind on instruments" >>(paraphrasing that Von Neumann quote). Well, I beg to >>differ, sorry. > >So do I. > Good, glad to hear it. >> I happen to think the calculus is based >>in intuitions, and these can be communicated, mind-to-mind, >>without indulging in a lot of squiggles (those can come >>later, when it comes time to program our computers), >>squiggles we need not inflict right from the get go on >>kids with no previous exposure to ancient Greek (at least >>lets build up some associations around the DELTA first >>-- as a signifier of the generic "change" concept). > >Some can, some can't. Some of the intuitions can't be communicated >until you have the vocabulary (including symbols) to express them. >And Greek has nothing to do with it. > Again, we agree. Nor English for that matter. >>Two quantities covary a little during a time-slice >>(change happens). > >This (mis)use of 'co-vary' is a perfect example of what sets teeth on >edge. What's wrong with saying that two quantities change over time, >and the change in one is related (somehow) to the change in the other? >When you say that x and y co-vary, I expect dy/dx to be positive. > To me "covary" simply means the variables are coupled in some way such that a change in one always occurs in tandem with a change in the other. I understand the difference between directly and inversely proportional, linear and non-linear, but I find "covary" a fine combination of public domain roots to convey the simple notion of "coupled change". I think maybe we'd have an easier time understanding one another if you thought of me as an Irishman who refuses to speak English. In Irish, "covary" means "coupled change". If that sets your teeth on edge, maybe that's because you speak English (a language I've never bothered to learn -- I have no need for it given I already have all the technical stuff I need in my native language -- i.e. this language here, what you're now reading). Just a thought experiment -- still trying to figure out why you think I'm second class e.g. why what _I_ mean by demon is "irrelevant". >> That's all you need for a ratio, and >>that suggests a slope, a rate, action in time (energy). > >*If* this were true, teaching calculus would be a snap. >Unfortunately, it's not: if you're lucky it suggests a rate, but it >certainly doesn't suggest a slope. > Could be a slippery slope, getting steeper and steeper. Call it a curve. Covariants plot a curve in phase space, and sometimes "circle" a strange attractor in dynamical systems. >>"Work" is also relative, implies a direction of "anti- >>entropy" or "a fight against noise" > >Not true. > Thinking of Stuart Kaufmann's comment that there's "something funny about the concept of work in physics". I've explored this in more detail on sci.physics. Anyway, I was talking about real work in the real world, what I'm likely to pay for, reward, accept as work. If it ain't a "fight against noise" or in the direction of "anti-entropy" then I have to wonder why you get paid for it. Physics doesn't own "work" anymore than mathematics owns "normal" and sometimes my work (i.e. my fight against entropy) puts me at loggerheads when it comes to how best to operate with key terms in the public domain. >Have you looked at the language that you actually used? If it isn't a >blatant appeal to anti-intellectual prejudice, you must have the >biggest tin ear this side of Oz. I quote: 'The stories are not all >about technogeeks circumventing strong players (in other dimensions) >using various dweeby cyphers that "the knuckleheads" can't grok. On >the contrary, many stories are about ordinary folk with no "special >training" or academic degrees networking to revector energy (aka >finances) in ways that keep the technogeeks from blowing everything >sky high because they feel "misunderstood" or "resent the >unintelligent" or whatever sick and twisted form of misanthropy feeds >their mad scientist fantasies of making others pay.' You will perhaps >respond that this is intended as a caricature. Perhaps it is, but if >so, the fact's not obvious; moreover, the view expressed is not >obviously inconsistent with your rhetoric here. > First of all, I'm competent to pass as a technogeek. And I use various dweeby cyphers and for the most part the knuckleheads I want to remain clueless do so remain. But I don't do so out of misanthropy, much as I may have personal differences with this or that jerk. As a technogeek, I am often exposed to the chauvanism of peers who speek disparagingly of those they consider less meritorious, (e.g. because not so technically oriented) while meanwhile devoting much of their time to the design and/or production of devices the main intent of which is to implement the killing of humans, efficiently, in great numbers, over great distances. I call this misanthropic behavior and appreciate the work of ordinary folk, many with no "special training" who take to the streets if necessary, or work in other more subtle ways, to make sure this brand of technogeekery has an ever harder time cowing politicians into providing it with funding (usually by means of scary pictures of what technogeeks on "the other side" might be doing to get funding of their own). In the 'for further reading' section of my essay I link to a "technogeeks of the world unite" cartoon (drawn by me). I am in the process of so uniting with technogeeks around the world. I thought "Dr. Strangelove" was a great movie and appropriate parody of the "mad scientist" as a stereotype. The American Friends Service Committee (mentioned in the essay) is the social action arm of Quakers, a religious society commited to nonviolence and removing opportunities for outward wars. Need I say more? I'm not apologetic about any of the above. Kirby --------------------------------------------------------- Kirby T. Urner http://www.teleport.com/~pdx4d/kirby.html 4D Solutions http://www.teleport.com/~pdx4d/ [PGP OK] --------------------------------------------------------- ========================================================================= Date: Mon, 27 Jul 1998 15:18:10 GMT Reply-To: List for the discussion of Buckminster Fuller's works Sender: List for the discussion of Buckminster Fuller's works From: Kirby Urner Organization: 4D Solutions Subject: Re: Calculus 102: A Humanistic Approach to Primitive Concepts MIME-Version: 1.0 Content-Type: text/plain; charset=us-ascii Content-Transfer-Encoding: 7bit lrmead@orca.st.usm.edu (Larry Mead) wrote: >Mr. Urner, I was very careful in my choice of words, intentionally seeking >to get across some essential points you keep talking around but not to, >without reference to personal feelings. Since you now want to reduce this >discussion to personal insults (see above) this will end our discussion. Insulting perhaps, but not all that personal -- reiterating points made before we met, more of my standard position. But true enough I was here to have a discussion with another intelligent individual on equal footing, not to sit at your feet as a student of your philosophy (which isn't to say I don't have teachers -- I do, and many). Kirby --------------------------------------------------------- Kirby T. Urner http://www.teleport.com/~pdx4d/kirby.html 4D Solutions http://www.teleport.com/~pdx4d/ [PGP OK] --------------------------------------------------------- ========================================================================= Date: Mon, 27 Jul 1998 15:52:26 GMT Reply-To: List for the discussion of Buckminster Fuller's works Sender: List for the discussion of Buckminster Fuller's works From: Kirby Urner Organization: 4D Solutions Subject: Re: Calculus 102: A Humanistic Approach to Primitive Concepts MIME-Version: 1.0 Content-Type: text/plain; charset=us-ascii Content-Transfer-Encoding: 7bit lrmead@orca.st.usm.edu (Larry Mead) wrote: >I objected to the flowery and pedantic use of language in the original >post (see firsst paragraph for a good example). Here's the first paragraph: The application of humanities techniques in the domain of teaching mathematics results in the practice of building associative semantic networks around idiom, alliteration, and word plays, as a way of anchoring the more crypto-compressed notational nuggets which traditionally populate a math text. I don't see this as particularly florid prose, more a listing of humanities techniques: use of idiom, alliteration, word plays, as a means of building semantic networks (standard practice, par for the course, tools of the trade). It's a style of thinking. We're using it to teach math. "Crypto-compressed notational nuggets" makes use of imagery, but also implies gold (suggesting these nuggets have value). I then proceed to demonstrate what I mean more operationally: "ch" (change, chunk = increment, delta = chunka change, "chugga" or "choo" as "work words" hyperlinking to steam engine roots of thermodynamics, link to relativity thought experiments, work related to energy as "ability to do work" -- but we "waste and squander energy" too, even if some physicists call it work no matter what). film: lights, camera, action. action = change (difference, with difference and "differentiation" having close conceptual ties). And to requote an earlier paragraph: That's why my notion of "film frames" as intervals (f = frequency) is cool, because it links in hf (an expression for energy, linear with frequency) while introducing the physics concept of "action" (mvd). Lights, camera, action! This was an attempt to get more into the content and substance of my brand of humanistic math (was in reply to your "Volkswagon post" about mv momentum). But from my point of view you chose to branch off by focusing on my "wordmeaning trajectories" meme instead (which I attempted to clarify), and then headed off into more dilute, less substantive discussions of philosophy (as a discipline) versus science (as a discipline). Less work, less gradient, more noise. Any real discussion of my essay and its approach was lost in the haze and smoke, maybe because you're too anxious to be pre-approved as an authority re science and to get the right deferential cues before getting into it heavier duty (all humanities issues, nonquantitative perhaps, but leading to disconnect nevertheless). >is what is an example of "humanities approach to mathematics" it is my >professional opinion (from 20 years of teaching physics and >mathematics complete with teaching awards and top student evaluations) >that it is inappropriate. > >I rest my case. The approach is controversial I agree. I for one doubt that you've had enough exposure to it for such a "case closed" judgement (seeing the training in action, not just in essay form, would be relevant I should think, along with student feedback, evaluations). But go ahead and slap your credentials on the table and walk away if you like. They may add some weight to your pan, tip the scales in your favor, in lieu of any further real discussion. Kirby --------------------------------------------------------- Kirby T. Urner http://www.teleport.com/~pdx4d/kirby.html 4D Solutions http://www.teleport.com/~pdx4d/ [PGP OK] --------------------------------------------------------- ========================================================================= Date: Mon, 27 Jul 1998 06:45:57 GMT Reply-To: List for the discussion of Buckminster Fuller's works Sender: List for the discussion of Buckminster Fuller's works From: osipdx@MY-DEJANEWS.COM Organization: Deja News - The Leader in Internet Discussion Subject: Dome Contract Info Sought Portland Oregon USA I work at a shelter and clinic for homeless and low-income people located in Portland, Oregon called Outside In. Outside In has existed for thirty years in a group of modest restored old houses. In the next few years, the agency would like to tear down several of the houses and build one new larger building. I am also an enthusiast for the work of Buckminster Fuller. I mentioned to Kathy Oliver, the executive director of Outside In, that a dome might be a good option for the new building. She said if I could present her with any information she would be glad to review it. Here is a quote from "The Orgegonian," July 16 1998 about what is needed from the new building: "[T]he plan is to build a three-story building of about 20,000 square feet at a cost of no more than $3 million [.]" If any dome contractors can meet this need at this cost or less, please send me printed information at the following address: Trevor Blake c/o OUTSIDE IN 1236 SW Salmon Portland OR 97205 USA I unfortunately cannot guarantee anything beyond a personal note of thanks from myself, but I do hope that I can find a dome contractor / manufacturer that can meet the agency's needs. Here's to good luck for us all! Please feel free to reproduce and distribute this message as you see fit. - Trevor -- Outside In - Since 1968 - osipdx@hotmail.com http://www.geocities.com/Athens/Oracle/3934/ -----== Posted via Deja News, The Leader in Internet Discussion ==----- http://www.dejanews.com/rg_mkgrp.xp Create Your Own Free Member Forum ========================================================================= Date: Mon, 27 Jul 1998 07:18:37 GMT Reply-To: List for the discussion of Buckminster Fuller's works Sender: List for the discussion of Buckminster Fuller's works From: fchristo@MY-DEJANEWS.COM Organization: Deja News - The Leader in Internet Discussion Subject: Re: Calculus 102: A Humanistic Approach to Primitive Concepts In article <6pa1sk$826$2@thorn.cc.usm.edu>, lrmead@orca.st.usm.edu (Larry Mead) wrote: > fchristo@my-dejanews.com wrote: > : In article <35b767eb.70309312@news.teleport.com>, > : pdx4d@teleport.com (Kirby Urner) wrote: > : > lrmead@orca.st.usm.edu (Larry Mead) wrote: > > : I think I agree with you here, Kirby, but your example of "business > : philosophy" [not quoted above] makes me think you are using the word > : "philosophy" in the sense of "an acquired set of beliefs or morals". It is > : not hard to see why that would evoke such a violent reaction from Larry. > > : Larry seems to think that philosophy is an anything-goes forum where any > : loonie idea will receive serious attention, provided one couches it in a > : sufficiently obscure fashion. I guess this is probably a common complaint > : from technical people who are ignorant of the literature, but it's quite far > : from the truth. > [\bigsnip] > Actually, that is not at all what he believes. Rather, only that pure > logic without quantitative analysis is too imprecise, and that there is > therefore no way to *check* (by experiementation and measurement) whether > or not any philosophical answer is correct or not. In no way (some > of my friends are professional philosophers btw) do I think that such > persons use less than rigorous rules of logic. In that case, although I have a problem with your choice of the term "imprecise" (I would say "fallible"), we might be able to agree, at least with respect the field of philosophy concerned with language, since that field generates a lot of scientifically treatable questions. On the other hand, I do think there is value in treating problems in a purely logical manner because it lets you build models in a "bottom-up" fashion, rather than the "top-down" fashion that's required by scientific method. Ultimately, one must connect the logically derived models with the empirically derived ones, but the interaction between ideas can be useful. After all, isn't this the idea behind theoretical physics? (Granted, I know that many physicists are getting fed up with untestable theories like superstrings.) And Einstein himself was fond of "gedankenexperimente." --FC -----== Posted via Deja News, The Leader in Internet Discussion ==----- http://www.dejanews.com/rg_mkgrp.xp Create Your Own Free Member Forum ========================================================================= Date: Mon, 27 Jul 1998 08:31:23 -0600 Reply-To: List for the discussion of Buckminster Fuller's works Sender: List for the discussion of Buckminster Fuller's works From: "John T. Lowry" Organization: Montana Communications Network Subject: Re: Calculus 102: A Humanistic Approach to Primitive Concepts My suggestion, to all those who wish to "loosen up the logic" and "expand the boundary" or otherwise modify standard intellectual or mathematical concepts, is that they write down their proposal as applied to a concrete circumstance. For example, in this current case, that they say write out their proposed analysis of Zeno's Paradox. And, to keep them honest, that they also write out the "standard" resolution of that Paradox. Faced with the bright light of a concrete performance, most of these impostors quickly fade away. John. John T. Lowry, PhD Flight Physics; Box 20919; Billings MT 59104 Voice: 406-248-2606 Larry Mead wrote in message <6phrsp$mro$5@thorn.cc.usm.edu>... >fchristo@my-dejanews.com wrote: >: In article <6pa1sk$826$2@thorn.cc.usm.edu>, >: lrmead@orca.st.usm.edu (Larry Mead) wrote: >: > fchristo@my-dejanews.com wrote: >: > : In article <35b767eb.70309312@news.teleport.com>, >: > : pdx4d@teleport.com (Kirby Urner) wrote: >: > : > lrmead@orca.st.usm.edu (Larry Mead) wrote: >: > >: > : I think I agree with you here, Kirby, but your example of "business >: > : philosophy" [not quoted above] makes me think you are using the word >: > : "philosophy" in the sense of "an acquired set of beliefs or morals". It is >: > : not hard to see why that would evoke such a violent reaction from Larry. >: > >: > : Larry seems to think that philosophy is an anything-goes forum where any >: > : loonie idea will receive serious attention, provided one couches it in a >: > : sufficiently obscure fashion. I guess this is probably a common complaint >: > : from technical people who are ignorant of the literature, but it's quite >: far >: > : from the truth. >: > [\bigsnip] >: > Actually, that is not at all what he believes. Rather, only that pure >: > logic without quantitative analysis is too imprecise, and that there is >: > therefore no way to *check* (by experiementation and measurement) whether >: > or not any philosophical answer is correct or not. In no way (some >: > of my friends are professional philosophers btw) do I think that such >: > persons use less than rigorous rules of logic. > >: In that case, although I have a problem with your choice of the term >: "imprecise" (I would say "fallible"), we might be able to agree, at least with >: respect the field of philosophy concerned with language, since that field >: generates a lot of scientifically treatable questions. > >: On the other hand, I do think there is value in treating problems in a purely >: logical manner because it lets you build models in a "bottom-up" fashion, >: rather than the "top-down" fashion that's required by scientific method. >: Ultimately, one must connect the logically derived models with the >: empirically derived ones, but the interaction between ideas can be useful. >: After all, isn't this the idea behind theoretical physics? (Granted, I know >: that many physicists are getting fed up with untestable theories like >: superstrings.) And Einstein himself was fond of "gedankenexperimente." >: --FC > >Well, having practiced theoretical physics for a long time, I must say >that "logical models" do indeed play a role in my thinking. On the other >hand, it is not an end in itself, nor is that activity a stopping point. >The theoretician at all times must keep in mind that his ultimate goal is >to predict the results of *measurement* . With that in mind, you are close >to the mark. > >-- >Lawrence R. Mead Ph.D. (Lawrence.Mead@usm.edu) >Eschew Obfuscation! Espouse Elucidation! >www-dept.usm.edu/~physics/mead.html > ========================================================================= Date: Mon, 27 Jul 1998 12:20:12 GMT Reply-To: List for the discussion of Buckminster Fuller's works Sender: List for the discussion of Buckminster Fuller's works From: Larry Mead Organization: University of Southern Mississippi Subject: Re: Calculus 102: A Humanistic Approach to Primitive Concepts lazariuk@my-dejanews.com wrote: : In article <35b916b5.24036715@news.csuohio.edu>, : scott@math.csuohio.edu (Brian M. Scott) wrote: : > On Fri, 24 Jul 1998 19:22:11 GMT, lazariuk@my-dejanews.com wrote: : > >Let me suggest that mathematics will become more relevant : > : > Relevant to what? It's hard to think of a facet of life to which : > mathematics is *not* relevant. : Forgive what may be my ignorance as I am not well school educated but I was : under the assumption that people were doing science because they wanted to : understand more about why we are here and where we are headed and what is the : proper course of behavior. At least that is what some have told me. [snip] Whoever told you that science can answer questions like "why are we here" and " how should we behave" have misinformed you. Science can answer the following - and so far the only - two questions: "What is there in the universe?" and " How does it behave." . -- Lawrence R. Mead Ph.D. (Lawrence.Mead@usm.edu) Eschew Obfuscation! Espouse Elucidation! www-dept.usm.edu/~physics/mead.html ========================================================================= Date: Mon, 27 Jul 1998 11:56:48 GMT Reply-To: List for the discussion of Buckminster Fuller's works Sender: List for the discussion of Buckminster Fuller's works From: Larry Mead Organization: University of Southern Mississippi Subject: Re: Calculus 102: A Humanistic Approach to Primitive Concepts Kirby Urner (pdx4d@teleport.com) wrote: : lrmead@orca.st.usm.edu (Larry Mead) wrote: : >This last (naive) statement seems to show that you simply do not yet : >fully understand how science operates and how numbers give precision : >wheras all other information does not. : Your (patronizing) statement seems to show that you are on the verge : of edifying us with your philosophical viewpoint re the relationship : between logic and history (principles and reality, numbers and energy) : -- but then you stop. : >While over time they have found lots of questions to ask, and certainly : >not to minimize either the importance or the depth of those questions, : >they as yet do not have the quantitative tools to supply the answers. : I don't necessarily accept you as an authority or teacher as to : what is science, how it operates BTW -- you seem to arrogate that : Ph.D. means "doctor of philosophy" and its worth, like any paper : security, can be way over-inflated, especially when our philo : degree holders are so often slackers who haven't bothered to Mr. Urner, I was very careful in my choice of words, intentionally seeking to get across some essential points you keep talking around but not to, without reference to personal feelings. Since you now want to reduce this discussion to personal insults (see above) this will end our discussion. -- Lawrence R. Mead Ph.D. (Lawrence.Mead@usm.edu) Eschew Obfuscation! Espouse Elucidation! www-dept.usm.edu/~physics/mead.html ========================================================================= Date: Mon, 27 Jul 1998 12:30:17 GMT Reply-To: List for the discussion of Buckminster Fuller's works Sender: List for the discussion of Buckminster Fuller's works From: Larry Mead Organization: University of Southern Mississippi Subject: Re: Calculus 102: A Humanistic Approach to Primitive Concepts fchristo@my-dejanews.com wrote: : In article <6pa1sk$826$2@thorn.cc.usm.edu>, : lrmead@orca.st.usm.edu (Larry Mead) wrote: : > fchristo@my-dejanews.com wrote: : > : In article <35b767eb.70309312@news.teleport.com>, : > : pdx4d@teleport.com (Kirby Urner) wrote: : > : > lrmead@orca.st.usm.edu (Larry Mead) wrote: : > : > : I think I agree with you here, Kirby, but your example of "business : > : philosophy" [not quoted above] makes me think you are using the word : > : "philosophy" in the sense of "an acquired set of beliefs or morals". It is : > : not hard to see why that would evoke such a violent reaction from Larry. : > : > : Larry seems to think that philosophy is an anything-goes forum where any : > : loonie idea will receive serious attention, provided one couches it in a : > : sufficiently obscure fashion. I guess this is probably a common complaint : > : from technical people who are ignorant of the literature, but it's quite : far : > : from the truth. : > [\bigsnip] : > Actually, that is not at all what he believes. Rather, only that pure : > logic without quantitative analysis is too imprecise, and that there is : > therefore no way to *check* (by experiementation and measurement) whether : > or not any philosophical answer is correct or not. In no way (some : > of my friends are professional philosophers btw) do I think that such : > persons use less than rigorous rules of logic. : In that case, although I have a problem with your choice of the term : "imprecise" (I would say "fallible"), we might be able to agree, at least with : respect the field of philosophy concerned with language, since that field : generates a lot of scientifically treatable questions. : On the other hand, I do think there is value in treating problems in a purely : logical manner because it lets you build models in a "bottom-up" fashion, : rather than the "top-down" fashion that's required by scientific method. : Ultimately, one must connect the logically derived models with the : empirically derived ones, but the interaction between ideas can be useful. : After all, isn't this the idea behind theoretical physics? (Granted, I know : that many physicists are getting fed up with untestable theories like : superstrings.) And Einstein himself was fond of "gedankenexperimente." : --FC Well, having practiced theoretical physics for a long time, I must say that "logical models" do indeed play a role in my thinking. On the other hand, it is not an end in itself, nor is that activity a stopping point. The theoretician at all times must keep in mind that his ultimate goal is to predict the results of *measurement* . With that in mind, you are close to the mark. -- Lawrence R. Mead Ph.D. (Lawrence.Mead@usm.edu) Eschew Obfuscation! Espouse Elucidation! www-dept.usm.edu/~physics/mead.html ========================================================================= Date: Mon, 27 Jul 1998 12:06:40 GMT Reply-To: List for the discussion of Buckminster Fuller's works Sender: List for the discussion of Buckminster Fuller's works From: Larry Mead Organization: University of Southern Mississippi Subject: Re: Calculus 102: A Humanistic Approach to Primitive Concepts jack@digimax.com wrote: : In article <6pa1hc$826$1@thorn.cc.usm.edu>, : Some of what you and Kirby write leads me to ponder that there may be a : concern that to the degree that we place a value on precision to that same : degree we ignor the totality of our understanding of life that cannot be : communicated precisely. Your statement brings out just the point I and others have been trying (apparently unsuccessfully) to make. There is no operational meaning to "the totality of our understanding of life" ; this is a vague phrase which - meaning something very different to every reader - cannot convey precise information. My last post merely pointed out (which Kirby took such umbrage from), that *any* statement of mine or anyone elses which is *not* mathematical and operational has insufficiently precise meaning to qualify as useful within science. Philosophy is one discipline which is very nonquantitative. Other branches of knowledge are not: economics, geology and so forth. None of this should be controversial. What started the discussion (now argument) was what should be used to *teach* science. I objected to the flowery and pedantic use of language in the original post (see firsst paragraph for a good example). If this is what is an example of "humanities approach to mathematics" it is my professional opinion (from 20 years of teaching physics and mathematics complete with teaching awards and top student evaluations) that it is inappropriate. I rest my case. -- Lawrence R. Mead Ph.D. (Lawrence.Mead@usm.edu) Eschew Obfuscation! Espouse Elucidation! www-dept.usm.edu/~physics/mead.html ========================================================================= Date: Mon, 27 Jul 1998 12:11:44 GMT Reply-To: List for the discussion of Buckminster Fuller's works Sender: List for the discussion of Buckminster Fuller's works From: Larry Mead Organization: University of Southern Mississippi Subject: Re: Calculus 102: A Humanistic Approach to Primitive Concepts lazariuk@my-dejanews.com wrote: : In article <6pa1hc$826$1@thorn.cc.usm.edu>, : lrmead@orca.st.usm.edu (Larry Mead) wrote: : > Let me suggest that some of the questions you want : > answered may not lie within the purvue of science ("why are we here?" : > "who created the universe?" , "What is the correct way to behave?"). : > Nonetheless, philosophy, while good at *stating* these questions, has : > absolutely no means of answering any of them until it somehow becomes : > quantitative and operational. : Let me suggest that mathematics will become more relevant when those teaching : it see that those questions are within the purview of science. At least to : the extent that they appreciate the mystery. : JAck No one appreciates the "mystery" more than persons who have devoted their lives to unraveling the universes deep secrets. Nonetheless, as yet, those particular mysteries above will be answered not by philosophers but by empirical science (like physics) for which the tools (hopefully enough tools!) exist. What makes a good teacher is to convey *both* the mystery along with the tools. Regards, -- Lawrence R. Mead Ph.D. (Lawrence.Mead@usm.edu) Eschew Obfuscation! Espouse Elucidation! www-dept.usm.edu/~physics/mead.html ========================================================================= Date: Mon, 27 Jul 1998 21:17:36 -0700 Reply-To: List for the discussion of Buckminster Fuller's works Sender: List for the discussion of Buckminster Fuller's works From: Joe S Moore Subject: Re: Bucky stuff Comments: To: ecosystems@econet.org MIME-Version: 1.0 Content-Type: text/plain; charset="iso-8859-1" Content-Transfer-Encoding: 7bit Ron, Been studying Fuller since 1970. See my web page below some of the results. Joe S Moore: joemoore@cruzio.com Buckminster Fuller Virtual Institute: http://www.cruzio.com/~joemoore/ -----Original Message----- From: Ron Swenson To: joemoore@mail.cruzio.com Date: Sunday, July 26, 1998 9:06 PM Subject: Bucky stuff >Hey, who's this guy around Santa Cruz who's into keeping track of Bucky >Fuller information? > >Ron Swenson >tel 425.8523 > >http://www.ecotopia.com/ >and especially >http://www.ecotopia.com/baggins.end/ > > > ========================================================================= Date: Tue, 28 Jul 1998 00:48:53 -0700 Reply-To: List for the discussion of Buckminster Fuller's works Sender: List for the discussion of Buckminster Fuller's works From: Brian Hutchings Subject: Re: Calculus 102: A Humanistic Approach to Primitive Concepts <> Brian Hutchings 28-JUL-1998 0:48 r001806@pen2.ci.santa-monica.ca.us hey, congratulation on finding your soulmate, in hte quadray field; and, he's got a patent! now, for *my* critique; thus quoth: The application of humanities techniques in the domain of teaching mathematics results in the practice of building associative semantic networks around idiom, alliteration, and word plays, as a way of anchoring the more crypto-compressed notational nuggets which traditionally populate a math text. firstly, "associative..networks" is redundant, if not flowery-powery. even, you could get most of it, like, semantically building idoms, alliteration, wordplay and onommotopia, if I could ever spell it. I mean, at times, it can read like the proverbially chocolate choo-choo. ha-ha, don't we all? -- The End of History -- again! http://www.tarpley.net ========================================================================= Date: Tue, 28 Jul 1998 00:55:54 -0700 Reply-To: List for the discussion of Buckminster Fuller's works Sender: List for the discussion of Buckminster Fuller's works From: Hentai Organization: http://www.supernews.com, The World's Usenet: Discussions Start Here Subject: Re: Calculus 102: A Humanistic Approach to Primitive Concepts and the humanities (fields of precessionally interacting wordmeaning >trajectories). Brain... hurting.... must... stop... reading... too... many... superfluous... conjunctions... infection... spreading... must... stop... nyarghle! -Hentai [in vita non pacem est] ========================================================================= Date: Tue, 28 Jul 1998 09:05:02 -0700 Reply-To: List for the discussion of Buckminster Fuller's works Sender: List for the discussion of Buckminster Fuller's works From: Kirby Urner Subject: Re: Calculus 102: A Humanistic Approach to Primitive Concepts In-Reply-To: <199807280748.AAA00072@pen2.ci.santa-monica.ca.us> Mime-Version: 1.0 Content-Type: text/plain; charset="us-ascii" > at times, it can read like the proverbially chocolate choo-choo. > I think you'd be especially open to idiosyncratic wordplay approaches to math, given that's already the cut of your self-styled straitjacket. Kirby ========================================================================= Date: Tue, 28 Jul 1998 09:09:34 -0700 Reply-To: List for the discussion of Buckminster Fuller's works Sender: List for the discussion of Buckminster Fuller's works From: Kirby Urner Subject: Re: Calculus 102: A Humanistic Approach to Primitive Concepts In-Reply-To: <6pk0b0$pmq$1@supernews.com> Mime-Version: 1.0 Content-Type: text/plain; charset="us-ascii" >Brain... hurting.... must... stop... reading... >too... many... superfluous... conjunctions... >infection... spreading... must... stop... nyarghle! > Why we need to teach more humanities to kids early, before they grow up not well rounded. Even "Green Eggs and Ham" can be painful to a mathematician used to a diet of crypto- compressed "nuggets". >-Hentai >[in vita non pacem est] > [in morto non pacem est either for some] Kirby ========================================================================= Date: Tue, 28 Jul 1998 13:13:28 GMT Reply-To: List for the discussion of Buckminster Fuller's works Sender: List for the discussion of Buckminster Fuller's works From: Larry Mead Organization: University of Southern Mississippi Subject: Re: Calculus 102: A Humanistic Approach to Primitive Concepts Kirby Urner (pdx4d@teleport.com) wrote: : lrmead@orca.st.usm.edu (Larry Mead) wrote: : >I objected to the flowery and pedantic use of language in the original : >post (see firsst paragraph for a good example). : Here's the first paragraph: : The application of humanities techniques in the domain of : teaching mathematics results in the practice of building : associative semantic networks around idiom, alliteration, and : word plays, as a way of anchoring the more crypto-compressed : notational nuggets which traditionally populate a math text. And I will re-iterate how I personally would have stated the above. " To try to better teach mathematics, use words, pictures and word-play instead of precise symbols." I will let the readers of these groups decide whether or not my prose or yours is better, and whether my advocacy of symbols (not Greek) is the more efficacious in teaching mathematics/science. : I don't see this as particularly florid prose, more a listing of : humanities techniques: use of idiom, alliteration, word plays, : as a means of building semantic networks (standard practice, par : for the course, tools of the trade). It's a style of thinking. : We're using it to teach math. "Crypto-compressed notational : nuggets" makes use of imagery, but also implies gold (suggesting : these nuggets have value). Notice how long it takes you below to say something very simple. : I then proceed to demonstrate what I mean more operationally: And once again, none of goes below is base upon operational definitions. Those refer again to the results of *measurement* . : "ch" (change, chunk = increment, delta = chunka change, "chugga" : or "choo" as "work words" hyperlinking to steam engine roots of : thermodynamics, link to