From MAILER-DAEMON Fri Oct 4 13:58:23 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 g94HwMmd024563 for ; Fri, 4 Oct 2002 13:58:22 -0400 Message-Id: <200210041758.g94HwMmd024563@linux00.LinuxForce.net> Received: (qmail 26165 invoked from network); 4 Oct 2002 17:58:14 -0000 Received: from listserv.buffalo.edu (listserv@128.205.7.35) by deliverance.acsu.buffalo.edu with SMTP; 4 Oct 2002 17:58:14 -0000 Date: Fri, 4 Oct 2002 13:58:12 -0400 From: "L-Soft list server at University at Buffalo (1.8e)" Subject: File: "GEODESIC LOG9805" To: Chris Fearnley Status: RO Content-Length: 364760 Lines: 8640 ========================================================================= Date: Fri, 1 May 1998 00:00:11 -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: *SEMI-MONTHLY POSTING* - GEODESIC 'how-to' info ------------------------------------------------------------------------------- This is the semi-monthly "How To" file about the GEODESIC list. 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(Can be in the same message.) ------------------------------------------------------------------------------- (You may want to save this file to forward on to people who are interested, as it tells what the list is about, and how to subscribe and unsubscribe.) Pat _____________________________Think For Yourself______________________________ Patrick G. Salsbury http://www.sculptors.com/~salsbury/ ----------------------- Don't break the Law...fix it. ;^) ========================================================================= Date: Fri, 1 May 1998 02:48:35 -0600 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: Volume of geodesic "sphere" (project) In article <354893a9.601411515@news.teleport.com>#1/1, pdx4d@teleport.com (Kirby Urner) wrote: > > Robin Chapman wrote: > > >You claimed ownership for him. Your phrase was "de Jong's expression". > > I still say "de Jong's expression" (similar to Euler's). But not > to make either immortal. I also say "my synergetics" even though > it's also Fuller's. > > >The square of the volume of a tetrahedron is a polynomial in the squares > ^^^^^^ ^^^^^^^ > > I don't usually say "square" for 2nd powering BTW as the triangle > serves just as well as a model of 2nd powering and is topologically > simpler, as does the tetrahedron for 3rd powering, which is why > Gerald's expression is slightly different -- 1^3 is not a cube. But you still wrote a^2. How do you say this? a triangled? What about a^3? Anyway there is a subtle disadvantage with using the regular tetrahedron as the model for measuring volume, as opposed to the cube and indeed either the equilateral triangle or the square for measuring area. One can estimate area of a plane figure, by superimposing a fine square grid and counting the number of little squares in your given figure. You can do the same with equilateral triangles. In three-dimensional space one can do the same with cubes, as we can tessellate space by cubes, BUT it is impossible to do the same with regular tetrahedra. > Boils down to a simple conversion constant of course, but also > has implications for visualization and terminology (not that we > have to abandon the "old religion" -- when in Rome...). Yes, you are an advocate of "quadray" coordinates. No doubt you would label me a slave to "hypercross dogmatics". I admit it. 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. > Euler's and Gerald's give out different numbers for the same inputs > -- misleading to name them the same, even if they're similar. It is misleading not to call them equivalent too. > >sides. This polynomial is uniquely determined - it's the same whoever > >derives it. The same is true for simplexes of any given dimension. > > > > I'm also prone to think volume is 4D but that's another story > (and I don't mean 3D + time). In one of the pages I cited above, > I use a 4D 4-tuple coordinate system to compute ray tracings of > volumes, have de Jong's expression tied in as source code, and > use my distance formula (similar to the Pythagorean) to get the > six edge lengths. I presume the formula is something like the square (SORRY triangle) root of x^2 + y^2 + z^2 + u^2 - xy - xz - xu - yz - yu - zu which must be easier to work with than the Pythagorean expression: the square (no apology) root of x^2 + y^2 + z^2. > > >> As a curriculum writer, I don't mind it when kids (or adults) > >> rediscover something on their own and share it, whether they were > > > >Good. I've lost count of the number of times my latest brilliant > >idea has turned out to have been discovered decades or even centuries ago. > > > > Exactly. You're no doubt brilliant and if anyone comes along and > tells you to put a lid on it because so-and-so proved whatever No one has ever told me to put a lid on it, or treated any of my ideas dismissively. But don't you think it's useful to find out whether some idea of yours is known, so then you can check it out and see if you can improve on it? > "ages ago" then you can be proud you're able to duplicate the > results of such an august personage (presuming said "me first" > awardee is indeed august). > > A lot of folks, professors especially, seem to delight in citing > an earlier source to be crushing, as if to say "shaddup kid, yer > not so smart after all". That's a dark ages attitude we'd like > to wipe out. So callow, so jealous, so mean. Professors of that > crushing type were usually crushed themselves at some point, and Gosh, an authority on academic psychology as well as synergetics! No doubt you have performed a major survey on exactly which proportion of professors have these supercilious attitudes, and how many of them were permanently traumatized by their seniors' casual remarks. > tend to grow up "kiss-ass" (you claimed ignorance of that idiom, > just trying to flesh it out for you -- that Pink Floyd tune > comes to mind as well, know the one?). Weren't they some popular beat group? Did they have a donkey fixation (I thought it was pigs)? > > >Actually I'd forgotten that this formula was credited to Euler, until > >you mentioned it. I guess this shows we have different attitudes to > >priority :-) I'll have to take your word about de Jong's applet. > >It wouldn't work on my system. > > > > It's in Java 1.1 (Gerald works closely with Sun in the NL and keeps > his stuff up to date). You can probably update your browser with > a patch -- Netscape makes it easy at least. Your browser is likely > running Java 1.0. > It is: any case it was a rhetorical point --- I can't run the up to date netscape as my computer's spec is not up to it. 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/ Now offering spam-free web-based newsreading ========================================================================= Date: Fri, 1 May 1998 02:55:31 -0600 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: Volume of geodesic "sphere" (project) In article <6iafu7$bc2$1@gte1.gte.net>#1/1, "Clifford J. Nelson" wrote: > > Will somebody on this address list please agree with me and tell Kirby > that a coordinate system which is one to one with the XYZ system is three > dimensional, not four dimensional!? I will agree with you on this. It won't make a scrap of difference to Urner of course. Robin Chapman + "They did not have proper Department of Mathematics - palms at home in Exeter." University of Exeter, EX4 4QE, UK + rjc@maths.exeter.ac.uk - Peter Carey, http://www.maths.ex.ac.uk/~rjc/rjc.html + Oscar and Lucinda -----== Posted via Deja News, The Leader in Internet Discussion ==----- http://www.dejanews.com/ Now offering spam-free web-based newsreading ========================================================================= Date: Fri, 1 May 1998 06:10:59 -0600 Reply-To: List for the discussion of Buckminster Fuller's works Sender: List for the discussion of Buckminster Fuller's works From: Robin Chapman Organization: University of Exeter Subject: Re: Volume of geodesic "sphere" (project) In article <6ibuoi$dj4$1@nnrp1.dejanews.com>#1/2, I wrote: > > I presume the formula is something like the square (SORRY triangle) root > of x^2 + y^2 + z^2 + u^2 - xy - xz - xu - yz - yu - zu which must be > easier to work with than the Pythagorean expression: the square (no apology) > root of x^2 + y^2 + z^2. On second thoughts, the quadray formula will look more like 3x^2 + 3y^2 + 3z^2 + 3u^2 - 2xy - 2xz - 2xu - 2yz - 2yu - 2zu. I do apologize. I mean these quadray formulae are so much more memorable than the Cartesian ones :-) 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/ Now offering spam-free web-based newsreading ========================================================================= Date: Fri, 1 May 1998 04:36:17 -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: Volume of geodesic "sphere" (project) Mime-Version: 1.0 Content-Type: text/plain; charset=US-ASCII Content-Transfer-Encoding: 7bit On Thu, Apr 30, 1998 12:35 PM, Kirby Urner wrote: >"Clifford J. Nelson" wrote: > >>On Thu, Apr 30, 1998 7:46 AM, Kirby Urner < >mailto:pdx4d@teleport.com> >>wrote: >> >>> >>>I'm also prone to think volume is 4D but that's another story >>>(and I don't mean 3D + time). ><> >> >> Will somebody on this address list please agree with me and tell Kirby >>that a coordinate system which is one to one with the XYZ system is three >>dimensional, not four dimensional!? >> >> Cliff Nelson >> > >Of course you'll find agreement on this Cliff! What we're all taught >in school is that three mutual orthogonals constitute a basis for >saying that space is 3D. > >Only Fuller has had the temerity to question this dogma, by suggesting >that conceptual volume implies both an observer and an observed, that >we have no way to force our awareness to a more primitive starting >point than that of a containment (a 'point' in your mind's eye is >still being observed in its spatial context, is contained by space). > >So he bravely tossed 0D...3D as relics (for his own purposes -- >anyone is free to make a new start) and began with 4D as his anchor, >with weight/energy constituting an additional 'frequency' dimension >(time-cyclic -- the world of hertz).[1] > And the quadray system you are pushing are points with zero volume! They are only 3D. They are all tetrahedra with a frequency of zero. Cliff Nelson ========================================================================= Date: Fri, 1 May 1998 17:04:59 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: Volume of geodesic "sphere" (project) MIME-Version: 1.0 Content-Type: text/plain; charset=us-ascii Content-Transfer-Encoding: 7bit Robin Chapman wrote: >> I don't usually say "square" for 2nd powering BTW as the triangle >> serves just as well as a model of 2nd powering and is topologically >> simpler, as does the tetrahedron for 3rd powering, which is why >> Gerald's expression is slightly different -- 1^3 is not a cube. > >But you still wrote a^2. How do you say this? a triangled? >What about a^3? > I might say "triangled" or "tetrahedroned" for rhetorical purposes (Fuller certainly did), but "to the 2nd power" or "to the 3rd power" is more my style. I'll also say "squared" and "cubed" sometimes, depending on the game I'm playing. I don't deny myself access to the omnipresent XYZ or much-hyped hyperdimensional versions thereof (to get my computer to render the quadray-defined polys at my website, I had to convert to XYZ anyway, as no ray tracing engine uses anything but -- the conversion algorithms are fully specified and built right into my class definitions). Cite: http://www.teleport.com/~pdx4d/quadxyz.html >Anyway there is a subtle disadvantage with using the regular tetrahedron >as the model for measuring volume, as opposed to the cube and >indeed either the equilateral triangle or the square for measuring area. Re triangles, note that *any* such can be subdivided into x^2 similar subtriangles by intervalling edges into x equal segments and running parallels in a 3-way cross-hatch. Quadrilaterals in general do not permit this. Cite: http://www.servtech.com/~rwgray/synergetics/s01/p0000.html#100.41 >can do the same with equilateral triangles. In three-dimensional space >one can do the same with cubes, as we can tessellate space by cubes, >BUT it is impossible to do the same with regular tetrahedra. > This is very true, but making the regular tetrahedron our unit of volume means the regular octahedron of the same edge length has a volume of 4 -- and these two complement to fill space, giving us the octet truss (skeleton of edges interconnecting centers of 12-around-1 kissing spheres in the fcc). And not only the octahedron falls into place with a whole number volume. Many other polys do as well: 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: Synergetics Concentric Hierarchy Cite: http://www.inetarena.com/~pdx4d/ocn/urner.html (apologies to any of you who might have checked this recently and gotton some blurb about "What's an Urner?" with a broken link to a Swiss bank -- Urner from Uri, 'Land of the Mountain Ox' in Switzerland -- I got my urner.html files mixed up). There is an irregular tetrahedron which fills space by the way -- the MInimum TEtrahedron (or MITE), with a volume of 1/8 (depicted on pg. 71 of Coxeter's 'Regular Polytopes' but not dignified with a name, nor assembled in terms of A and B modules). Cite: http://www.teleport.com/~pdx4d/modules.html >Yes, you are an advocate of "quadray" coordinates. No doubt you would >label me a slave to "hypercross dogmatics". I admit it. 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. > You might want to just paint your own position instead of trying to characterize mine (including mine about yours). As you're a professional mathematician maybe you can help me with this: I read in a book about Georg Cantor that he was interested in how the "number of coordinates" might relate (or not) to the "number of dimensions" we say characterizes a space. Did he or did he not raise issues in this neighborhood? Care to elaborate? I find quadrays interesting from a pedagogical point of view because they use 4-tuples to map space, but lose the negative numbers. I see 4 "basis vectors" coming from the origin (0,0,0,0) whereas in the Cartesian apparatus I see 6 vectors, even though three of them are "negative mirrors". We say only 3 of the six Cartesian vectors are "basis vectors" and use that to feed the notion that volume is '3D' (did Cantor have any problem with this?). But quadrays are all equally positive, none 'more basic'. And there's something minimal about using 4 vectors to map volume. 4 'spokes' is the lowest number you can have and still partition the surrounding space into equal 'quadrants'. 3 'spokes' (e.g. the Cartesian positives, without their mirrors) can't 'splay out' to give a symmetric partitioning of volume (which is what the complementary negatives do for us -- partitioning volume into 8 octants). Anyway, you can add pairs of quadrays (6 combinations) to get the XYZ apparatus. So I tell my students they can look at quadrays as more logically primitive than XYZ (because fewer spokes), and use them to "build" XYZ -- at which point we "paint" the axes positive/negative as per usual and continue with whatever XYZ games. Quadrays insert themselves in my curriculum somewhat invisibly therefore, as logical underpinnings of what we already take for granted. Cite: http://www.teleport.com/~pdx4d/quadphil.html >> Euler's and Gerald's give out different numbers for the same inputs >> -- misleading to name them the same, even if they're similar. > >It is misleading not to call them equivalent too. > Damned if I do, damned if I don't. I certainly don't shy away from giving either Euler or de Jong plenty of credit for their respective contributions to the field. I have a clear conscience is what's important to me, given I use the hard work of both of these guys in my own thinking quite a bit. I do want to give credit where credit is due, but with less emphasis on the "me first" criterion (see below). >I presume the formula is something like the square (SORRY triangle) root >of x^2 + y^2 + z^2 + u^2 - xy - xz - xu - yz - yu - zu which must be >easier to work with than the Pythagorean expression: the square (no apology) >root of x^2 + y^2 + z^2. > This is close enough. It was my decision to make the distance from (0,0,0,0) to (1,0,0,0) be Root(6)/2, i.e. to have the 'home base' tetrahedron have length 2 edges (because interconnecting centers of unit-radius spheres in the fcc packing). Other conventions would be tolerable no doubt. Kinda strange to have a 'basis vector' not have 'unit length' but come to think of it, it didn't matter -- and I'm breaking so many conventions anyway... As to the 'memorability' of my distance expression, I agree it's less so, although one coordinate is always 0 (different one, depending on which basis vector is unused), so after doing vector subtraction between P1 and P2, I can always simplify a bit. In any case, having such algebra buried as class methods in my quadray objects (along with the de Jong version of the Euler thing) shields me from needing to "remember" in that "pop quiz" sense. I can happily forget, and just check the source code when I want to remind myself what's going on in the guts of this gizmo. I don't remember all the details of how an engine works when I drive my Subaru either. Lots of mathematics is automated these days -- quadray algorithms just go into the bit bucket with all the rest of it. Quadrays were first introduced to me by David Chako on Synergetics-L BTW (I have a link to the postings). I added the distance formula, xyz-quadray conversion algorithms, source code implementation, text and graphics for the 'quadray papers' at my site. I also collaborated with Josef Hasslberger on the CYMT colorized tetrahedron (using quadrays again). Cite: http://www.teleport.com/~pdx4d/quadcolors.html >No one has ever told me to put a lid on it, or treated any of my ideas >dismissively. Lucky you. I dismiss a lot of ideas, both mine and others -- because I don't see the relevance (I can be pretty blind sometimes, but on the other hand I pretty good at tuning in a lot of systems). >But don't you think it's useful to find out >whether some idea of yours is known, so then you can check it out and see >if you can improve on it? > Sometimes sure. But I don't think a kid who figures something out for him or herself is duty-bound to then go to the library or patent office and waste hours, days, years trying to find out if this is already known. If the kid plans to claim "me first" or "priority" that's different. But if you've hit on something brilliant and just want to move on, making use of what you've learned or discovered, then by all means go for it. I can even claim "discovery" if I simply mean by that I "uncovered it for myself" -- I don't think we should say to a kid: "no, you didn't discover anything, Newton knew that long before you were born." To me, that's a misuse of the term. "I've discovered spring is a fine time of year" is not something I should be hauled before the judge for saying. My theory is the Ivory Tower culture of "me first" obsessing grew up in tandem with a scarcity model with respect to food and/or good living -- you had to prove priority at every turn in order to merit being kept alive in the style to which you'd become accustomed. As the historical record filled with "me first" claims, the disciplines had to subdivide and specialize more and more, giving more room for newcomer professionals to stake turf and "be special" in some way. But in the rush to prove merit, academia has specialized itself to such a degree that the curriculum has decayed, from the point of view of latecomers, who now look at a subject like math and sometimes think there's really no point trying to master it unless the goal is to gain merit by Ivory Tower criteria, and the only way to do that is learn hundreds of years of stuff so as not to be made a fool of when finally staking turf. That's just too long a road for a lot of kids (longer with every passing generation) and they give up. There's something really stultifying about a discipline in which "the frontier" is considered so far distant, with so many prerequisites to getting anywhere close. With this synergetics stuff, I'm hoping to move "the frontier" much closer to home, giving kids a sense of pioneering new and meritorious material where without as much emphasis on priority (or intellectual property in general, because profligate generousity with one's ideas, including software, music, animations, will be rewarded, not punished). With the internet and multi-media, the allure of mathematics is increasing exponentially and I think we'll be breaking away from the culture of "me first" quite a bit. With better access to the historical record, it'll both be easier to organize the timeline, and less critical who or what was first discovered by whom, because we'll not be using such stringent criteria to provide lifestyle security. So many ways to "value add" by edit/recombining existing inventory, without having to waste so much time eking out priority and ownership claims. In sum, we'll feed you even if you never make a claim to being "the original inventor/discoverer of...". That'll cut down on the bullshit factor enormously, I'm projecting, by giving teachers more time to design learning experiences, keep things current and relevant for people new to a subject. Like, Bill Nye the Science Guy may not have made any "me first" discoveries in the annals of science, but he's a damn fine design scientist nevertheless. >Gosh, an authority on academic psychology as well as synergetics! >No doubt you have performed a major survey on exactly which >proportion of professors have these supercilious attitudes, and how many >of them were permanently traumatized by their seniors' casual remarks. > No, but it'd be an interesting study I'm sure. >> tend to grow up "kiss-ass" (you claimed ignorance of that idiom, >> just trying to flesh it out for you -- that Pink Floyd tune >> comes to mind as well, know the one?). > >Weren't they some popular beat group? Did they have a donkey fixation >(I thought it was pigs)? > Still in action I think, though with turnover (the name lives on -- and by the way, which one's 'Pink'?). Pigs, yes, floating ones. >> >It is: any case it was a rhetorical point --- I can't run the up to >date netscape as my computer's spec is not up to it. > If you're at all interested, I think you can maybe patch just the Java component on whatever Netscape that already runs 1.0 -- w/o having to download a whole new Netscape. Maybe I'm wrong about that -- I patched mine from 1.0 to 1.1 but it was already a fairly recent version. In the meantime, I hope the University of Exeter sees its ways clear to giving you a much better computer. Finding a mathematician willing to use the word 'synergetics' in print, even dismissively, is a rarity. So many of them seem completely oblivious that such a philosophy even exists. Kirby Urner 4D Solutions Portland, Oregon http://www.teleport.com/~pdx4d/ --------------------------------------------------------- Kirby T. Urner http://www.teleport.com/~pdx4d/kirby.html 4D Solutions http://www.teleport.com/~pdx4d/ [PGP OK] --------------------------------------------------------- ========================================================================= Date: Fri, 1 May 1998 17:08:04 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: Volume of geodesic "sphere" (project) MIME-Version: 1.0 Content-Type: text/plain; charset=us-ascii Content-Transfer-Encoding: 7bit > And the quadray system you are pushing are points with zero volume! They >are only 3D. They are all tetrahedra with a frequency of zero. > > Cliff Nelson > We were talking about Bucky's use of 4D and what he meant by it. Let's forget about quadrays, which he didn't need to make his points (nor do I). Read about the zerovolume tetrahedron in 'Synergetics' -- even if zerovolume, it's still conceptually a 4D tetrahedron, strange as that might sound to a 3D-XYZ 'blockhead' such as yourself. Kirby --------------------------------------------------------- Kirby T. Urner http://www.teleport.com/~pdx4d/kirby.html 4D Solutions http://www.teleport.com/~pdx4d/ [PGP