relativity thought experiments, work : related to energy as "ability to do work" -- but we "waste : and squander energy" too, even if some physicists call it work : no matter what). : film: lights, camera, action. action = change (difference, : with difference and "differentiation" having close conceptual : ties). And to requote an earlier paragraph: : That's why my notion of "film frames" as intervals : (f = frequency) is cool, because it links in hf (an expression : for energy, linear with frequency) while introducing the : physics concept of "action" (mvd). Lights, camera, action! : This was an attempt to get more into the content and substance : of my brand of humanistic math (was in reply to your "Volkswagon : post" about mv momentum). Which unfortunately fails. The *entire* meaning of momentum is contained within those symbols. The explanation of their meaning requires some talking, yes. But try sitting in on a physics course once or twice when this comes up. The explanation of the meaning and utility of p = mv will sound nothing like your prose. There is good reason for it. [snip] : The approach is controversial I agree. I for one doubt that you've : had enough exposure to it for such a "case closed" judgement (seeing : the training in action, not just in essay form, would be relevant : I should think, along with student feedback, evaluations). : But go ahead and slap your credentials on the table and walk away : if you like. They may add some weight to your pan, tip the scales : in your favor, in lieu of any further real discussion. There isn't any real discussion anymore as I have already pointed out. -- Lawrence R. Mead Ph.D. (Lawrence.Mead@usm.edu) Eschew Obfuscation! Espouse Elucidation! www-dept.usm.edu/~physics/mead.html ========================================================================= Date: Tue, 28 Jul 1998 16:20:53 GMT Reply-To: List for the discussion of Buckminster Fuller's works Sender: List for the discussion of Buckminster Fuller's works From: Kirby Urner Organization: 4D Solutions Subject: Re: Calculus 102: A Humanistic Approach to Primitive Concepts MIME-Version: 1.0 Content-Type: text/plain; charset=us-ascii Content-Transfer-Encoding: 7bit lrmead@orca.st.usm.edu (Larry Mead) wrote: > " To try to better teach mathematics, use words, pictures and >word-play instead of precise symbols." > How about "I seek mathematical precision in my use of symbols, using word-play and pictures, not just geeky greeky stuff." >I will let the readers of these groups decide whether or not my prose >or yours is better, and whether my advocacy of symbols (not Greek) is >the more efficacious in teaching mathematics/science. > I'm not pushing a humanistic approach as a substitute but as another, complementary on-ramp into the same material. Obviously you win if it looks like I'm advocating we toss computer languages out with the bathwater. >Notice how long it takes you below to say something very simple. > Notice how quickly you say very little. >: I then proceed to demonstrate what I mean more operationally: > >And once again, none of goes below is base upon operational definitions. >Those refer again to the results of *measurement* . > Once again, my use of "operational" traces back to Wittgenstein's "meaning through use" approach to philosophical investigations. My key terms develop their trajectories (mv) through usage patterns. A 'pawn' means what it means because of how it gets used, according to the rules of chess. P-K4 is symbolic notation, part of a language game, and a mathematically-treatable one at that >Which unfortunately fails. The *entire* meaning of momentum is contained >within those symbols. The explanation of their meaning requires some >talking, yes. But try sitting in on a physics course once or twice when >this comes up. The explanation of the meaning and utility of p = mv >will sound nothing like your prose. There is good reason for it. >[snip] > But for how long does the Volkswagon have this momentum? For some distance in a time interval. mv d/t or mvdf (f=1/t) which was my link to energy (dimensional analysis: mvd = action, action/t = energy, links to hf or Planck's action x frequency). > >There isn't any real discussion anymore as I have already pointed out. I know, I know, because you felt insulted. Case closed. Kirby --------------------------------------------------------- Kirby T. Urner http://www.teleport.com/~pdx4d/kirby.html 4D Solutions http://www.teleport.com/~pdx4d/ [PGP OK] --------------------------------------------------------- ========================================================================= Date: Tue, 28 Jul 1998 17:51:57 -0700 Reply-To: List for the discussion of Buckminster Fuller's works Sender: List for the discussion of Buckminster Fuller's works From: Brian Hutchings Subject: Re: Calculus 102: A Humanistic Approach to Primitive Concepts MESSAGE from ="List 28-JUL-1998 17:42 > at times, it can read like the proverbially chocolate choo-choo. > I think you'd be especially open to idiosyncratic wordplay approaches to math, given that's already the cut of your self-styled straitjacket. Kirby - - - - - <> Brian Hutchings 28-JUL-1998 17:51 r001806@pen2.ci.santa-monica.ca.us tee-hee! -- The End of History -- again! http://www.tarpley.net ========================================================================= Date: Tue, 28 Jul 1998 10:33:31 -0800 Reply-To: List for the discussion of Buckminster Fuller's works Sender: List for the discussion of Buckminster Fuller's works From: "Clifford J. Nelson" Organization: gte.net Subject: Re: Calculus 102: A Humanistic Approach to Primitive Concepts Mime-Version: 1.0 Content-Type: text/plain; charset=US-ASCII Content-Transfer-Encoding: 7bit On Tue, Jul 28, 1998 5:13 AM, Larry Mead wrote: [snip] > " To try to better teach mathematics, use words, pictures and >word-play instead of precise symbols." > >I will let the readers of these groups decide whether or not my prose >or yours is better, and whether my advocacy of symbols (not Greek) is >the more efficacious in teaching mathematics/science. > [snip] >-- >Lawrence R. Mead Ph.D. (Lawrence.Mead@usm.edu) >Eschew Obfuscation! Espouse Elucidation! >www-dept.usm.edu/~physics/mead.html > > Pictures or not. What would Newton himself say? Here are two contradictory views from good books: Men of Mathematics, 1965 by E. T. Bell page 400 of my copy. "If there is any mysterious virtue in talking about situations which arise in analysis as if we were back with Archimedes drawing diagrams in the dust, it has yet to be revealed. Pictures after all may be suitable only for young children; Lagrange dispensed entirely with such infantile aids when he composed his analytical mechanics. Our propensity to "geometrize" our analysis may only be evidence that we have not yet grown up. Newton himself, it is known, first got his marvellous results analytically and re-clothed them in the demonstrations of an Apollonious partly because he knew that the multitude -- mathemticians less gifted than himself -- would believe a theorem true only if it were accompanied by a pretty picture and a stilted Euclidean demonstration, partly because he himself still lingered by preference in the pre-Cartesian twilight of geometry." And the opposite point of view from: The Theoretic Arithmetic of the Pythagoreans first published 1816 Thomas Taylor 1983 page VI of my copy: "... Newton himself, as may be conjectured from what he says of Euclid, was convinced of this when it was too late, and commenced his mathematical career with the partial study only of these geometrical heroes. "For he spoke with regret, says Dr. Hutton, of his mistake at the beginning of his mathematical studies, in applying himself to the works of Des Cartes, and other algebraic writers, before he had considered the Elements of Euclid with that attention, which so excellent a writer deserves."" Cliff Nelson ========================================================================= Date: Wed, 29 Jul 1998 00:49:30 GMT Reply-To: List for the discussion of Buckminster Fuller's works Sender: List for the discussion of Buckminster Fuller's works From: Jim Carr Organization: Supercomputer Computations Research Institute Subject: Re: Calculus 102: A Humanistic Approach to Primitive Concepts ... major trim in followups ... lrmead@orca.st.usm.edu (Larry Mead) wrote: } } : Computers use "words" (variable number of bits, depending on the } : operating system). "Simple symbol" is somewhat relative as to } : simplicity -- if Greek isn't a native alphabet for example. } } Why is that relevant? You mean one never learns any symbol use not in } one's native language? Hogwash. pdx4d@teleport.com (Kirby Urner) writes: > >Relevant because you were saying "simple" and I'm saying we should >recognize it takes work to accommodate alien charactersets in one's >thinking -- both humanities and math face this same challenge. Trivial at any university with an active 'greek' system ... except they don't know the lower case letters. >We call it "the visual arts" -- the computer has become in important >tool in this department (cite Ken Snelson's recent visualizations of >the atom, early SGI renditions of tensegrity sculptures). Recent? That has been done for decades; only the cost of the machines has changed. -- James A. Carr | Commercial e-mail is _NOT_ http://www.scri.fsu.edu/~jac/ | desired to this or any address Supercomputer Computations Res. Inst. | that resolves to my account Florida State, Tallahassee FL 32306 | for any reason at any time. ========================================================================= Date: Wed, 29 Jul 1998 03:50:03 GMT Reply-To: List for the discussion of Buckminster Fuller's works Sender: List for the discussion of Buckminster Fuller's works From: BMScott@MY-DEJANEWS.COM Organization: Deja News - The Leader in Internet Discussion Subject: Re: Calculus 102: A Humanistic Approach to Primitive Concepts In article <35bbc673.148158253@news.teleport.com>, pdx4d@teleport.com (Kirby Urner) wrote: > scott@math.csuohio.edu (Brian M. Scott) wrote: > >>You've argued that I "demonize" an inner circle that doesn't > >>exist and I've replied that "demons" are clever in my cosmology, > >How *you* use the term is irrelevant; you apparently understood my > >meaning. > What, I'm a second class user of my own language? This is a more blatant non sequitur than your first response. > Yawn. School yard invective is no substitute for intelligent > communication. You made a specific claim: that too many mathematicians 'bash superstition on the one hand, but encourage laypersons to channel latent spirituality through this "higher dimensions" chatter on the other, which hyperdimensional talk academics are all too inclined to parley into some kind of awe for their supposed priest-like abilities to "visualize in any number of dimensions"'. I called it horseshit. Where's the failure to communicate? With one word I've told you that I think the claim not just false but clearly so, and I've implied that I think that you know better (or at least ought to). What's more, I sketched my reasons later in the post. Frankly, I consider my response more honest, more communicative, and more useful than your polemics and deliberate use of terms loaded just this side of slander. > >To say that four lines in R^4 are mutually orthogonal is perfectly > >meaningful and certainly not nonsense. If you have a problem with it, > >it's because you're still naively trying to give it a physical meaning > >in everyday physical space. Worse, you're imagining that most > >mathematicians do the same. > It's meaningful as a tautology, sure. A tautology? Don't be silly: you can obviously pick four lines in R^4 that aren't mutually orthogonal. > You label as "naive" those > who think "orthogonal" means something "physical" in "physical > space". That's arrogant on your part -- as if people had no > right to expect anything physical. *You* are naive to expect it. And a student taking linear algebra had better be able to get used to the idea that vectors and orthogonality needn't have physical significance. > >Elsewhere you write: 'The ego's best defense is to project itself as > >powerless, a victimized, innocent bystander to the holocaust. The > >circle is vicious: a self-righteous, abused "little me" is a painful > >thing to be, begetting a stronger need for comforting palliatives and > >escapist blockbuster fantasies.' Physician, heal thyself. > I appreciate your providing us with a quote by the way. Now maybe > we're getting someplace. Do I sound like a powerless, victimized > innocent bystander to you? You're certainly self-righteous, and you sound like someone trying to present himself as victimized and abused. I don't know whether your picture of the mathematical community is escapist, but it's certainly a fantasy. The match isn't perfect, but it's close enough to intrigue. > >>You may (a) deny such a cultural phenomenon exists (but I > >>supply many exhibits of what I'm talking about at my > >>hypercross.html) > >No, you don't. You mention Abbott's _Flatland_, and you provide links > >to several pages where various people associate some notion(s) of > >dimension with various more or less religious concepts, in contexts > >ranging from science fiction through what appears to be some form of > >spiritualism to quantum mechanics. > Exactly. That's the cultural phenomenon I'm talking about. But then you tell us that mathematicians as a group either are subject to the same delusion or at least encourage it, and you present these links as evidence. They aren't, and the claim is false in both forms. > But I don't buy that the reason I can't visualize 4 mutual orthogonals > has anything to do with my "physical limitations" Yours personally? No. Human physical limitations? Obviously. > >Do you know enough mathematics to be aware of the fact that there are > >many different notions of dimension? [irrelevant response] > >If so, you must also be aware > >that for R^n all of the important ones coincide: the dimension of R^n > >is n. > I usually am interested in discrete spaces, point populations. That would be fine, *if* you made that point clearly. But you don't: your screeds here and on your site(s) give the distinct impression that you're talking about ordinary Euclidean space. Moreover, some of your discussions (e.g., involving finer and finer triangulations of a polyhedron) require a space in which any two points have a midpoint (or some similar but more complicated requirement), so it's not clear in what sense they are discrete. > Seems like sometimes mathematicians give lip service to how consistency > and precision are the hallmarks of their game-playing, but then turn up > their noses if someone comes along with a consistent and precise symbol > game that just doesn't happen to be the same as theirs. You don't present yours as a consistent and precise symbol game. You present it as the Holy Grail that will Save us from the Evils of Hyper-Cross Dogmatics, without offering the slightest indication that its topological foundations are different from those of Euclidean geometry. I've discussed this with you before, at some length, and I'm not convinced that you've ever even thought out the underpinnings; this seems to be an excuse you use when you're trying to sound mathematically respectable. > As if Universe > had room for only one consistent "dimension talk" (e.g. the R^n stuff). You know, I fancy that I just pointed out a while back that there are lots of different mathematical notions of dimension. Would you like to make a more supportable accusation? > I note that a discrete set of points addressed as (x,y,z) in Cartesian > style, or (a,b,c,d) in NeoCartesian style, may also be addressed purely > sequentially, i.e. that the number of coordinates bears no intrinsic > relationship to either (a) degrees of freedom or (b) the number of > dimensions. You have some misconceptions here. First, it's obvious to anyone who's taken a decent calculus course, never mind linear algebra, that the number of coordinates used may exceed the number needed; it's only the latter that (in intuitive terms) corresponds to the dimension or number of degrees of freedom. Your comment about sequential addressing is irrelevant. You can just as well address all points in R^3 using a single real number, since there's a bijection between R^3 and R, but this bijection fails to capture the relevant geometry. > >Any doubts that you raise are unjustified, and raising them is > >therefore a disservice. > I disagree. This is healthy give and take and to try suppressing > it out of hand because "a disservice" is to sound like a dogmatist. I really think that in your exaggerated fear of orthodoxy you miss the point completely. Would you argue that a parent should teach his children to fear monsters under the bed? I wouldn't, even if he turns around and explains exactly why such fears are groundless. > >The rough-and-ready notion of dimension as a > >degree of freedom, on the other hand, *is* a useful notion. If you > >wanted to do something useful with your essentially barycentric > >coordinates, > ...not essentially barycentric, I disagree... Eh? Of course they are: the basic idea's exactly the same. > >This is particularly evident after you've normalized them. > I can add pairs of quadrays to get 6 pairs of orthogonal > vectors emanating from the origin in an XYZ "jack" apparatus > -- is this what you mean by "normalized"? No. > Remember, in your game 'vector reversal' (application of > the '-' sign) is lumped under scalar multiplication. No, it's not: look at the axioms for a vector space. What *is* true is that one can prove as a derived fact that for any x, -x = (-1)x. > I don't see '-' vectors as "less basic" than '+' > vectors in XYZ. Well of course not! If V is a real vector space - I don't care which - and x is a vector in V, then -x is simply the additive inverse of x. If I like, I can give -x the name y, in which case x is -y. Perfect symmetry. Where's the problem? > Positive mirrors Negative and vice versa, > but