OK] --------------------------------------------------------- ========================================================================= Date: Fri, 1 May 1998 09:41:17 -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: Volume of geodesic "sphere" (project) Mime-Version: 1.0 Content-Type: text/plain; charset=US-ASCII Content-Transfer-Encoding: 7bit On Fri, May 1, 1998 9:08 AM, Kirby Urner wrote: > >> And the quadray system you are pushing are points with zero volume! >They >>are only 3D. They are all tetrahedra with a frequency of zero. >> >> Cliff Nelson >> > >We were talking about Bucky's use of 4D and what he meant by it. >Let's forget about quadrays, which he didn't need to make his >points (nor do I). > >Read about the zerovolume tetrahedron in 'Synergetics' -- even >if zerovolume, it's still conceptually a 4D tetrahedron, strange >as that might sound to a 3D-XYZ 'blockhead' such as yourself. > >Kirby > You call your company 4D Solutions and yet have no idea of what 4D means. You think it means (X,Y,Z,0). All of the work in Synergetics coordinates could and can be translated into perpendicular coordinates (as Bucky explicitly stated), but it would make things awkward. And when a tetrahedron of non-vero volume is translated into perpendicular coordinates, there are four coordinates, not just three. Cliff Nelson ========================================================================= Date: Fri, 1 May 1998 20:00:15 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: Volume of geodesic "sphere" (project) MIME-Version: 1.0 Content-Type: text/plain; charset=us-ascii Content-Transfer-Encoding: 7bit "Clifford J. Nelson" wrote: > You call your company 4D Solutions and yet have no idea of what 4D means. >You think it means (X,Y,Z,0). > I've posted exhaustively on what I think Fuller meant by '4D', with citations back to '4D Timelock' and rolling foward through 'Synergetics 2'. The first question should be whether my scholarship is on target -- have I captured Fuller's meaning here? Then we can look at quadrays, as a secondary topic -- he never used this gizmo and I don't consider knowing anything about quadrays essential to getting where he was coming from with this '4D' business. As for quadrays, I find your (X,Y,Z,0) characterization misleading, as it implies my X,Y and Z stand for mutual perpendiculars, which they do not. (a,b,c,d) with a,b,c,d = positive scalars, with at least one of these 0, is more accurate. The 0 might be in any position e.g. (34.1, 0, 18.9, 6) (04.9 3 10.1, 0) are both equally valid 4-tuples and point to unique points relative to the origin (0,0,0,0). Just a few minutes ago, I answered a query from some dude at the London Life Insurance Company in Canada, the text of which I'll cc: here for everyone's edification (some details X'd to protect confidentiality): ======== [XXX] -- You have four basis vectors pointing from the center of a tetrahedron to its four corners (a tripod of vectors and a fourth sticking straight up). Any location in the volume surrounding (0,0,0,0) may be expressed as a sum of three of these four vectors (one of them will remain unused, depending on where our point is). Just stretch (i.e. scale), clone (translate), and place the vectors tip-to-tale (without changing orientation -- what we call "vector addition" as per usual) and you've got your result i.e.: P1 = a(1,0,0,0) + b(0,1,0,0) + c(0,0,1,0) + d(0,0,0,1) where a,b,c,d are positive scaling factors, and where at least one of these factors is 0. P1 is any point in space. Maybe my 'quadpod' analogy will help. Imagine a rocket ship with four thrusters, aimed as described (to the corners of a tetrahedron). Some blast-mix out through the rockets (exact magnitudes courtesy of on-board computer) will enable our pod to move smoothly, in a straight line, towards any target. The Cartesian rocketship (XYZ) is overbuilt in contrast, using six thrusters instead of just four, using some to counter others at 180 degrees (unnecessary, if the goal is simply to move in any direction using thruster-sums). Hope this helps. Kirby PS: I use quadrays for pedagogical purposes, as a tool for philosophy department types wanting to shake things up a bit re the philo of math. I also found the system practical and usable enough for building up a database of polys, with mostly positive integer coordinates (exceptions are the 5-fold symmetric), as per the HTML papers at my site. But I haven't worked out a whole set of algorithms in parallel with the XYZ, contrived a host of 'canned' vector ops and so on. As quadray vectors are convertible to XYZ, I can always do so, use something from the XYZ library (vast), and then convert back to quadrays. This may sound like cheating but it's not, especially in light of the fact that I can use quadrays to build the XYZ apparatus in the first place. PPS: the original quadrays concept was first introduced to me by David Chako, at the time a VP at [XXX] in New York as I recall. I fleshed out his idea with some additional features and details and imported the whole gizmo into the philosophy department, where it does service on the front lines against creeping mindless dogmatism. |At 01:22 PM 5/1/98 -0400, you wrote: | |Mr. Urner, | | A quick question if you don't mind. Using a NSEW analogy, if I start at |point (0,0,0,0) and continue to go North , instead of moving a straight line |(on a flat floor), wouldn't I be moving on an incline (walking up stairs)? I |still trying to visualize how an 4D object moves in space (translation, |rotation, scaling, etc.). | |thanks, |[XX] | |----------------------------------------------------- |London Life Insurance Company, London, Ontario, Canada. ==== >All of the work in Synergetics coordinates could and can be translated into >perpendicular coordinates (as Bucky explicitly stated), but it would make >things awkward. And when a tetrahedron of non-vero volume is translated >into perpendicular coordinates, there are four coordinates, not just three. > > > Cliff Nelson > As I've said many times before, I think you overly confuse things by talking about a tetrahedron having 4-tuple coordinates. Points have coordinates and you define a tetrahedron with four points not in the same plane. In XYZ, that means 4 x 3 or 12 distinct numbers. In quadrays we'd need 16, but with no need for negatives. Now I realize you can create an apparatus where dialing in 4 parameters will get you a regular tetrahedron by some algorithm (as you have defined in a Mathematica worksheet -- which you can't assume I haven't seen BTW, even if I maybe haven't), but that's not an excuse to call these parameters "coordinates" in my book. Quadray 4-tuples are true "coordinates" because the quadray apparatus is very like the Cartesian one, but with fewer spokes. Again, forgetting all about coordinate system gizmos, of which there are a great many, Fuller was saying that containment is primitive and furthermore that the simplest container, the box with the fewest sides, is the tetrahedron ("sphere" not simpler because he's using only wire- frames -- Euler's E,F and V -- to define stuff and "spheres" are therefore high frequency networks e.g. his classic icosasphere). Given the primal nature of containment, Fuller used his '4D' to circle some of the tetrahedron's distinguishing characteristics (4 vertices, 4 facets) and to vector "dimension" (the 'D' part) away from its more conventional usage patterns, into self-consistent (and I think valid and comprehensible) usage patterns of his own. Kirby --------------------------------------------------------- Kirby T. Urner http://www.teleport.com/~pdx4d/kirby.html 4D Solutions http://www.teleport.com/~pdx4d/ [PGP OK] --------------------------------------------------------- ========================================================================= Date: Fri, 1 May 1998 13:28:40 -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: Volume of geodesic "sphere" (project) Mime-Version: 1.0 Content-Type: text/plain; charset=US-ASCII Content-Transfer-Encoding: 7bit On Fri, May 1, 1998 12:00 PM, Kirby Urner wrote: >"Clifford J. Nelson" wrote: > >> You call