both should be on equal footing -- the XYZ game seems > unbalanced because of its positive bias. My students think > so too. Well, here's part of the problem. There is no such bias. Indeed, it's your normalized 'quadray' system that seems designed to accommodate student bias toward positive numbers. > >> That's all you need for a ratio, and > >>that suggests a slope, a rate, action in time (energy). > >*If* this were true, teaching calculus would be a snap. > >Unfortunately, it's not: if you're lucky it suggests a rate, but it > >certainly doesn't suggest a slope. Your response was a non sequitur; do you want to try again, or do you grant the point? To make matters absolutely clear, I am talking about what it suggests to students. Brian M. Scott -----== Posted via Deja News, The Leader in Internet Discussion ==----- http://www.dejanews.com/rg_mkgrp.xp Create Your Own Free Member Forum ========================================================================= Date: Wed, 29 Jul 1998 06:09:56 GMT Reply-To: List for the discussion of Buckminster Fuller's works Sender: List for the discussion of Buckminster Fuller's works From: Harry H Conover Organization: The Internet Access Company, Inc. Subject: Re: Calculus 102: A Primitive Approach to Humanistic Concepts Robin Chapman (rjc@maths.ex.ac.uk) wrote: : : Credentials are another Urnerian obsession. Rather than to attempt : to refute one's argument he will instead insult one's supposed : credentials while at all times brandishing his as "curriculum writer". : A "curriculum writer." Now isn't that just special! Harry C. ========================================================================= Date: Tue, 28 Jul 1998 22:02:45 -0700 Reply-To: List for the discussion of Buckminster Fuller's works Sender: List for the discussion of Buckminster Fuller's works From: Matthew Kaidor Subject: Re: Calculus 102: A Humanistic Approach to Primitive Concepts Mime-Version: 1.0 Content-Type: text/plain; charset=us-ascii Content-Transfer-Encoding: 7bit Anata wa hentai desu ka? Saa, watashi wa hentai desu. Hentai wrote: > Brain... hurting.... must... stop... reading... > too... many... superfluous... conjunctions... > infection... spreading... must... stop... nyarghle! > > -Hentai > [in vita non pacem est] -- The statement below is true. The statement above is false. MoonieCode [2.0.14] SM:4[1]m+ F:sPl++Ma++Ve++vGa+aAr O:d--?s?oa?h+++ P:a+s:w-:f---:eBrD:hBkD-:cW:y+++:r-|+ ========================================================================= Date: Wed, 29 Jul 1998 09:28:01 GMT Reply-To: List for the discussion of Buckminster Fuller's works Sender: List for the discussion of Buckminster Fuller's works From: Kirby Urner Organization: 4D Solutions Subject: Re: Calculus 102: A Humanistic Approach to Primitive Concepts MIME-Version: 1.0 Content-Type: text/plain; charset=us-ascii Content-Transfer-Encoding: 7bit BMScott@my-dejanews.com wrote: >just this side of slander. > You called me a liar (in CubeWorld), my ideas horseshit. Lets just admit this is the internet and tell our lawyers to go home and have a drink. >A tautology? Don't be silly: you can obviously pick four lines in R^4 >that aren't mutually orthogonal. > What's tautologous is your use of the word "orthogonal" to mean whatever you define it to mean within your game. The link to "physical meaning" is broken (by your own admission) so I don't see much to stop you from working in a vacuum. >*You* are naive to expect it. And a student taking linear algebra >had better be able to get used to the idea that vectors and >orthogonality needn't have physical significance. > I'm still casting about for some better metaphors. "Orthogonal" seems sloppy -- as if even (x,y) grids had to be built from axes at 90 degrees. Basis vector independence and perpendicularity are not synonymous concepts -- or shouldn't be. The quadrays game makes this clear (4 basis vectors, no 90-degree angles between them). > >You're certainly self-righteous, and you sound like someone trying to >present himself as victimized and abused. I don't know whether your >picture of the mathematical community is escapist, but it's certainly >a fantasy. The match isn't perfect, but it's close enough to intrigue. > I don't project "the mathematical community" as if this were some kind of homogenous culture consisting of all like-minded individuals. My "hypercross dogmatists" aren't all mathematicians and not all mathematicians are hypercross dogmatists (and some are even feeding me ammo behind the scenes). >But then you tell us that mathematicians as a group either are subject >to the same delusion or at least encourage it, and you present these >links as evidence. They aren't, and the claim is false in both forms. > If I could link to a video clip from the PBS series 'Life By the Numbers' I would, but I don't have the technical means. To some extent I'm depending on the ability of my readers to recognize the memes and do their own detective work as to sources. My 'exhibits' should be enough to get them going. I do think a lot of professionals in the math-sciences have pushed 'Flatland' as a kind of on-ramp for learning "dimension talk" and that book certainly encourages one to think in terms of "physical limitations" and to pity the poor flatlanders who have no clue re a sphere (and by extension the poor "3Ders" who can't quite grok four mutual perpendiculars -- the hypercross -- for analogous reasons). But maybe we just disagree on nuances. I'm not especially interested in defining some monocultural "mathematical community" in order to villify it. I'm more interested in circling what I consider an abuse of metaphors in service of a dogmatic belief system -- who exactly is to blame is not my concern. More, I'd like to enable whomever feels like becoming free of such dogmatism to do so, maybe getting a boost from my writings or writings of others mounting a similar critique. If you haven't a trace of superstition yourself, then fine, but I feel pretty clear that a lot of people are unnecessarily awed and befuddled by "dimension talk" and the curriculum as currently promulgated seems curiously unable to help them "snap out of it". >> But I don't buy that the reason I can't visualize 4 mutual orthogonals >> has anything to do with my "physical limitations" > >Yours personally? No. Human physical limitations? Obviously. > No, not physical limitations at all. You yourself said "4 orthogonals" had no physical meaning, yet you ascribe an inability to attach an image to this metaphor to "human physical limitations". "Obviously" you say. Obviously? What about that Coxeter quote? Probably the most respected geometer of the century. He's talking about "physical limitations" keeping people from seeing the hypercross. What I'm seeing is the bewitchment of our intelligence by deep grammatical confusions i.e. I'm developing a Wittgensteinian critique of what I call "hypercross dogmatics". I think that my approach is interesting and original and worthy of more enlightened discussion, at least among philosophers. This isn't stupid or malicious thinking in which I'm engaged. If you think it is, then I honestly think you're not very well trained in philosophy -- but then you haven't claimed that you were. >> >Do you know enough mathematics to be aware of the fact that there are >> >many different notions of dimension? > >[irrelevant response] > I gave an example of a different notion of dimension, using a different mathematically-informed language -- hardly irrelevant. >> I usually am interested in discrete spaces, point populations. > >That would be fine, *if* you made that point clearly. But you don't: >your screeds here and on your site(s) give the distinct impression >that you're talking about ordinary Euclidean space. I say ordinary Euclidean space is discrete. Atoms don't touch. Call it Democritus-onian space if that makes you feel better. Euclid and his buddies scribed with sticks in the sand on a locally flat beach. 'The Elements' does not require a lot of metaphysics about 'infinite, infinitely thin planes' -- a strictly operational approach will stay with the sand and the beach, and still come up with the same theorems. >Moreover, some >of your discussions (e.g., involving finer and finer triangulations >of a polyhedron) require a space in which any two points have a midpoint >(or some similar but more complicated requirement), so it's not clear >in what sense they are discrete. > I posit frequency limits -- resolution limits -- which have to do with the coordinate system, its precision. A coordinate system is a measuring device and our instruments are not "infinitely precise" -- ever. 'The Elements' was done in sand. Sand is discrete. Another thread. >You don't present yours as a consistent and precise symbol game. You >present it as the Holy Grail that will Save us from the Evils of >Hyper-Cross Dogmatics, without offering the slightest indication that >its topological foundations are different from those of Euclidean >geometry. I've discussed this with you before, at some length, and >I'm not convinced that you've ever even thought out the underpinnings; >this seems to be an excuse you use when you're trying to sound >mathematically respectable. I present it as not invested in the standard "dimension talk" and therefore perhaps better positioned to help some students dig out from under the manure pile of confusion I call "hypercross dogmatics". This is a different thread from my "humanities mathematics" one. I'm not sure what you mean by "Euclidean geometry". If you mean R^n, then I'd point out that Euclid never messed with R^n, or even R (real numbers not defined until much later). You can do proofs ala "The Elements" without defining R^n. My "underpinnings" have to do with taking the electronic computer as a metaphor for nature. I see what operations a computer can do and count those as operations in a discrete space, not in a continuous or infinite one. I see computer memory as a space to be addressed and note that various schemes may be used, including simple sequential. In computer memory, a "hyperdimensional polytope" is just one more data structure of labeled nodes and edges defined by pairs of nodes. The World Wide Web is such a data structure (no need to ascribe its dimension). I have no problem with people playing R^n games, play them myself. But I also think hypercross dogmatics is a real cultural phenomenon and that other angles on mathematics, including ones which don't define key terms the same way, have a mind-expanding impact and are not out of place in a liberal arts curriculum. If you think I'm being messianic, that's not my problem. I see myself as struggling to keep some important ideas and approaches alive and in circulation -- stuff that doesn't get taught much more out of prejudice and overspecialization than for reasons that make a lot of sense. I am not alone in this struggle nor am I particulary frustrated ("coming along splendidly" is my report back from the front). >> As if Universe >> had room for only one consistent "dimension talk" (e.g. the R^n stuff). > >You know, I fancy that I just pointed out a while back that there are >lots of different mathematical notions of dimension. Would you like >to make a more supportable accusation? > And then you deleted my example as "irrelevant". You call people "naive" for trying to attach "physical meaning" to 4 orthogonals and then say "obviously" our "human physical limitations" are to blame for our inability to get the hypercross through our thick skulls. You really don't impress me as a particularly consistent thinker. If you accept that mathematics has room for a different "dimension talk" then why not accept mine? What's all the fuss? If our only disagreement is you don't see anyone encouraging superstitious belief in the hypercross, then lets just drop it. I do, you don't. End of story. >You have some misconceptions here. First, it's obvious to anyone >who's taken a decent calculus course, never mind linear algebra, that >the number of coordinates used may exceed the number needed; Quadrays have no redundant coordinates. It's the mirror imaging of scalars by means of the '-' operator which we don't need to include in point addresses. Four directions omnisymmetric from the origin are not distinguished into two groups, positive and negative. It's not that I discriminate against "negative numbers" it's that I don't need to divide numbers into two sets (if you don't have negatives, you don't have positives either, and the '-' sign becomes an operator, not an attribute of any scalar). We still have additive inverse for every vector e.g.: (2,1,1,0) + (0,1,1,2) = (2,2,2,2) = (0,0,0,0) >I really think that in your exaggerated fear of orthodoxy you miss the >point completely. I know you think so. We disagree. That's all. And not really fear at this point either, as I feel pretty confidant we've creamed the opposition. >Eh? Of course they are: the basic idea's exactly the same. > People on geometry_research (besides me that is) disagree. I wonder if you've done any studying of quadrays. >> Remember, in your game 'vector reversal' (application of >> the '-' sign) is lumped under scalar multiplication. > >No, it's not: look at the axioms for a vector space. What *is* true >is that one can prove as a derived fact that for any x, -x = (-1)x. > Right. Multiplication by -1 is considered scaler multiplication, rather than two operations i.e. multiplication by scalar 1 (leaves x unchanged), followed by application of the '-' operator, which reverses its direction. >> I don't see '-' vectors as "less basic" than '+' >> vectors in XYZ. > >Well of course not! If V is a real vector space - I don't care which - >and x is a vector in V, then -x is simply the additive inverse of x. If >I like, I can give -x the name y, in which case x is -y. Perfect symmetry. >Where's the problem? > The problem is in XYZ we call only 3 of the 6 vectors protruding from the origin "basic" i.e. the "positive" ones. What's so special about the positives versus the negatives? >Well, here's part of the problem. There is no such bias. Indeed, it's >your normalized 'quadray' system that seems designed to accommodate >student bias toward positive numbers. > Negative mirroring is used to achieve bilateral symmetry, but '+' is 'passive' whereas '-' is 'active' (reverses a vector). That's why ++2 = +2 but --2 = +2. In a trully symmetric system, we might have L and R as signs and '-' for reversal i.e. -2L = 2R and -2R = 2L, and --2L = 2L and --2R = 2R. Instead of using '-' to generate symmetry around the origin, quadrays uses n-tuples. In a single degree of freedom: <--------------*---------------> (0,1) (0,0) (1,0) The '-' operator is still defined, and with the usual meaning (reversal), but positionality relative the origin is not achieved by using the '-' operator as in XYZ. >Your response was a non sequitur; do you want to try again, or do you >grant the point? To make matters absolutely clear, I am talking about >what it suggests to students. > I'm not sure what your concern is -- I'll grant the point and hope I'm not sliding into a clever trap. I note you deleted all the rest of my reply -- maybe you were conceding to a fellow technogeek. Kirby --------------------------------------------------------- Kirby T. Urner http://www.teleport.com/~pdx4d/kirby.html 4D Solutions http://www.teleport.com/~pdx4d/ [PGP OK] --------------------------------------------------------- ========================================================================= Date: Wed, 29 Jul 1998 09:04:05 GMT Reply-To: List for the discussion of Buckminster Fuller's works Sender: List for the discussion of Buckminster Fuller's works From: Robin Chapman Organization: HyperCross HeadQuarters Subject: Re: Calculus 102: A Primitive Approach to Humanistic Concepts In article <6pm65a$3i5$1@nnrp1.dejanews.com>, BMScott@my-dejanews.com wrote: > In article <35bbc673.148158253@news.teleport.com>, > pdx4d@teleport.com (Kirby Urner) wrote: > > > scott@math.csuohio.edu (Brian M. Scott) wrote: > > > >>You've argued that I "demonize" an inner circle that doesn't > > >>exist and I've replied that "demons" are clever in my cosmology, > > > >How *you* use the term is irrelevant; you apparently understood my > > >meaning. > > > What, I'm a second class user of my own language? Second class? Third rate more like! > > >To say that four lines in R^4 are mutually orthogonal is perfectly > > >meaningful and certainly not nonsense. If you have a problem with it, > > >it's because you're still naively trying to give it a physical meaning > > >in everyday physical space. Worse, you're imagining that most > > >mathematicians do the same. > > > It's meaningful as a tautology, sure. > > A tautology? Don't be silly: you can obviously pick four lines in R^4 > that aren't mutually orthogonal. I wouldn't lay bets on Urner being able to do it. > > >Elsewhere you write: 'The ego's best defense is to project itself as > > >powerless, a victimized, innocent bystander to the holocaust. The > > >circle is vicious: a self-righteous, abused "little me" is a painful > > >thing to be, begetting a stronger need for comforting palliatives and > > >escapist blockbuster fantasies.' Physician, heal thyself. (Soppy violin music in the background). > > I appreciate your providing us with a quote by the way. Now maybe > > we're getting someplace. Do I sound like a powerless, victimized > > innocent bystander to you? To me Urner sounds like an arrogant buffoon who wants to buy into the cult of victimhood. > > I usually am interested in discrete spaces, point populations. Strange. Why then does Urner constantly preach about his approach to geometry (continuous mathematics par excellence), but has nothing to say about any form of discrete mathematics. > > Seems like sometimes mathematicians give lip service to how consistency > > and precision are the hallmarks of their game-playing, but then turn up > > their noses if someone comes along with a consistent and precise symbol > > game that just doesn't happen to be the same as