your company 4D Solutions and yet have no idea of what 4D >means. >>You think it means (X,Y,Z,0). >> > >I've posted exhaustively on what I think Fuller meant by '4D', with >citations back to '4D Timelock' and rolling foward through 'Synergetics 2'. >The first question should be whether my scholarship is on target -- have >I captured Fuller's meaning here? No. Synergetics coordinates can be transformed into perpendicular coordinates. That is what Bucky Fuller said. >Then we can look at quadrays, as a secondary topic -- he never used this >gizmo and I don't consider knowing anything about quadrays essential to >getting where he was coming from with this '4D' business. > >As for quadrays, I find your (X,Y,Z,0) characterization misleading, as >it implies my X,Y and Z stand for mutual perpendiculars, which they >do not. (a,b,c,d) with a,b,c,d = positive scalars, with at least one >of these 0, is more accurate. The 0 might be in any position e.g. > First you say that you transform quadrays into perpendicular XYZ to graph them, and they equal (X,Y,Z,0), and then you say it is misleading. > >==== > >>All of the work in Synergetics coordinates could and can be translated into >>perpendicular coordinates (as Bucky explicitly stated), but it would make >>things awkward. And when a tetrahedron of non-vero volume is >translated >>into perpendicular coordinates, there are four coordinates, not just three. >> >> >> Cliff Nelson >> > >As I've said many times before, I think you overly confuse things by >talking about a tetrahedron having 4-tuple coordinates. Points have >coordinates and you define a tetrahedron with four points not in the >same plane. In XYZ, that means 4 x 3 or 12 distinct numbers. In >quadrays we'd need 16, but with no need for negatives. > No. I define a tetrahedron by four numbers representing the perpendicular displacement of the four enclosing planes, the way it says to do it in Synergetics 1 & 2. Synergetics coordinates can be transformed into perpendicular coordinates and vice-versa. Whether you like it or not, that is what Bucky Fuller said, and what I do to graph them. Cliff Nelson ========================================================================= Date: Fri, 1 May 1998 22:08:03 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: Volume of geodesic "sphere" (project) MIME-Version: 1.0 Content-Type: text/plain; charset=us-ascii Content-Transfer-Encoding: 7bit pdx4d@teleport.com (Kirby Urner) wrote: >But quadrays are all equally positive, none 'more basic'. And >there's something minimal about using 4 vectors to map volume. >4 'spokes' is the lowest number you can have and still partition >the surrounding space into equal 'quadrants'. 3 'spokes' (e.g. >the Cartesian positives, without their mirrors) can't 'splay >out' to give a symmetric partitioning of volume (which is >what the complementary negatives do for us -- partitioning >volume into 8 octants). > To be more precise, 3 vectors might "splay" symmetrically in a plane at 120 degrees (Mercedes-Benz logo) to divide volume into two halves, but these spokes won't vector-sum to span volume, i.e. all grow/shrink scaling, cloning and sliding of vectors into tip-to-tail zigzags will keep us stuck on the flatlander plane. With 4 vectors splayed to the vertices of a regular tetrahedron (or through face centers -- same diff = to the vertices of the dual), we have a minimal space-spanning set. Although we might define a vector reversing 'negatation' operation -- and in fact do so, to give meaning to -(1,0,0,0) -- 'vector reversal' is not needed to span volume. Positive scaling (which includes shrinking, but without an orientation switch) will do fine. In XYZ, on the other hand, the positive basis vectors alone are helpless to reach all of volume, but are stuck in the first octant (the 3 positives define an asymmetric partitioning of space). That's why vector reversal (an orientation-changing operation) is required (to restore symmetry), and yet the "negative mirrors" that comprise 3 of the 6 XYZ spokes aren't dignified as "basis vectors" in their own right for some reason (because left is superior to right? because 'positive' is a priori while 'negative' is derivative? why so?). This is philosophy of mathematics here, as we're questioning design-decisions, investigating conventions and terminology. Some call these 'foundational' investigations but that's just one metaphor we might choose. To paraphrase Wittgenstein re mathematical logic: it underpins the superstructure the way a painted foundation upholds a painted tower. In a lot of ways, systems just hang together spherically in zero G (a network, connecting around circumferentially, everywhichway -- do we trust it? is it secure?) -- the idea of "up" and "down" ain't so relevant in logical space ("in" "out" and "around" make more sense as primary freedoms). Kirby --------------------------------------------------------- Kirby T. Urner http://www.teleport.com/~pdx4d/kirby.html 4D Solutions http://www.teleport.com/~pdx4d/ [PGP OK] --------------------------------------------------------- ========================================================================= Date: Fri, 1 May 1998 19:33:20 -0700 Reply-To: pgoodson@zapcom.net Sender: List for the discussion of Buckminster Fuller's works From: Patricia Goodson Subject: Information MIME-Version: 1.0 Content-Type: text/plain; charset=ISO-8859-1 Content-Transfer-Encoding: 7bit Hello, I am a member of Unity Clear Lake Center in Lake county. We are thinking of building a church on the geodesic design. Any information that you can give me I would appreciate it. I know very little about domes and I would like to learn. Thank You and Blessings! Pat ========================================================================= Date: Fri, 1 May 1998 23:33:55 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: Volume of geodesic "sphere" (project) MIME-Version: 1.0 Content-Type: text/plain; charset=us-ascii Content-Transfer-Encoding: 7bit "Clifford J. Nelson" wrote: >>The first question should be whether my scholarship is on target -- have >>I captured Fuller's meaning here? > > No. > >Synergetics coordinates can be transformed into perpendicular coordinates. >That is what Bucky Fuller said. > So, what's the problem? He's decoupling "dimension" from "gizmo used" with his 4D trajectory (I think Cantor was sniffing up the same trail -- let's see what Dr. Chapman has to say (I've interviewed a good many mathematicians on this topic already)). You can use XYZ, quadrays, whatever. That's a machine, a clockworks, an apparatus, a software device, a memory management scheme. Regardless of what you put in there, the volume is conceptually and prefrequency 4D (in Fuller's language, which anyone can learn and make their own). A tetrahedron is like the most primitive logo for volume, as is a triangle for a plane (but then planes float in volume -- we can't think of them otherwise -- I'll still say 2D for shorthand, since that's laymanese for 'flat like a pancake', which is how I think of planes (not 'infinitely thin' and not 'infinite' either -- dispensable greek metaphysics, too ghostly and pale, too unreal)). XYZ vectors point to the vertices of an octahedron, or through the mid-edges of a regular tetrahedron (why I sometimes call them e-rays). That octahedron is 4D. An icosahedron is 4D. Any blob is 4D, including a zerovolume point (might be hyperlinked though -- VRML supports this). In contrast, a rhombic triacontahedron with butterflies and acorns around it is 4D+ (more than 4D because we've added energy to the picture, frequency, fleshed out purely Platonic angularly-defined shapes with time-size attributes (at least in the mind's eye)). >>As for quadrays, I find your (X,Y,Z,0) characterization misleading, as >>it implies my X,Y and Z stand for mutual perpendiculars, which they >>do not. (a,b,c,d) with a,b,c,d = positive scalars, with at least one >>of these 0, is more accurate. The 0 might be in any position e.g. >> > > First you say that you transform quadrays into perpendicular XYZ to graph >them, and they equal (X,Y,Z,0), and