theirs. Urner's quadray system (or barycentrics made difficult) is easily translated to Cartesians and vice versa. The only difference is that Cartesians are easier to use. The easiest way of doing quadray computations is to translate to Cartesians, do the computations in Cartesians, and translate back! > > ...not essentially barycentric, I disagree... > > Eh? Of course they are: the basic idea's exactly the same. Well said, Brian. > > Positive mirrors Negative and vice versa, > > but both should be on equal footing -- the XYZ game seems > > unbalanced because of its positive bias. My students think > > so too. Urnerian logic at its most entertaining. I note that like all teachers, Urner has trained his charges to give the answers he wants. So much for his radical pose. As Brian points out it is Cartesians in which positive and negative have an equal role, and Urner's quadrays in which negativity is suppressed. In view of his attempts to eliminate an entire half of the real numbers, one wonders with dread what Urner's views on social issues might be. Robin Chapman -----== Posted via Deja News, The Leader in Internet Discussion ==----- http://www.dejanews.com/rg_mkgrp.xp Create Your Own Free Member Forum ========================================================================= Date: Tue, 28 Jul 1998 19:37:06 GMT Reply-To: List for the discussion of Buckminster Fuller's works Sender: List for the discussion of Buckminster Fuller's works From: Robin Chapman Organization: HyperCross HeadQuarters Subject: Re: Calculus 102: A Primitive Approach to Humanistic Concepts In article <6pkipo$t7e$1@thorn.cc.usm.edu>, lrmead@orca.st.usm.edu (Larry Mead) wrote: > Kirby Urner (pdx4d@teleport.com) wrote: > : lrmead@orca.st.usm.edu (Larry Mead) wrote: > > : >I objected to the flowery and pedantic use of language in the original > : >post (see firsst paragraph for a good example). > > : Here's the first paragraph: > > : The application of humanities techniques in the domain of > : teaching mathematics results in the practice of building > : associative semantic networks around idiom, alliteration, and > : word plays, as a way of anchoring the more crypto-compressed > : notational nuggets which traditionally populate a math text. > > And I will re-iterate how I personally would have stated the above. > > " To try to better teach mathematics, use words, pictures and > word-play instead of precise symbols." > > I will let the readers of these groups decide whether or not my prose > or yours is better, and whether my advocacy of symbols (not Greek) is > the more efficacious in teaching mathematics/science. > > : I don't see this as particularly florid prose, more a listing of > : humanities techniques: use of idiom, alliteration, word plays, > : as a means of building semantic networks (standard practice, par > : for the course, tools of the trade). It's a style of thinking. > : We're using it to teach math. "Crypto-compressed notational > : nuggets" makes use of imagery, but also implies gold (suggesting > : these nuggets have value). > > Notice how long it takes you below to say something very simple. Yes, Urner will always use ten long words when one short one would suffice. If he didn't then (a) people might understand what he was talking about, (b) he wouldn't sound so impressive. Stripped of their inessential verbiage, Urner's arguments aspire to the banal, so he is not likely to abandon his deliberate mystification. > : But go ahead and slap your credentials on the table and walk away > : if you like. They may add some weight to your pan, tip the scales > : in your favor, in lieu of any further real discussion. Credentials are another Urnerian obsession. Rather than to attempt to refute one's argument he will instead insult one's supposed credentials while at all times brandishing his as "curriculum writer". Robin Chapman -----== Posted via Deja News, The Leader in Internet Discussion ==----- http://www.dejanews.com/rg_mkgrp.xp Create Your Own Free Member Forum ========================================================================= Date: Wed, 29 Jul 1998 16:28:55 GMT Reply-To: List for the discussion of Buckminster Fuller's works Sender: List for the discussion of Buckminster Fuller's works From: Kirby Urner Organization: 4D Solutions Subject: Re: Calculus 102: A Primitive Approach to Humanistic Concepts MIME-Version: 1.0 Content-Type: text/plain; charset=us-ascii Content-Transfer-Encoding: 7bit conover@tiac.net (Harry H Conover) wrote: >Robin Chapman (rjc@maths.ex.ac.uk) wrote: >: >: Credentials are another Urnerian obsession. Rather than to attempt >: to refute one's argument he will instead insult one's supposed >: credentials while at all times brandishing his as "curriculum writer". >: > >A "curriculum writer." Now isn't that just special! > > Harry C. > Now who's obsessing? I call myself a curriculum writer because I write curriculum (duh). I'm also a programmer and a scuba diver. Kirby --------------------------------------------------------- Kirby T. Urner http://www.teleport.com/~pdx4d/kirby.html 4D Solutions http://www.teleport.com/~pdx4d/ [PGP OK] --------------------------------------------------------- ========================================================================= Date: Wed, 29 Jul 1998 16:26:29 GMT Reply-To: List for the discussion of Buckminster Fuller's works Sender: List for the discussion of Buckminster Fuller's works From: Kirby Urner Organization: 4D Solutions Subject: Re: Calculus 102: A Primitive Approach to Humanistic Concepts MIME-Version: 1.0 Content-Type: text/plain; charset=us-ascii Content-Transfer-Encoding: 7bit Robin Chapman wrote: >Yes, Urner will always use ten long words when one short one would >suffice. If he didn't then >(a) people might understand what he was talking about, A fair number do. >(b) he wouldn't sound so impressive. Do I? >Stripped of their inessential verbiage, Urner's arguments aspire >to the banal, so he is not likely to abandon his deliberate mystification. > Banal = obvious? >> : But go ahead and slap your credentials on the table and walk away >> : if you like. They may add some weight to your pan, tip the scales >> : in your favor, in lieu of any further real discussion. > >Credentials are another Urnerian obsession. Rather than to attempt >to refute one's argument he will instead insult one's supposed >credentials while at all times brandishing his as "curriculum writer". > Brandish? Wow. >Robin Chapman > Thanks guy. Urner finds Chapman a most entertaining geek. Kirby --------------------------------------------------------- Kirby T. Urner http://www.teleport.com/~pdx4d/kirby.html 4D Solutions http://www.teleport.com/~pdx4d/ [PGP OK] --------------------------------------------------------- ========================================================================= Date: Wed, 29 Jul 1998 17:02:11 GMT Reply-To: List for the discussion of Buckminster Fuller's works Sender: List for the discussion of Buckminster Fuller's works From: Kirby Urner Organization: 4D Solutions Subject: Re: Calculus 102: A Primitive Approach to Humanistic Concepts MIME-Version: 1.0 Content-Type: text/plain; charset=us-ascii Content-Transfer-Encoding: 7bit Robin Chapman wrote: >Second class? Third rate more like! > The judge speaks! (Note: Chapman is the guy who refuses to read my posts except vicariously through the replies of others -- the hallmark of a true scholar). > >I wouldn't lay bets on Urner being able to do it. > Hah hah! Such a wit! (Sorry, this thread has degenerated to this sophomoric level ya'll -- not the first time). >> > >Elsewhere you write: 'The ego's best defense is to project itself as >> > >powerless, a victimized, innocent bystander to the holocaust. The >> > >circle is vicious: a self-righteous, abused "little me" is a painful >> > >thing to be, begetting a stronger need for comforting palliatives and >> > >escapist blockbuster fantasies.' Physician, heal thyself. > >(Soppy violin music in the background). > Full text of essay Brian quoted: http://www.teleport.com/~pdx4d/politics.html See also: http://members.xoom.com/Urner/working4.html >> > I usually am interested in discrete spaces, point populations. > >Strange. Why then does Urner constantly preach about his approach >to geometry (continuous mathematics par excellence), but has nothing >to say about any form of discrete mathematics. > I do my stuff on a computer. My computer is incapable of registering "infinite proximity" between two points, is a discrete math machine. >From what I read of physics, so is the energized reality into which my computer is plugged. >Urner's quadray system (or barycentrics made difficult) is easily translated >to Cartesians and vice versa. The only difference is that Cartesians >are easier to use. The easiest way of doing quadray computations >is to translate to Cartesians, do the computations in Cartesians, and >translate back! > You exaggerate. Getting the distance between 2 4-tuples using my distance formula (quadrays.html) is far easier than using my two matrices (quadxyz.html) with the standard XYZ version of Pythagoras in between. >> > ...not essentially barycentric, I disagree... >> >> Eh? Of course they are: the basic idea's exactly the same. > >Well said, Brian. > "Neither trilinears nor barycentric coordinates represent distances from a common origin. Yours looks like the regular basis vectors in 3D space." >From Steve Sigur in "Re: Conway on Trilinear vs Barycentric" on geometry_research: http://forum.swarthmore.edu/epigone/geometry-research/skexkhangax >Urnerian logic at its most entertaining. I note that like all teachers, >Urner has trained his charges to give the answers he wants. So >much for his radical pose. How's this? >As Brian points out it is Cartesians in which >positive and negative have an equal role, and Urner's quadrays in which >negativity is suppressed. Negative operator works fine. Scalars not divided in two groups for the apparatus to work. -(1,0,0,0) = (-1,0,0,0) = (0,1,1,1). You could define f(x) = (sin(x),cos(x),0,0) and let x have negative values, and get some curve in Euclidean space. That sin(x) and cos(x) output negative numbers is not a problem as in xyz this is about positionality in a quadrant, i.e. permuted signage has to do with which xyz octant -- a function we solve using 4-tuples without need of permuted signage. >In view of his attempts to eliminate an entire half >of the real numbers, one wonders with dread what Urner's views on >social issues might be. > Using floating point numbers, terminals + algorithmics, "real numbers" not defined as such -- probably some starving kid in India already thought of doing this. But that's another thread. Just a different game Chapman, a "philosophers' toy". You probably think chess players are "attempting to eliminate checkers" because they use the same game board, but according to a different set of rules. My views on social issues are well documented. Yours? Kirby PS: I'll make a more sincere attempt to not post responses to Chapman's, who doesn't have time to engage in any serious discussions. Those wishing to read the only substantive Urner-Chapman exchange are invited to scroll down to the bottom of my http://www.teleport.com/~pdx4d/bio.html, click on my May 15 98 letter to Ivars Peterson, scroll down to appended May 14 post to Synergetics-L, find URL. --------------------------------------------------------- Kirby T. Urner http://www.teleport.com/~pdx4d/kirby.html 4D Solutions http://www.teleport.com/~pdx4d/ [PGP OK] --------------------------------------------------------- ========================================================================= Date: Wed, 29 Jul 1998 19:38:26 GMT Reply-To: List for the discussion of Buckminster Fuller's works Sender: List for the discussion of Buckminster Fuller's works From: WLauritzen Organization: AOL http://www.aol.com Subject: New Web Site Dear Gentle Readers, I have recently, with the help of a friend, created a Web site with two articles. One of these is entitled, "Atlantis at Last?" The other is entitled, "The Ancient Hieroglyphs of the Nile." The entire Web site is called, "The Volcano God of the Ancients." I believe you may find these articles to be stimulating. You will undoubtable not agree with everything in them. I invite you to look at this site. I am open to comments and suggestions, but I must say, that I am going to be out of the country for several weeks, starting Aug 2, and I may not be able to respond immediately. Even so, I look forward to any comments when I return. http://home.earthlink.net/~wlauritzen William Lauritzen ========================================================================= Date: Wed, 29 Jul 1998 19:57:11 -0700 Reply-To: List for the discussion of Buckminster Fuller's works Sender: List for the discussion of Buckminster Fuller's works From: Brian Hutchings Subject: I forget! <> Brian Hutchings 29-JUL-1998 19:57 r001806@pen2.ci.santa-monica.ca.us only the human mind can dystinguish between suc "precision", as in "...01.0...", using Munk's "congruence surds" --sorry!... also, see McCarthy's _Chaos and [Something]_ on granularity in machines. -- The End of History -- again! http://www.tarpley.net ========================================================================= Date: Wed, 29 Jul 1998 21:12:23 -0700 Reply-To: List for the discussion of Buckminster Fuller's works Sender: List for the discussion of Buckminster Fuller's works From: Kirby Urner Subject: Thanks for your patience... Comments: cc: synergetics-l@teleport.com In-Reply-To: <35c14df4.379489902@news.teleport.com> Mime-Version: 1.0 Content-Type: text/plain; charset="us-ascii" To GEODESIC readers: Those of you well-versed in synergetics will have maybe seen the relevance of some of these altercations in the newsgroups: alternative vector for "dimension" as per Fuller's 4D, emphasis on a kind of mathematical precision that's not so crypto- compressed, is more world-readable and visual as per 'Synergetics' (a work in the humanities). But I think the Fuller-relevant points have pretty much been made (at least the one's I have to make in this context), so now I'm doing my best to snip bit.listserv.geodesic out of further replies to these 'Calculus 102' threads. I really appreciate your patience with this seemingly endless series of posts here on GEODESIC. If any of you still find this chatter interesting, I invite you to participate via sci.math, sci.philosophy.meta or one of the other non-GEODESIC NGs in the header -- or via Deja News. My experience is we're establishing a beach head for synergetics in the standard curriculum from this point forward. It'll be very difficult to write serious retrospectives that make no mention of Fuller, as has been the lazy/heedless practice (with notable exceptions) since 'Synergetics' was published over 20 years ago. Many are have contributed to our victory here and I am personally grateful for all the assistance I've received getting work accomplished in my own neck of the woods. So hey, I think we've won. So now lets get back to our studies. This Egyptian hieroglyphics translation Will has been doing, suggesting tie-backs to events and phenomena in Indonesia looks pretty interesting. The dome pages are looking good all around -- David, finally got a link to your http://w3.one.net/~monkey/ from new page linked from my http://www.teleport.com/~pdx4d/dome.html, which gets lots of hits. Thanks again, ya'll. Urner out. ========================================================================= Date: Thu, 30 Jul 1998 00:11:40 GMT Reply-To: List for the discussion of Buckminster Fuller's works Sender: List for the discussion of Buckminster Fuller's works From: mahipal@MY-DEJANEWS.COM Organization: Deja News - The Leader in Internet Discussion Subject: Re: Calculus 102: A Primitive Approach to Humanistic Concepts In article <35bf4cd9.379206430@news.teleport.com>, pdx4d@teleport.com (Kirby Urner) wrote: > Robin Chapman wrote: > > >Yes, Urner will always use ten long words when one short one would > >suffice. If he didn't then > >(a) people might understand what he was talking about, > > A fair number do. > > >(b) he wouldn't sound so impressive. > > Do I? In a domain of satisfying diminished standards, we all sound impressive. > >Stripped of their inessential verbiage, Urner's arguments aspire > >to the banal, so he is not likely to abandon his deliberate mystification. > > > > Banal = obvious? > > >> : But go ahead and slap your credentials on the table and walk away > >> : if you like. They may add some weight to your pan, tip the scales > >> : in your favor, in lieu of any further real discussion. > > > >Credentials are another Urnerian obsession. Rather than to attempt > >to refute one's argument he will instead insult one's supposed > >credentials while at all times brandishing his as "curriculum writer". > > Brandish? Wow. > > >Robin Chapman > > Thanks guy. Urner finds Chapman a most entertaining geek. The problem with people who can use long sentences to obfuscate, is that they can also resort to shorter phrases when prompted to do so. Nevertheless, unless you're writing "War And Peace" -- the longer you take to say something, the greater the likelihood that your wasting the Readers. Nevertheless, Urner continually attempting, I mean _attempting_, to denigrate others leads one -- that would be Me, c? -- to think that [Withholding the words of the now _Predictable_ future trajectory of my Meaning] Mahipal 'Marveling at others tracking Semantic Momentum -- is it?' Virdy / == \ / \/\/ The |meforce> Paradox \/ http://www.geocities.com/Athens/3178/GateWay2DREAMScomeTrue.html -----== Posted via Deja News, The Leader in Internet Discussion ==----- http://www.dejanews.com/rg_mkgrp.xp Create Your Own Free Member Forum ========================================================================= Date: Thu, 30 Jul 1998 02:16:02 GMT Reply-To: List for the discussion of Buckminster Fuller's works Sender: List for the discussion of Buckminster Fuller's works From: Jim Carr Organization: Supercomputer Computations Research Institute Subject: Re: Calculus 102: A Humanistic Approach to Primitive Concepts urnerk@my-dejanews.com writes: > >For those of you who liked my "An Intro to Math", I've got more re the >calculus implementing my computer language approach. Got a positive >review on sci.math (below). For the full text, see website original >at: http://www.inetarena.com/~pdx4d/ocn/calculus1.html What is new about Newton's divided differences? That even used to be taught in calculus, and is in some places, very much the way you do it. Another useful method is to use a ruler to get the slope at different points -- directly from the graph -- and see that it agrees with the numerical and analytic results, as one should expect. There are also some excellent resources on the web. My favorite is at http://www.math.psu.edu/dna/graphics.html with particular emphasis on the examples of tangents and derivatives. This graphically illustrates what your program or a student's spreadsheet is doing as you make the grid size smaller. >NOTE: calculus2.html (same website) is proving far more controversial >however, given it claims to be a contribution to "humanistic math" ... There are a few interesting things in there, but you also include a bunch of ideas that are hard enough to teach in physics after students understand calculus. Although they make good illustrations of where calculus is used (sorely lacking in some classes), I doubt if they will help non-traditional students. The concrete examples you use are more likely to work in my experience. By the way, you seem not to have noted that the integral symbol is a stylized "S" for summation (in the sense of measure theory), just as the greek "S" (sigma) is used for a discrete summation. Why not dispense with all of the educationese and just say that it helps students remember a new notation if you tell them where the notation came from or tie it linguistically or by example to something they already know? -- James A. Carr | Commercial e-mail is _NOT_ http://www.scri.fsu.edu/~jac/ | desired to this or any address Supercomputer Computations Res. Inst. | that resolves to my account Florida State, Tallahassee FL 32306 | for any reason at any time. ========================================================================= Date: Thu, 30 Jul 1998 15:22:41 -0000 Reply-To: List for the discussion of Buckminster Fuller's works Sender: List for the discussion of Buckminster Fuller's works From: hal mc whinnie Subject: fractals of the week Comments: cc: moderator@acn.net.au for any who might be interested I have a free service in which I send one of my fractal designs each week to my list of subscribers. these are sent as attached files in Jpeg, gif, or html format for the pc or windows. to subscribe send me an email halchaos ========================================================================= Date: Thu, 30 Jul 1998 12:37:36 -0700 Reply-To: List for the discussion of Buckminster Fuller's works Sender: List for the discussion of Buckminster Fuller's works From: Brian Hutchings Subject: Re: Calculus 102 <> Brian Hutchings 30-JUL-1998 12:37 r001806@pen2.ci.santa-monica.ca.us oy, Kirby has gained control of Geodesic-L, two -- thanks for telling us, man! of course, the summation notation was due to Leibniz, the dyscoverer of calculus. while it is true, according to J.Conway, that the "dotism" of Newton is better for certain things --forgotten, which, but it should be on the Geometry Forum archive-- that doesn't forgive his slander of Leibniz, with the help of Halley and the Royal Effin'Society! thus quoth: a stylized "S" for summation (in the sense of measure theory), just as the greek "S" (sigma) is used for a discrete summation. Why not -- The End of History -- again! http://www.tarpley.net ========================================================================= Date: Thu, 30 Jul 1998 07:34:49 GMT Reply-To: List for the discussion of Buckminster Fuller's works Sender: List for the discussion of Buckminster Fuller's works From: Robin Chapman Organization: HyperCross HeadQuarters Subject: Re: Calculus 102: A Primitive Approach to Humanistic Concepts In article <6podns$4f9$1@nnrp1.dejanews.com>, mahipal@my-dejanews.com wrote: > In article <35bf4cd9.379206430@news.teleport.com>, > pdx4d@teleport.com (Kirby Urner) wrote: > > Thanks guy. Urner finds Chapman a most entertaining geek. ??? I don't find the word "geek" in my dictionary (Chambers 1983). Is being described as a "geek" a compliment or an insult? Is being described by Urner as a "geek" a compliment or an insult? Robin Chapman -----== Posted via Deja News, The Leader in Internet Discussion ==----- http://www.dejanews.com/rg_mkgrp.xp Create Your Own Free Member Forum ========================================================================= Date: Thu, 30 Jul 1998 15:43:20 EDT Reply-To: List for the discussion of Buckminster Fuller's works Sender: List for the discussion of Buckminster Fuller's works From: Zac Elston Subject: Re: Calculus 102: A Primitive Approach to Humanistic Concepts Mime-Version: 1.0 Content-type: text/plain; charset=US-ASCII Content-transfer-encoding: 7bit In a message dated 98-07-30 15:38:02 EDT, rjc@MATHS.EX.AC.UK writes: > I don't find the word "geek" in my dictionary (Chambers 1983). try other sources. Merriam-Webster's Collegiate Dictionary, Tenth Edition (not the greatest..) geek (noun) [probably from English dialect geek, geck fool, from Low German geck, from Middle Low German] First appeared 1914 1 : a person often of an intellectual bent who is disapproved of 2 : a carnival performer often billed as a wild man whose act usu. includes biting the head off a live chicken or snake -- geeky (adjective) > Is being described as a "geek" a compliment or an insult? depends on the context and what you pride yourself on I would guess. > Is being described by Urner as a "geek" a compliment or an insult? depends on the context and what you pride yourself on I would guess. -zac ========================================================================= Date: Thu, 30 Jul 1998 12:55:26 -0700 Reply-To: List for the discussion of Buckminster Fuller's works Sender: List for the discussion of Buckminster Fuller's works From: Brian Hutchings Subject: Re: Calculus 102 <> Brian Hutchings 30-JUL-1998 12:55 r001806@pen2.ci.santa-monica.ca.us re Newtonian "calculus", his supposed geometrical demonstrations, in priciple, in "Principia", could have been done by him, as he was a student of Barrow, whose work has many such proto-calculus, or Archimedean demonstrations. of actual calculus, in the Halley-co-ordinated Principia --the one that was "reconstructed" after the "15yo trunk burned-up, unfortunately"-- there is just the simplest rectangle, the elementary "dydx", I think at Book 2, Section 2, paragraph 2 (he was not just an alchemist, but a numerologist -- "not the first of the scientists, but the last of the Magi", as Lawd Keynes said! good book: Arnol'd's _Barrow, Huyghens, Newton_ and I forget, the other guy! -- The End of History -- again! http://www.tarpley.net ========================================================================= Date: Thu, 30 Jul 1998 20:54:55 GMT Reply-To: List for the discussion of Buckminster Fuller's works Sender: List for the discussion of Buckminster Fuller's works From: BMScott@MY-DEJANEWS.COM Organization: Deja News - The Leader in Internet Discussion Subject: Re: Calculus 102: A Humanistic Approach to Primitive Concepts In article <35bed37c.348133000@news.teleport.com>, pdx4d@teleport.com (Kirby Urner) wrote: > BMScott@my-dejanews.com wrote: > >A tautology? Don't be silly: you can obviously pick four lines in R^4 > >that aren't mutually orthogonal. > What's tautologous is your use of the word "orthogonal" to mean > whatever you define it to mean within your game. The link to > "physical meaning" is broken (by your own admission) so I don't > see much to stop you from working in a vacuum. No, the link to physical meaning is *not* broken, and I never made such a claim. Orthogonality in inner-product spaces is a very straightforward generalization of the everyday notion of perpendicularity. The link remains in the case of R^2 and R^3 with the usual dot product. Moreover, if you take any 3-dim. subspace of a real inner-product space, it is naturally isomorphic to R^3 in a way that takes orthogonal vectors in the subspace to perpendicular ones (in the usual sense) in R^3. Your mathematical background may be insufficient for you to see the link, but it's certainly there. In fact, this is a very well-chosen mathematical term. > >*You* are naive to expect it. And a student taking linear algebra > >had better be able to get used to the idea that vectors and > >orthogonality needn't have physical significance. > I'm still casting about for some better metaphors. "Orthogonal" > seems sloppy -- as if even (x,y) grids had to be built from axes > at 90 degrees. Basis vector independence and perpendicularity > are not synonymous concepts -- or shouldn't be. They aren't, of course: surely your first course in linear algebra taught you that 'linearly independent' and 'orthogonal' aren't synonymous! It should have gone further and made clear that orthogonality is meaningful only in a space with an inner product, while linear independence is a fundamental notion in all vector spaces. > The quadrays > game makes this clear (4 basis vectors, no 90-degree angles > between them). Makes *what* clear? Your basis vectors aren't mutually perpendicular[1] in the geometric sense, but they also aren't linearly independent over the reals. You could talk about linear independence over the non-negative reals, I suppose, but why, save as an exercise? You don't get a particularly nice theory. [1] I avoid the more technical term 'orthogonal' here because you don't appear to have an inner product handy. > If you haven't a trace of superstition yourself, then fine, but I feel > pretty clear that a lot of people are unnecessarily awed and befuddled > by "dimension talk" I don't know about 'a lot of people', but it's clear that you are. > >> But I don't buy that the reason I can't visualize 4 mutual orthogonals > >> has anything to do with my "physical limitations" > >Yours personally? No. Human physical limitations? Obviously. > No, not physical limitations at all. You yourself said "4 orthogonals" > had no physical meaning, No, I did not. I said that there was no reason to try to give it a physical meaning. What if your four mutually orthogonal vectors are square-integrable functions, for instance? The physical space in which we live is (so far as we can tell) three-dimensional. We are physically limited to this space, as are our spatial perceptions. But it certainly isn't obvious that three is the only possible number of physical dimensions. > yet you ascribe an inability to attach an > image to this metaphor to "human physical limitations". Again you paraphrase inaccurately: I did not say that it's impossible to attach an image to the phrase 'four mutually orthogonal vectors'; I said that you are naive to *expect* to be able to do so. The intuitive motivation for the term comes from the everyday notion of perpendicularity, but the mathematical term has its own definition. > "Obviously" > you say. Obviously? Yes. > >> >Do you know enough mathematics to be aware of the fact that there are > >> >many different notions of dimension? > >[irrelevant response] > I gave an example of a different notion of dimension, using a different > mathematically-informed language -- hardly irrelevant. But it was, since the point of my question - no longer evident from what remains here, unfortunately - was the remark that followed, namely, that the ones that have proven mathematically significant (e.g., covering dimension and large and small inductive dimension) assign the same dimension, n, to R^n. This strongly suggests that the relationship of the space R^n to the number n is mathematically significant. (For a parallel, consider that independent and very different attempts to formalize the notion of a computable function provably yield the same class, a fact that reinforces the intuition that this is the 'right' class to consider.) > >> I usually am interested in discrete spaces, point populations. > >That would be fine, *if* you made that point clearly. But you don't: > >your screeds here and on your site(s) give the distinct impression > >that you're talking about ordinary Euclidean space. > I say ordinary Euclidean space is discrete. Then you're simply wrong. Euclidean space is a mathematical construct defined by certain axioms. Whether you use a purely geometric formalization or a Cartesian one, it isn't discrete. You appear to be talking about real, physical space, which is irrelevant to the mathematics (though not the history) of Euclidean space. > Atoms don't touch. So? The physical space in which they exist isn't Euclidean anyway. > Euclid and his buddies scribed with sticks in the sand on a locally > flat beach. So? Euclid also knew that the pictures were just visual aids, not exact representations of the subject matter. > 'The Elements' does not require a lot of metaphysics about > 'infinite, infinitely thin planes' Euclid's fifth postulate requires that a straight line be indefinitely extensible. In attempting to define 'line', he described it as 'breadthless length'. In other words, he seems to have been thinking of infinitely (or at least arbitrarily) long, infinitely thin lines. > >Moreover, some > >of your discussions (e.g., involving finer and finer triangulations > >of a polyhedron) require a space in which any two points have a midpoint > >(or some similar but more complicated requirement), so it's not clear > >in what sense they are discrete. > I posit frequency limits -- resolution limits -- which have to do with > the coordinate system, its precision. This is mere hand-waving until you work out the underlying mathematics. What is the topological structure of your stand-in for the real line? What is its algebraic structure? If your spacial geometry is discrete, how are the points arranged? Until you answer questions like those, you're just writing science fiction. > A coordinate system is a measuring > device and our instruments are not "infinitely precise" -- ever. A coordinate system is not a measuring device, but rather a standard of measurement. Whether our instruments can take full advantage of the standard, or whether the standard actually applies to physical space, are matters that have no bearing on the coordinate system itself. (Or do you deny that the real numbers, with their usual properties, can be rigorously defined?) > 'The > Elements' was done in sand. Sand is discrete. Another thread. The geometry of 'The Elements' is continuous, so the nature of sand is irrelevant. > >You don't present yours as a consistent and precise symbol game. [...] > >I'm not convinced that you've ever even thought out the underpinnings; > I'm not sure what you mean by "Euclidean geometry". Primarily I was thinking of the distinction between Euclidean and non-Euclidean geometry, since the context of the discussion pretty much excludes anything further afield. > If you mean > R^n, then I'd point out that Euclid never messed with R^n, or even > R (real numbers not defined until much later). Euclid had no idea what an abstract (or for that matter concrete) vector space is, and he didn't have the handy tools of coordinates and analytic geometry, but the geometry of 'The Elements' is that of R^2 and R^3. Then there are the results that are essentially geometric versions of such basic algebraic properties of R as the distributive law, geometric solutions of quadratic equations with real roots, and the classification of different types of irrational numbers (incommensurable lengths); these are 'messing with R', or at least the non-negative part of it, in all but name. > My "underpinnings" have to do with taking the electronic computer as > a metaphor for nature. A metaphor may serve as an inspiration; it is not a foundation. You've had the inspiration, but you haven't followed up by doing the mathematics, so you're still writing science fiction. > I see > myself as struggling to keep some important ideas and approaches > alive and in circulation -- stuff that doesn't get taught much > more out of prejudice and overspecialization than for reasons > that make a lot of sense. Your picture isn't very accurate, then. Your 'quadrays' stuff can't be *kept* alive and in circulation, since it never was, and it isn't particularly important. There may be ideas on your calculus2 page that could be put to use in some classrooms, but not without a great deal of work; you've just shovelled them out in a disorganized heap. If I remember correctly, there are a couple of decent expository ideas on the calculus1 page, but they're old hat; the same is true in spades of the intro-to-symbols page. (I don't have the URL handy, but I expect that you know the one I mean.) > >> As if Universe > >> had room for only one consistent "dimension talk" (e.g. the R^n stuff). > >You know, I fancy that I just pointed out a while back that there are > >lots of different mathematical notions of dimension. Would you like > >to make a more supportable accusation? > And then you deleted my example as "irrelevant". It was, in context; see above. Here, on the other hand, I merely noted that I'd already made it abundantly clear that I *don't* think that the universe has room for only one consistent notion of dimension; your insinuation to the contrary was rather foolish, since the refutation was available in the same post. > You call people > "naive" for trying to attach "physical meaning" to 4 orthogonals > and then say "obviously" our "human physical limitations" are to > blame for our inability to get the hypercross through our thick > skulls. You really don't impress me as a particularly consistent > thinker. The problem isn't my lack of consistency; it's your lack of reading skills. I said nothing about 'our inability to get the hypercross through our thick skulls'. You seem to think that everything has to have