then you say it is misleading. They don't equal (X,Y,Z,0), I never said that. I have a web page giving the algorithms for going back and forth between quadrays and XYZ, including in matrix notation, but it's not like you just go: Quadrays XYZ (2 3 4 0) --> (2 3 4) or XYZ Quadrays (1 2 3) --> (1 2 3 0) or something. It's a little more complicated than that. Sounds like you've never bothered to study what quadrays are about, despite their easy availability. This is typical of your lazy, 'shoot first, check for a target later' approach. > >No. I define a tetrahedron by four numbers representing the perpendicular >displacement of the four enclosing planes, the way it says to do it in >Synergetics 1 & 2. > I'm familiar with that passage, but then quadrays may be taken as following the same instruction: the 4 basis vectors are perpendicular to the faces of a regular tetrahedron (going to the vertices of its dual). Best wishes with your invention Cliff. I just wish you'd stop saying I don't know what I'm talking about, without doing the work necessary to make your case. I take a more live and let live approach. You seem to have a real problem with competition. Re: the synergetics coordinate system (my view thereof) Fuller was basically showing that when you're communicating with humans, you get away with a lot of a precise and geometrically sophisticated nature without over-indulging in symbolic manipulation games which are great for running chips (if turned into computer codes) but are too opaque, too crypto-compressed, for most of humanity. So he self-disciplined himself to write 'Synergetics' using a more narrative, humanities-style language, something layfolks can parse, not just computers. This is a feature of his philosophy, not a bug or short-coming. The 'coordinate system of nature' was the so-called 'isotropic vector matrix' (IVM) or octet truss, important to Alexander Graham Bell as well, and which metaphysical stage-setting he imparted to his students minus much of the symbolic claptrap we associate with 'hard core mathematics' but including a lot of key terms we're more used to seeing in philosophy texts -- which is partly how come at least some synergetics ended up as required reading for today's philosophers and/or led to the erosion of the "doctor of philosophy" degree (a paper security) for those fuddy-duds failing to keep up with their homework. >Synergetics coordinates can be transformed into perpendicular coordinates >and vice-versa. Whether you like it or not, that is what Bucky Fuller said, >and what I do to graph them. > > Cliff Nelson The more awkward XYZ-informed languages we use with kids today pack in less information per time unit than we'll be seeing in a more synergetics-informed curriculum, especially when more of our animations start getting out and about. We'll still use the vast library of existing algorithms of course, whatever their coordinate-framing assumptions (many of them works of pure genius) even as we do a better job of schooling our imaginations to work more directly with the isotropic vector matrix, without so much mediating awkwardness. Fuller's 'coordinating system' was his synergetics language as shared, not some future symbolica ala quadrays or your Mathematica thing, although such 'analytic' devices certainly don't hurt our cause. Synergetics, a work in the humanities, aims at schooling our reflexes on the human side of the cell-silicon interface, in the way Java is aimed at putting electrons through their paces on the other side of the I/AI divide. We will be evolving this language of course (as he was, up to the end), but with strong ties to laymanese, lingua franca, the vernacular, always -- and not as a popularization of something with an "inner core" that's couched in some other more "crypto- opaque" language (this is not Kabalism). Synergetics is anchored in "everyday mind" as a self-discipline, as a real world philosophy -- which isn't to say that all that other stuff is going away, or should. Certainly we'll be adding to our software library of Java, Logo and xBase applications and whatever else (and certainly I'll always have a place in my heart for APL). Synergetics is not a "replacement discipline" for much of what already passes for science (racism is pseudoscience), is not an "in lieu of" for crystallography for example. Synergetics, as defined by Bucky himself is: The integration of geometry and philosophy in a single conceptual system providing a common language and accounting for both the physical and metaphysical. Synergetics 251.50 And that's what I use for intro on my banner page at 'Synergetics on the Web' (winner of a Dr. Matrix award for science excellence). Cite: http://www.teleport.com/~pdx4d/synhome.html At least this is what I see as Bucky's hoped-for trajectory, and my FAQ re 'pseudo-synergetics' is designed to make it harder for future Fuller Schoolers to retreat into any dark ages scholaticism, given all the hard work we've done to dig out of such a hell hole already. Kirby --------------------------------------------------------- Kirby T. Urner http://www.teleport.com/~pdx4d/kirby.html 4D Solutions http://www.teleport.com/~pdx4d/ [PGP OK] --------------------------------------------------------- ========================================================================= Date: Fri, 1 May 1998 16:50:26 -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: Volume of geodesic "sphere" (project) Mime-Version: 1.0 Content-Type: text/plain; charset=US-ASCII Content-Transfer-Encoding: 7bit Sorry Kirby, but I don't believe anyone can be so obtuse. I don't think you are even trying. So, I'm signing off. Cliff Nelson On Fri, May 1, 1998 3:33 PM, Kirby Urner wrote: >"Clifford J. Nelson" wrote: > >>>The first question should be whether my scholarship is on target -- have >>>I captured Fuller's meaning here? >> >> No. >> >>Synergetics coordinates can be transformed into perpendicular >coordinates. >>That is what Bucky Fuller said. >> > >So, what's the problem? > >He's decoupling "dimension" from "gizmo used" with his 4D trajectory >(I think Cantor was sniffing up the same trail -- let's see what >Dr. Chapman has to say (I've interviewed a good many mathematicians >on this topic already)). > >You can use XYZ, quadrays, whatever. That's a machine, a clockworks, >an apparatus, a software device, a memory management scheme. >Regardless >of what you put in there, the volume is conceptually and prefrequency >4D (in Fuller's language, which anyone can learn and make their own). > >A tetrahedron is like the most primitive logo for volume, as is a >triangle for a plane (but then planes float in volume -- we can't >think of them otherwise -- I'll still say 2D for shorthand, since >that's laymanese for 'flat like a pancake', which is how I think >of planes (not 'infinitely thin' and not 'infinite' either -- >dispensable greek metaphysics, too ghostly and pale, too unreal)). > >XYZ vectors point to the vertices of an octahedron, or through the >mid-edges of a regular tetrahedron (why I sometimes call them e-rays). >That octahedron is 4D. An icosahedron is 4D. Any blob is 4D, >including a zerovolume point (might be hyperlinked though -- VRML >supports this). > >In contrast, a rhombic triacontahedron with butterflies and acorns >around it is 4D+ (more than 4D because we've added energy to the >picture, frequency, fleshed out purely Platonic angularly-defined >shapes with time-size attributes (at least in the mind's eye)). > >>>As for quadrays, I find your (X,Y,Z,0) characterization misleading, as >>>it implies my X,Y and Z stand for mutual perpendiculars, which they >>>do not. (a,b,c,d) with a,b,c,d = positive scalars, with at least one >>>of these 0, is more accurate. The 0 might be in any position e.g. >>> >> >> First you say that you transform quadrays into perpendicular XYZ to >graph >>them, and they equal (X,Y,Z,0), and then you say it is misleading. > >They don't equal (X,Y,Z,0), I never said that. I have a web page >giving the algorithms for going back and forth between quadrays and >XYZ, including in matrix notation, but it's not like you just go: > >Quadrays XYZ > >(2 3 4 0) --> (2 3 4) > >or > >XYZ Quadrays > >(1 2 3) --> (1 2 3 0) > >or something. It's a little more complicated than that. > >Sounds like you've never bothered to study what quadrays are about, >despite their easy availability. This is typical of your lazy, >'shoot first, check for a target later' approach. > >> >>No. I define a tetrahedron by four numbers representing the perpendicular >>displacement of the four enclosing planes, the way it says to do it in >>Synergetics 1 & 2. >> > >I'm familiar with that passage, but then quadrays may be taken as >following the same instruction: the 4 basis vectors are perpendicular >to the faces of a regular tetrahedron (going to the vertices of its >dual). > >Best wishes with your invention Cliff. I just wish you'd stop >saying I don't know what I'm talking about, without doing the work >necessary to make your case. I take a more live and let live >approach. You seem to have a real problem with competition. > >Re: the synergetics coordinate system (my view thereof) > >Fuller was basically showing that when you're communicating with >humans, you get away with a lot of a precise and geometrically >sophisticated nature without over-indulging in symbolic manipulation >games which are great for running chips (if turned into computer >codes) but are too opaque, too crypto-compressed, for most of >humanity. So he self-disciplined himself to write 'Synergetics' >using a more narrative, humanities-style language, something >layfolks can parse, not just computers. This is a feature of >his philosophy, not a bug or short-coming. > >The 'coordinate system of nature' was the so-called 'isotropic >vector matrix' (IVM) or octet truss, important to Alexander >Graham Bell as well, and which metaphysical stage-setting he >imparted to his students minus much of the symbolic claptrap >we associate with 'hard core mathematics' but including a lot >of key terms we're more used to seeing in philosophy texts -- >which is partly how come at least some synergetics ended up >as required reading for today's philosophers and/or led to >the erosion of the "doctor of philosophy" degree (a paper >security) for those fuddy-duds failing to keep up with their >homework. > >>Synergetics coordinates can be transformed into perpendicular >coordinates >>and vice-versa. Whether you like it or not, that is what Bucky Fuller said, >>and what I do to graph them. >> >> Cliff Nelson > >The more awkward XYZ-informed languages we use with kids today pack >in less information per time unit than we'll be seeing in a more >synergetics-informed curriculum, especially when more of our >animations start getting out and about. > >We'll still use the vast library of existing algorithms of course, >whatever their coordinate-framing assumptions (many of them works >of pure genius) even as we do a better job of schooling our >imaginations to work more directly with the isotropic vector matrix, >without so much mediating awkwardness. > >Fuller's 'coordinating system' was his synergetics language as >shared, not some future symbolica ala quadrays or your Mathematica >thing, although such 'analytic' devices certainly don't hurt our >cause. Synergetics, a work in the humanities, aims at schooling >our reflexes on the human side of the cell-silicon interface, >in the way Java is aimed at putting electrons through their >paces on the other side of the I/AI divide. > >We will be evolving this language of course (as he was, up to >the end), but with strong ties to laymanese, lingua franca, the >vernacular, always -- and not as a popularization of something >with an "inner core" that's couched in some other more "crypto- >opaque" language (this is not Kabalism). > >Synergetics is anchored in "everyday mind" as a self-discipline, >as a real world philosophy -- which isn't to say that all that >other stuff is going away, or should. Certainly we'll be adding >to our software library of Java, Logo and xBase applications and >whatever else (and certainly I'll always have a place in my heart >for APL). > >Synergetics is not a "replacement discipline" for much of what >already passes for science (racism is pseudoscience), is not >an "in lieu of" for crystallography for example. Synergetics, >as defined by Bucky himself is: > > The integration of geometry and philosophy in > a single conceptual system providing a common language > and accounting for both the physical and metaphysical. > Synergetics 251.50 > > >And that's what I use for intro on my banner page at 'Synergetics >on the Web' (winner of a Dr. Matrix award for science excellence). > >Cite: http://www.teleport.com/~pdx4d/synhome.html > >At least this is what I see as Bucky's hoped-for trajectory, and >my FAQ re 'pseudo-synergetics' is designed to make it harder for >future Fuller Schoolers to retreat into any dark ages scholaticism, >given all the hard work we've done to dig out of such a hell hole >already. > >Kirby > >--------------------------------------------------------- >Kirby T. Urner http://www.teleport.com/~pdx4d/kirby.html >4D Solutions http://www.teleport.com/~pdx4d/ [PGP OK] >--------------------------------------------------------- > ========================================================================= Date: Sat, 2 May 1998 02:48:51 GMT Reply-To: List for the discussion of Buckminster Fuller's works Sender: List for the discussion of Buckminster Fuller's works From: Kirby Urner Organization: 4D Solutions Subject: Re: Volume of geodesic "sphere" (project) MIME-Version: 1.0 Content-Type: text/plain; charset=us-ascii Content-Transfer-Encoding: 7bit "Clifford J. Nelson" wrote: >Sorry Kirby, but I don't believe anyone can be so obtuse. I don't think you >are even trying. So, I'm signing off. > > Cliff Nelson > Very wasteful to quote that whole thing back to me with just a line or two at the top. You should learn your netiquette, on top of your synergetics. You seem to have no clue about either. Take care. I suggest you stop bad-mouthing my work unless you have something more intelligent to say about it. If you ever do a website, I'll link to it. Urner out. --------------------------------------------------------- Kirby T. Urner http://www.teleport.com/~pdx4d/kirby.html 4D Solutions http://www.teleport.com/~pdx4d/ [PGP OK] --------------------------------------------------------- ========================================================================= Date: Sat, 2 May 1998 17:40:40 -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: Sunsight/Sunclipse Comments: To: "C. J. Monahan" MIME-Version: 1.0 Content-Type: text/plain; charset=us-ascii Content-Transfer-Encoding: 7bit Casey Monahan said: >I thought Fuller recommended sun in (as in sun comes into view) and sun >out. Kirby Urner says Gene Fowler said: >> 'suntake' and 'suncut' -- Hollywood-informed replacements I've been trying unsuccessfully to find references in some of Fuller's books for his use of 'sunsight' and 'sunclipse'. I recall him explaining his use of these terms at various speakings I attended. We are rolled into sight of the sun as a function of the Earth's rotation; the sun does not 'come' into view, nor do we 'take' anything. As we are rotated shadyside, our view of the sun is eclipsed by the horizon; the sun does not set, nor does it go 'out', nor do we 'cut' anything. In and out relate to (and are reserved for) navigable vectors/directions. 