a physical meaning, or at least that if it doesn't, we can't understand and work with it. This simply isn't so. > If you accept that mathematics has room for a different "dimension > talk" then why not accept mine? What's all the fuss? The fuss has nothing to do with the idea itself. There's nothing wrong with playing around with your version of barycentric coordinates; I can think of classroom settings in which it might be quite worthwhile. The fuss has to do with the way you approach the matter, and your use of 'accept' is symptomatic. What's to accept? That it's possible to coordinatize R^3 in this way? Sure, but so what? There are lots of other ways, too, many of them more generally useful. No, the fuss has to do (in no particular order) with: (1) your insistence on seeing this as a battle ('report back from the front', 'creamed the opposition'); (2) your intellectual sloppiness, e.g., the notion that a metaphor is an adequate foundation for a consistent geometry; (3) more generally, a strong tendency to confuse style with substance; (4) your persistent inability to distinguish between mathematical space and physical space; (5) your rhetorical style, which is frequently a blend of bad Madison Avenue, MTV, and rabble-rouser. Of these (1) and (5) are probably the most immediately annoying and the proximate cause of the unpleasant tone of many reponses, but it's (2) and (3) that really bother me. Whatever manipulative facility you may have acquired, you don't appear to understand mathematics very well at all. More generally, I can't see that you have any understanding of or use for intellectual rigor, so I wouldn't let you anywhere near a curriculum of any sort - mathematics, history, you name it - let alone an academic classroom. Here's a specific example. Somewhere in your pages you make the throwaway claim that 'our decimal numbering system traces back to the abacus'. Perhaps it does, but do you actually have any evidence? Positional notation, decimal or otherwise, seems to have been invented in India and in Central America; did both cultures use some form of abacus? (It's quite likely, but do you *know* that they did?) And how do you account for the fact that many other cultures that certainly did use the abacus in some form did *not* develop positional notation? Or for the fact that if - as in medieval Europe - you have the abacus or counting board as an efficient computational tool and use numerals only to *record* numbers, you don't *need* the computational advantages of positional notation and therefore have one less incentive to develop it? > >You have some misconceptions here. First, it's obvious to anyone > >who's taken a decent calculus course, never mind linear algebra, that > >the number of coordinates used may exceed the number needed; > Quadrays have no redundant coordinates. This is true but irrelevant, as I didn't say that they did. *If* you use that coordinatization, you cannot dispense with any of the coordinates. Nevertheless, it *does* have one more coordinate than is *needed*, since the three standard Cartesian coordinates suffice. (And of course once you allow negative coefficients, any one 'quadray' coordinate may be dispensed with as redundant.) > It's the mirror imaging of > scalars by means of the '-' operator which we don't need to include > in point addresses. Four directions omnisymmetric Poor choice of terminology: e.g., they aren't symmetric under reflection through the origin. > from the origin > are not distinguished into two groups, positive and negative. It's > not that I discriminate against "negative numbers" it's that I > don't need to divide numbers into two sets (if you don't have > negatives, you don't have positives either, and the '-' sign > becomes an operator, not an attribute of any scalar). You've already divided the reals into two sets; you've simply thrown one out. Whether the '-' in '-3' is an 'attribute of [the] scalar' or an 'operator' is largely a matter of point of view: are you looking at -3 simply as a real number, or are you looking at it as the additive inverse of 3? You've pointed out, for instance, that you still have an additive inverse for each vector, e.g., > (2,1,1,0) + (0,1,1,2) = (2,2,2,2) = (0,0,0,0) In other words, in the algebra of vector spaces (without which they haven't much point), (0,1,1,2) = -(2,1,1,0). Okay, how does one find -x systematically? The straightforward approach of finding (-2,-1,-1,0) and normalizing obviously brings in the negative reals, so let's be cleverer: let M be the max. coord. of x = (x1, x2, x3, x4) and find (M-x1, M-x2, M-x3, M-x4). But we're still using subtraction in R, which is formally addition of additive inverses, i.e., of negative reals. ===== You had disagreed with my assertion that 'quadrays' were essentially just barycentric coordinates. > >Eh? Of course they are: the basic idea's exactly the same. > People on geometry_research (besides me that is) disagree. Then they're mistaken too. > >> Remember, in your game 'vector reversal' (application of > >> the '-' sign) is lumped under scalar multiplication. > >No, it's not: look at the axioms for a vector space. What *is* true > >is that one can prove as a derived fact that for any x, -x = (-1)x. > Right. Multiplication by -1 is considered scaler multiplication, > rather than two operations i.e. multiplication by scalar 1 (leaves > x unchanged), followed by application of the '-' operator, which > reverses its direction. What do you mean 'is considered'? Since we're talking about vector spaces over R, and -1 is a real number, -1 *is* a scalar, and the operation represented by (-1)(x) *is* scalar multiplication. Multiplication by scalar 1 followed by taking the additive inverse is a different sequence of operations altogether. To avoid confusion between the '-' of '-1' and the operation of taking the additive inverse in the vector space, I'll use '_' for the latter. (They are distinct, and I suspect that some of your confusion stems from the fact that we use the same symbol for both.) Then, since 1 is also a scalar, we can combine it by scalar multiplication with _x to get the vector (1)(_x). Finally, we can combine 1 with x by scalar multiplication to get (1)(x) and then take the additive inverse to get _[(1)(x)]. Formally these are three distinct objects, but the vector space axioms allow us to prove that in fact they're the same vector. There is no lumping together of distinct ideas. Rather, we simply prove that various sequences of operations are guaranteed to yield the same result. That doesn't mean that we consider them to be the same sequences of operations, however! > >> I don't see '-' vectors as "less basic" than '+' > >> vectors in XYZ. > >Well of course not! If V is a real vector space - I don't care which - > >and x is a vector in V, then -x is simply the additive inverse of x. If > >I like, I can give -x the name y, in which case x is -y. Perfect symmetry. > >Where's the problem? > The problem is in XYZ we call only 3 of the 6 vectors protruding from > the origin "basic" i.e. the "positive" ones. No, we single out three of the *infinitely* many vectors as basic. Any other three orthonormal vectors would have done equally well. You do the same when you choose the origin and orientation of the 'quadray' system. > What's so special about > the positives versus the negatives? Nothing much in this context; but *you're* the one investing them with 'specialness', not I. In R^3 you can start with four linearly independent vectors, x, y, and z, and notice that every vector in R^3 is uniquely a linear combination of these over the field of real numbers. Uniqueness is useful, and R is algebraically a nice object. Or you can start with three lin. indep. vectors x, y, and z, throw in as a fourth vector w = -(x + y + z), and note that every element of R^3 is expressible as a non-negative linear combination of x, y, z, and w. (Yes, you can be more general, but this will do.) You can even get uniqueness if you add the requirement that at least one coefficient be 0. But the uniqueness does require an additional constraint, and the set of non-neg. reals isn't as nice an object as R. Unlike R, it is genuinely asymmetric. One can of course construct the negative reals as equivalence classes of ordered pairs of non-negative reals, so that '-3', for instance, is simply a label for {(x,y) : x, y are non-neg. reals & x = y + 3}. Using square brackets for equivalence classes, we can then write the vector -2e1 + 3e2 - e3 as [(2,0)]e1 + [(0,3)]e2 + [(2,1)]e3, for instance, with no minus signs at all and all the superficial symmetry you could want. But it's inconvenient and generally serves no useful purpose. Moreover, it's got the same asymmetry as 'quadrays': the negative reals have been carefully removed from the picture. > >Well, here's part of the problem. There is no such bias. Indeed, it's > >your normalized 'quadray' system that seems designed to accommodate > >student bias toward positive numbers. > Negative mirroring is used to achieve bilateral symmetry, but '+' is > 'passive' whereas '-' is 'active' (reverses a vector). Essentially you're talking about symmetry operations here and merely noting that the operation that corresponds to prefixing '+' is the identity operation. That's no more 'passive' than any other symmetry operation; it just happens to yield the input as output. Here again you seem to be having trouble mostly because you're laboring under the same misunderstandings as many students. (The extreme form of this one is unwillingness to accept that f(x) = x is 'really' a function.) ===== > >Your response was a non sequitur; do you want to try again, or do you > >grant the point? To make matters absolutely clear, I am talking about > >what it suggests to students. > I'm not sure what your concern is -- I'll grant the point and hope I'm > not sliding into a clever trap. You had claimed that a lot of calculus was intuitions that could be developed without any complex symbology. As an example you had said: > >Two quantities covary a little during a time-slice > >(change happens). > > That's all you need for a ratio, and > >that suggests a slope, a rate, action in time (energy). And I responded: >*If* this were true, teaching calculus would be a snap. >Unfortunately, it's not: if you're lucky it suggests a rate, but it >certainly doesn't suggest a slope. Now you are apparently agreeing that your original claim was a bit exaggerated, that perhaps the intuitions in question aren't so accessible as you originally implied. Brian M. Scott -----== Posted via Deja News, The Leader in Internet Discussion ==----- http://www.dejanews.com/rg_mkgrp.xp Create Your Own Free Member Forum ========================================================================= Date: Fri, 31 Jul 1998 01:34:36 -0700 Reply-To: List for the discussion of Buckminster Fuller's works Sender: List for the discussion of Buckminster Fuller's works From: Brian Hutchings Subject: we would like to welcome you to Nashville. <> Brian Hutchings 31-JUL-1998 1:34 r001806@pen2.ci.santa-monica.ca.us GEODESIC FAST RESPONSE TEEN ALERT -- the sky is glowing! 13:403) AIR AND SPACE Brian Hutchings 31-JUL-19 1:25 did anyone hear (on, say, KPFK, as I think I did) or read (in the Times e.g.of yesterday, I think) about the pausited "collapse of the ice shelf" ??... as I grokked, it was the "fast ice-stream" off of Pine Islnad, retreating, which I guess is in the central sea, that was a putative threat to the *shelf* of ice; yet, I seemed to have the weird sensation, that the shelf is supposed to be floating, *now*. I mean, if that is the case, it's worse than the brouhooha over the 75 square miles o'berg that calved, recently (recall, the second root of 75 -- thank you). I mean, Dumb and Dumber, and Dumbest is still below the horizon! thak God, the lifeboats are all ... are ... decorative? -- The End of History -- and every thing -- AGAIN ?? http://www.tarpley.net ========================================================================= Date: Fri, 31 Jul 1998 15:09:46 +0200 Reply-To: List for the discussion of Buckminster Fuller's works Sender: List for the discussion of Buckminster Fuller's works From: tom aagdii Subject: Cities-Boston In-Reply-To: MIME-Version: 1.0 Content-Type: TEXT/PLAIN; charset=US-ASCII if you want to build a new city you better understand a digital one. tagdi ========================================================================= Date: Fri, 31 Jul 1998 08:30:43 -0700 Reply-To: List for the discussion of Buckminster Fuller's works Sender: List for the discussion of Buckminster Fuller's works From: Kirby Urner Subject: Re: Calculus 102: A Humanistic Approach to Primitive Concepts In-Reply-To: <6pqmiv$v9f$1@nnrp1.dejanews.com> Mime-Version: 1.0 Content-Type: text/plain; charset="us-ascii" At 08:54 PM 7/30/98 GMT, you wrote: >In article <35bed37c.348133000@news.teleport.com>, > pdx4d@teleport.com (Kirby Urner) wrote: > >> BMScott@my-dejanews.com wrote: > Sorry GEODESIC readers -- that one (from Brian Scott) snuck through. My reply was even longer and is findable on sci.math, sci.physics, sci.philsophy.meta or via Deja News. I welcome any input for GEODESIC scholars, just feeling somewhat embarrassed that my postings have triggered such an avalanche (a welcome sign). Kirby ========================================================================= Date: Fri, 31 Jul 1998 07:33:46 GMT Reply-To: List for the discussion of Buckminster Fuller's works Sender: List for the discussion of Buckminster Fuller's works From: Robin Chapman Organization: HyperCross HeadQuarters Subject: Re: Calculus 102: A Primitive Approach to Humanistic Concepts In article <6pqmiv$v9f$1@nnrp1.dejanews.com>, BMScott@my-dejanews.com wrote: > In article <35bed37c.348133000@news.teleport.com>, > pdx4d@teleport.com (Kirby Urner) wrote: > > > People on geometry_research (besides me that is) disagree. > I gave up reading geometry.research ages ago because of its dire signal/noise ratio, mostly due to Urner's logorrhoeic drivel. The group should be retitled geometry.remedial. Were I still reading it I would certainly assent to Brian's assertion that Urner's "quadrays" are basically barycentrics. Robin Chapman -----== Posted via Deja News, The Leader in Internet Discussion ==----- http://www.dejanews.com/rg_mkgrp.xp Create Your Own Free Member Forum ========================================================================= Date: Fri, 31 Jul 1998 06:41:35 -0400 Reply-To: List for the discussion of Buckminster Fuller's works Sender: List for the discussion of Buckminster Fuller's works From: nicksanspam@ECE.VILL.EDU Organization: Villanova University Subject: Re: Lift a weight (5Kg) with the energy from a candel >Let's say we don't use levers, and the balloon material weighs 10 grams >per square meter, and it has a thermal conductance of 5 W/m^2C, and the >candle makes 50 watts and weighs 500 grams, and the 20 C air in the room >weighs 1.2 kg per cubic meter... And how large does the balloon have to be if it has no candle, but the top hemisphere is transparent and it receives 1 kW/m^2 of vertical sun, and the bottom hemisphere is black inside and silvery outside, with a thermal conductance of 1 W/m^2C? And can we keep the balloon up overnight by storing some solar heat in some water inside, if the top receives 5 kWh/m^2 on an average January day, when the outdoor temperature is 0 C? Nick ========================================================================= Date: Fri, 31 Jul 1998 04:36:44 -0800 Reply-To: List for the discussion of Buckminster Fuller's works Sender: List for the discussion of Buckminster Fuller's works From: "Clifford J. Nelson" Organization: gte.net Subject: Re: Calculus 102: A Primitive Approach to Humanistic Concepts Mime-Version: 1.0 Content-Type: text/plain; charset=US-ASCII Content-Transfer-Encoding: 7bit On Thu, Jul 30, 1998 11:33 PM, Robin Chapman wrote: >In article <6pqmiv$v9f$1@nnrp1.dejanews.com>, > BMScott@my-dejanews.com wrote: >> In article <35bed37c.348133000@news.teleport.com>, >> pdx4d@teleport.com (Kirby Urner) wrote: >> >> > People on geometry_research (besides me that is) disagree. >> > >I gave up reading geometry.research ages ago because of its dire signal/ >noise >ratio, mostly due to Urner's logorrhoeic drivel. The group should be retitled >geometry.remedial. Were I still reading it I would certainly assent to >Brian's assertion that Urner's "quadrays" are basically barycentrics. > >Robin Chapman Has Kirby Urner sent obscene hate email to you yet? I guess you are not a high priority target if he hasn't. Score a point for him if he got you to stop reading geometry.research. Cliff Nelson ========================================================================= Date: Fri, 31 Jul 1998 12:36:11 -0700 Reply-To: List for the discussion of Buckminster Fuller's works Sender: List for the discussion of Buckminster Fuller's works From: Kirby Urner Subject: Re: Calculus 102: A Primitive Approach to Humanistic Concepts In-Reply-To: <6prs0q$jgd$1@nnrp1.dejanews.com> Mime-Version: 1.0 Content-Type: text/plain; charset="us-ascii" At 07:33 AM 7/31/98 GMT, you wrote: >In article <6pqmiv$v9f$1@nnrp1.dejanews.com>, > BMScott@my-dejanews.com wrote: >> In article <35bed37c.348133000@news.teleport.com>, >> pdx4d@teleport.com (Kirby Urner) wrote: >> >> > People on geometry_research (besides me that is) disagree. >> > >I gave up reading geometry.research ages ago because of its dire signal/noise >ratio, mostly due to Urner's logorrhoeic drivel. The group should be retitled >geometry.remedial. Were I still reading it I would certainly assent to >Brian's assertion that Urner's "quadrays" are basically barycentrics. > >Robin Chapman > I've posted rather sparingly to geometry_research over the years, and appreciate the intelligent conversations I've had with various individuals (Hart, Nelson, Conway, Yoder...). Kirby ========================================================================= Date: Fri, 31 Jul 1998 12:46:53 -0700 Reply-To: List for the discussion of Buckminster Fuller's works Sender: List for the discussion of Buckminster Fuller's works From: Kirby Urner Subject: Re: Calculus 102: A Primitive Approach to Humanistic Concepts In-Reply-To: <6psecu$ro8$1@news-1.news.gte.net> Mime-Version: 1.0 Content-Type: text/plain; charset="us-ascii" >Has Kirby Urner sent obscene hate email to you yet? I guess you are not a >high priority target if he hasn't. Score a point for him if he got you to >stop reading geometry.research. > > > Cliff Nelson > You like to suck up to these guys (who never seem to give you the time of day) in hopes of getting an audience for your Mathematica stuff, and meanwhile shoot at me (hoping this will assist in your efforts to endear yourself with my opponents). When I show you my bona fide scholarship, and how what I'm doing is consistent with what's printed in Fuller's 'Synergetics', this falls on deaf ears, because your program is mostly political, not rigorously intellectual. You need me for an enemy, is the long and short of it. If I call you a little shit in private (is that what it was?), that's not because I don't think it out loud as well. That being said, I have no problem with you marketing your stuff and finding an audience. Kirby ========================================================================= Date: Fri, 31 Jul 1998 13:10:08 -0700 Reply-To: List for the discussion of Buckminster Fuller's works Sender: List for the discussion of Buckminster Fuller's works From: Kirby Urner Subject: Alternative investor-reward systems Comments: To: SE-Cafe@csf.colorado.edu In-Reply-To: <35C1C049.F5E52B09@top.monad.net> Mime-Version: 1.0 Content-Type: text/plain; charset="us-ascii" At 09:02 AM 7/31/98 -0400, you wrote: >Paul Isaacs: >It seems to me that "economics" is the sum total of human activity. >The proof is that if everyone on the planet simply took a day off, >the net economic activity for that day would be precisely zero. > Shutting the store down for a day would take a tremoundous amount of work and would take quite awhile to recover from, especially if you mean halting all the automated functions which continue by default. Humans are under extreme pressure to work and "stopping altogether" would take more work (against the grain of nature) than "keeping it going". The default is to breathe, not to hold your breath. The "economy" is humanly-contrived circuitry embedded in natural circuits of extra-human origin -- with no hard line between the two, given humans didn't contrive humans to begin with (not getting religious on ya, just pointing out that most of what we call "reality" is operating cybernetically and with no human egos at the helm -- our economy being a subrealm of the whole in which human decision-makers get to exercise their so-called free wills). Included in the humanly-contrived circuitry are switching systems for channeling work-potential (energy) to credit accounts. If I have a lot of credit to my name, I can turn some big wheels whereas if I've been left out of the game (no chips), I may have a hard time keeping my kids alive. The energy is mostly solar and derivatives, with human intelligence operating to float its economy atop larger ecosystemic circuits (e.g. hydro dam inserts in the sun-driven evaporation-condensation cycle). Stocks are a way of limiting the liability of investors who want vicarious risk-taking to net them returns. If too many people want to leave the serious risk-taking to others, then real and looming challenges fail to be addressed (everyone waiting for someone else to deal with it) and what could have been a fairly profitable scenario (in terms of higher living standards) turns out to be more disasterous because the ethos of "no risk, big returns" is a kind of irresponsible escapism, a kind of immaturity, which historically often leads to war. As Thurow (MIT) put it in a radio broadcast awhile ago, there's nothing in the theory that says capitalists can't also be cowards. We can always wait for exponentially increasing debt loads to drive enough people into despair and misery to get a war started, and unleash a lot of innovative engineering via the prime contractor irrigation system (aka defense spending). But many planners don't call this a "plan" so much as "waiting for disaster to strike" -- a cowardly stance, not befitting the self-styled "captains of industry" persona of the mythical past (J.P. Morgan would probably scoff at today's "industry leaders" for their "follow the pack" mindset). Clearly the Russian economy needed an unleashing of innovative engineering yesterday. Capitalism has not performed well.[1] The challenge, as I see it, is figuring out how to get more people off the sidelines, expecting all the benefits of the good life minus needing to honestly face looming challenges (a job mostly left to scape-goat politicians with few relevant skills). Part of the answer may be the issuance of surplus (profits) in forms other than cash-redeemable certificates e.g. paper securities earmarked against tuition costs. IBM will help its backers get through school if the company does well, and "school" (at least for the more serious-minded investors) may include a tour at some prototyping facility where new ideas get hammered out (e.g. beta tested) prior to commercial release. This is a trend today in a lot of ways, with Microsoft looking for "developer partners" who test and use its products in the real world. As a partner, my tickets to skill-building courses increase in value as the skills in question (e.g. installing Windows NT) become more in demand (a self-reinforcing feedback loop, as the spread of NT depends on a growing supply of affordable installers). Couple this with ESOP compensation to in-house engineers (who know their stock value is tied to performance on the job) and you have a picture of how a corporation can tie compensation to profitability in ways that blur the distinction between "investor" and "crew member". Of course we all want cold cash (as dividends or profit from selling appreciated paper) with its "liquid" ability to bring in anything "money can buy" and as long as others are offering this reward, you won't find many takers for other forms of credit. On the other hand, if "money can't buy" some of the benefits and experiences that corporations are willing to offer those investors who partner more than just front cash from the sidelines (that comes from sales), then in a sense we're reducing the "convertability" of cash. Bottom line: what we're starving for out here in the Silicon Forest isn't money so much as skills. All the money in the world can't buy you skills -- you need to do the work, make the effort, hit the books, take the trainings. As employe- ownership grows, investors may be finding (this is a projection not a certainty) that more corporations are experimenting with ways to include investors which are rewarding, and certainly worth more than the purchase price, but aren't 100% cash payouts. This is becoming easier to implement given computers, personal identity authentication (required for non-transferrable certificates), the capability to build credit accounts for people that are far more detailed than before. Certainly these ideas have application in the not-for-profit world, where already donor benefits (premiums) might include outdoor wilderness experiences or privileged access to an in-house library or internet chat room. Kirby [1] of course part of the problem is lingering paranoia: the Qualcomm kid was arrested for using GPS on a Russian target er city because Russian military planners still feared the data was headed for cruise missile guidance computers. Technological innovation is bottle-necking everywhere these days because the exact same systems have both profitable civilian and lethal uses (anything GIS/GPS, Motorola's Iridium system and so on). For example, Iraq needs serious high tech to give its people a good living standard, but the State Department insists on a Cubafication strategy because of the "dual use" nature of just about anything high tech. The solution is to brand long-term unprofitable weaponry-design as a form of misanthropy and turn up the volume against "mad scientists" who cow politicians with their designed- to-scare tactics. ========================================================================= Date: Fri, 31 Jul 1998 14:30:55 -0400 Reply-To: List for the discussion of Buckminster Fuller's works Sender: List for the discussion of Buckminster Fuller's works From: nicksanspam@ECE.VILL.EDU Organization: Villanova University Subject: Re: Lift a weight (5Kg) with the energy from a candel Eur van Andel wrote: >>Let's say we don't use levers, and the balloon material weighs 10 grams >>per square meter, and it has a thermal conductance of 5 W/m^2C, and the >>candle makes 50 watts and weighs 500 grams, and the 20 C air in the room >>weighs 1.2 kg per cubic meter... >Let's take round balloon, radius r, air temp in balloon T. > >surface of balloon 4 pi r^2 >contents of balloon 4/3 pi r^3 >weight of balloon 9.81*0.04 pi r^2 Why 9.81, I wonder... >power to heat balloon 4 pi r^2 *5 * (T-20) I think the idea was to use only one candle... Just 50 watts. >so, to lift 5 kg: > >9.81*(5+0.04 pi r^2)=4/3 pi r^3 (1.2-ro_T) Or maybe just 5+0.5+0.04 pi r^2 = 4/3 pi r^3 (1.2-ro_T), including the weight of the candle. >oops. Excel to the rescue... So: a 7.16 m diameter balloon, with 16 candles. With only 1 candle, it seems to me the answer is "it can't be done." The optimum balloon diameter is about 6.6 m, with a lift/weight of about 0.2. Now how about those solar versions? Nick Hint: Bill Sturm @ Specialty CEA Structures Inc. in Calgary Alberta Canada (403) 274-8800 now has a 12,000 SF greenhouse that uses soap bubbles as the insulation/shading method, and they are building a 120,000 SF greenhouse... ========================================================================= Date: Fri, 31 Jul 1998 21:11:06 GMT Reply-To: List for the discussion of Buckminster Fuller's works Sender: List for the discussion of Buckminster Fuller's works From: Kirby Urner Organization: 4D Solutions Subject: Re: Calculus 102: A Humanistic Approach to Primitive Concepts MIME-Version: 1.0 Content-Type: text/plain; charset=us-ascii Content-Transfer-Encoding: 7bit lrmead@orca.st.usm.edu (Larry Mead) wrote: >Seriously, if that is so, I feel somewhat sorry for them; they have >learned certain pictorial analogies which, I believe, will not help >them understand deep mathematics later on, and in any case are not very >useful in general. In the same time, they would already have learned >about functions and graphing by rote practice, for example. > We do sphere packing in successive layers around a nuclear sphere: layers 12, 42, 92... 10 ff + 2 where f = frequency (intervals between spheres). This gives the so-called "face-centered cubic" lattice (a Barlow packing) and we can find polyhedra embedded in it, e.g. 4 spheres touching one-another = tetrahedron, our unit voxel. Tetrahedra of volume 1 and octahedra of volume 4 (in population ration 2:1) comprise this packing. The spheres, if expanded to press flat against one another (anologous to circles becoming hexagons in a plane) are rhombic dodecahedra of volume 6. We can build tetrahedron, octahedron, cube, rhombic dodeca, cuboctahedron using A and B modules (irregular tetrahedra of volume 1/24). These also build the space-filling coupler of volume 1. Quicktime animations linked from http://www.teleport.com/~pdx4d/modules.html give a better idea. Feeling conversant in this lattice or matrix is not irrelevant to my curriculum goals -- on the contrary I think too much time is spent on exclusively rectilinear, orthonormal coordination at the expense of not giving kids much fluency with such a sphere packing geometry. That's unfortunate. I don't think any 8th grader should be in the dark about all of the above and my curriculum (part web, part television, part classroom, part other) is designed to relay the above information quickly, during afterschool hours (not expecting text book industry to shift gears in a hurry). >While this post has been the clearest I have seen and it went a long >way to explaining in simple fashion what you are doing and why, I still >believe strongly that this kind of approach is a big mistake. > That's an opinion based on a lot of experience with your preferred curriculum but I don't think with sufficient experience with mine. Nevertheless, you are of course entitled to your opinion and only time will tell. If I think I have a better way, I have to prove it. Someone mentioned longitudinal studies. I think these will be important. >Again, it is not a matter of who programs the computer; rather, the lack >of practice in *using* numbers which accompanies the too-early use of >calculating devices. Liken this as I do to art students who watch films of >sculpting techniques and finished products of the masters, but never once >touch, feel and manipulate the clay which is supposedly their medium. > This is an important debate and is going on all over the internet via many threads. I think computer languages provide alternative math notations in a lot of ways, such that kids feeling alienated by SIGMA might get it if finding it repackaged as a do-loop -- same for other math. APL originally started as a chalkboard notation for math concepts and then became an interpreted computer language -- this shows how fine to non-existent is the distinction between a symbolic math language and a computer language. I live in the Silicon Forest and employers in my area are hungry for more competent computer users, so obviously a curriculum which is computer-centric is more likely to fly in this neck of the woods than some other places. A local community college classroom has trapezoidal desks, Pentium notebooks on each, all networked by radio frequency. This is prototypical of a standard math class in our region. >"multicultural" has become a politically correct catch phrase for all >sorts of things. It matters not where you are from or what your background >is - if you are going to do a derivative or integral, there is but one >correct result (you must admit)and that will be gotten only by >sufficiently understanding the intellectual content of the processes >involved. In my view, this type of "mtv-age" presentation of mathematics - >while perhaps well-meaning -will only fail; it may even exacerbate the problem. > Think of my library of short animations, clips, archived for splicing in many different orders, as a kind of 'Sesame Street' for people heading into your classroom some years from now. My kids will have a comfort level with the symbols, an appreciation for applications, an understanding of historical origins of many of the concepts and debates associated with the calculus. How well these kids perform with symbols will vary. I'll be interested to run tests vis-a-vis a control group. The animations are "multicultural" in the sense that many of them easily cross language lines, much as to international symbols for baggage collection, car rental, restrooms, in today's global airports. Today, televised math tends to feature some guy with a felt pen scribbling symbols on overhead cells while droning. The show is close to zero-budget, devoid of glitz. At the other extreme, you get a lot of glitz, but with emphasis on "professional mathematicians" with very little real math content (like in that movie "Good Will Hunting" -- the math is "implicit", like sex in an old black and white movie). I'm aiming for something in between -- a lot better production values than in obscure cable squiggle sharing, but a lot more content-packed (real training, exercises on the web) than that PBS 'Life by the Numbers'. Kids will watch, but adults too, and not feel patronized or talked down to. >: If I say the way to reach these kids is by analogies to film and TV, >: then those are the media I should be using, yes? Web too. > >No and no. > Not exclusively, but certainly these are very important tools. I'm somewhat amazed if you don't think so. Computer graphics have come a long way in recent decades and we can go a lot further with spatial geometry (important to chemistry, crystallography, architecture, astronomy...) in a short time via TV than ever before, and with much younger audiences tracking (my 4 year old knows what a dodecahedron is, and a jitterbug transformation). >: Brian made fun of my style as MTV-like. Maybe that's a good way to close. >: Stay tuned. >: Kirby > >I'll be here. Check you program guide -- sooner rather than later if all goes according to plan. Kirby --------------------------------------------------------- Kirby T. Urner http://www.teleport.com/~pdx4d/kirby.html 4D Solutions http://www.teleport.com/~pdx4d/ [PGP OK] --------------------------------------------------------- ========================================================================= Date: Fri, 31 Jul 1998 20:45:50 GMT Reply-To: List for the discussion of Buckminster Fuller's works Sender: List for the discussion of Buckminster Fuller's works From: Kirby Urner Organization: 4D Solutions Subject: Re: Calculus 102: A Humanistic Approach to Primitive Concepts MIME-Version: 1.0 Content-Type: text/plain; charset=us-ascii Content-Transfer-Encoding: 7bit pdx4d@teleport.com (Kirby Urner) wrote: >pdx4d@teleport.com (Kirby Urner) wrote: > >And for u dot v corresponds to -(tr UV/2) were tr is the >transpose. > >So that's not "n-tuples of any degree". > >Source: Howard Eves, Elementary Matrix Theory, (Dover Publications, >1966) pp 53-56. > Goofed again. Sorry folks. Of course 'tr' couldn't mean 'transpose' as that would leave us with a matrix for an answer, and of course inner product (dot) outputs a scalar. 'tr' means 'trace' or 'spur' and is the sum of the diagonal elements of a matrix (descending left to right). Ibid pg. 18. I admit my linear algebra is a bit rusty. Kirby --------------------------------------------------------- Kirby T. Urner http://www.teleport.com/~pdx4d/kirby.html 4D Solutions http://www.teleport.com/~pdx4d/ [PGP OK] ---------------------------------------------------------