'Take' and 'cut' are active verbs. In this application, we do no such thing; they are irrelevant and wrong. They are as wrongly misinforming sensorially as 'rise ' and 'set'. My couple of kopecks worth. ========================================================================= Date: Sat, 2 May 1998 18:08:18 -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: Sunsight/Sunclipse Comments: To: Bruce Ward In-Reply-To: <354BCAC3.1129@metro.net> MIME-Version: 1.0 Content-Type: TEXT/PLAIN; charset=US-ASCII On Sat, 2 May 1998, Bruce Ward wrote: > Casey Monahan said: > >I thought Fuller recommended sun in (as in sun comes into view) and sun >out. > > Kirby Urner says Gene Fowler said: > >> 'suntake' and 'suncut' -- Hollywood-informed replacements > > I've been trying unsuccessfully to find references in some of Fuller's > books for his use of 'sunsight' and 'sunclipse'. I recall him > explaining his use of these terms at various speakings I attended. Consult "Utopia or Oblivion" and "Everything I Know" among other sources. -T. -- Trevor Blake box2321@teleport.com http://www.teleport.com/~box2321/ Post Office Box 2321, Portland Oregon 97208-2321, United States ========================================================================= Date: Sun, 3 May 1998 13:14:25 -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: Sunsight/Sunclipse In-Reply-To: <354BCAC3.1129@metro.net> Mime-Version: 1.0 Content-Type: text/plain; charset="us-ascii" >'Take' and 'cut' are active verbs. In this application, we do no such >thing; they are irrelevant and wrong. They are as wrongly misinforming >sensorially as 'rise ' and 'set'. > Are you quite convinced? 'See' is an active verb too ya know. The movie metaphors help with 'dawning awareness' -- the sense that you, the one with the brain-TV studio (another Fullerism) have a role to play in 'getting the experience on tape'. When Hollywood types say 'roll camera, take two!', they mean you're grabbing some frames (to sleep: "grab some z's"), so when you're aware of the sun's rays getting to you, you might think of that as the start of a 'take'. Then, when the sun is taken out, by whatever obstruction (earth, moon, building), that's a 'cut' in your 'take of the sun'. Anyway, I'm not heavily invested in any of this. Like I say, these were proposals from Gene Fowler, not Buckyisms, nor Kirbyisms -- and Gene is not into dogmatism, just likes to roll words around for look and feel purposes. But I do like the Hollywood angle in some respects. >My couple of kopecks worth. > Gracias por los kopecks. Kirby ========================================================================= Date: Sun, 3 May 1998 19:07:30 -0400 Reply-To: monkey@one.net Sender: List for the discussion of Buckminster Fuller's works From: David Anderson Organization: Flying Monkey Software Subject: A Simple Bolted PVC Geodesic Strut Design MIME-Version: 1.0 Content-Type: text/plain; charset=us-ascii Content-Transfer-Encoding: 7bit Here's how I put together the framework for the greenhouse... http://w3.one.net/~monkey/geodesics/pvcstruts -- - Dave Anderson monkey@one.net http://w3.one.net/~monkey ========================================================================= Date: Sun, 3 May 1998 16:36:05 -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: A Simple Bolted PVC Geodesic Strut Design Comments: cc: monkey@one.net In-Reply-To: <354CF8B2.135D3FA2@one.net> Mime-Version: 1.0 Content-Type: text/plain; charset="us-ascii" At 07:07 PM 5/3/98 -0400, David Anderson wrote: >Here's how I put together the framework for the greenhouse... > > http://w3.one.net/~monkey/geodesics/pvcstruts > >-- > >- Dave Anderson monkey@one.net http://w3.one.net/~monkey > Very well illustrated and clearly explained -- the whole site, from chord factor calculation to the nuts and bolts of hubs and assembly. Definitely one of the better 'how to' geodesic dome sites, including with Java source code to boot. Bravo! I'll definitely be adding a link from my 'Synergetics on the Web' from near http://www.teleport.com/~pdx4d/dome.html (probably I'll do a new 'resources' page instead of linking directly to Rick Bono's site, which I also highly recommend -- more freeware and other goodies, especially for those into playing with the full geodesic sphere from a purely geometric point of view). The only thing I missed seeing, and was very curious about, was any photographs of the finished prototypes. Got those? Kirby ========================================================================= Date: Sun, 3 May 1998 19:45:19 -0400 Reply-To: monkey@one.net Sender: List for the discussion of Buckminster Fuller's works From: David Anderson Organization: Flying Monkey Software Subject: Re: A Simple Bolted PVC Geodesic Strut Design Comments: To: Kirby Urner MIME-Version: 1.0 Content-Type: text/plain; charset=us-ascii Content-Transfer-Encoding: 7bit > The only thing I missed seeing, and was very curious about, > was any photographs of the finished prototypes. Got those? > > Kirby Ah, but for a scanner. I'm looking to get another system in the next month or two and that'll probably have a scanner (and a lot more memory so I can write some killer AI apps in Java) - when I'm there I'll put up a dome gallery... -- - Dave Anderson monkey@one.net http://w3.one.net/~monkey ========================================================================= Date: Sun, 3 May 1998 18:35:17 -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: MSNBC - MIT envisions the home of the future (http://www.msnbc.com/news/162724. MIME-Version: 1.0 Content-Type: multipart/mixed; boundary="----=_NextPart_000_0006_01BD76C2.38432760" This is a multi-part message in MIME format. ------=_NextPart_000_0006_01BD76C2.38432760 Content-Type: text/plain; charset="iso-8859-1" Content-Transfer-Encoding: 7bit http://www.msnbc.com/news/162724.asp ------=_NextPart_000_0006_01BD76C2.38432760 Content-Type: application/octet-stream; name="MSNBC - MIT envisions the home of the future.url" Content-Transfer-Encoding: 7bit Content-Disposition: attachment; filename="MSNBC - MIT envisions the home of the future.url" [InternetShortcut] URL=http://www.msnbc.com/news/162724.asp Modified=A064D9CBFC76BD01D8 ------=_NextPart_000_0006_01BD76C2.38432760-- ========================================================================= Date: Sun, 3 May 1998 19:30:59 -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: BUILDING TECH PROG Comments: To: wjm@mit.edu MIME-Version: 1.0 Content-Type: text/plain; charset="iso-8859-1" Content-Transfer-Encoding: 7bit William J. Mitchell Dean, School of Architecture and Planning Massachusetts Institute of Technology Dear Sir, I certainly hope that the ideas of R. Buckminster Fuller are seriously included in MIT's "Building Technology Program" (http://web.mit.edu/bt/www/bt.html), otherwise it would seem to appear that a cruel hoax and intellectual fraud may being perpetrated on your students. Sincerely, **************************************** * Joe S. Moore * Independent Buckminster Fuller Scholar * joemoore@cruzio.com * Buckminster Fuller Virtual Institute * http://www.cruzio.com/~joemoore/ **************************************** ========================================================================= Date: Sun, 3 May 1998 22:51:45 -0400 Reply-To: Kevin Sender: List for the discussion of Buckminster Fuller's works From: Kevin Subject: Re: BUILDING TECH PROG MIME-Version: 1.0 Content-Type: text/plain; charset="iso-8859-1" Content-Transfer-Encoding: 7bit Way to go Joe! -----Original Message----- From: Joe S. Moore Newsgroups: bit.listserv.geodesic To: GEODESIC@LISTSERV.ACSU.BUFFALO.EDU Date: Sunday, May 03, 1998 10:40 PM Subject: BUILDING TECH PROG >William J. Mitchell >Dean, School of Architecture and Planning >Massachusetts Institute of Technology > >Dear Sir, > >I certainly hope that the ideas of R. Buckminster Fuller are seriously >included in MIT's "Building Technology Program" >(http://web.mit.edu/bt/www/bt.html), otherwise it would seem to appear that >a cruel hoax and intellectual fraud may being perpetrated on your students. > >Sincerely, > >**************************************** >* Joe S. Moore >* Independent Buckminster Fuller Scholar >* joemoore@cruzio.com >* Buckminster Fuller Virtual Institute >* http://www.cruzio.com/~joemoore/ >**************************************** > ========================================================================= Date: Sun, 3 May 1998 20:55:42 -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: BUILDING TECH PROG In-Reply-To: <000101bd7704$ac8df180$dcdae3a5@kelp220.cruzio.com> Mime-Version: 1.0 Content-Type: text/plain; charset="us-ascii" Joe -- Re: MSNBC web story re House of the Future (MIT consortium) I don't think these ideas will completely slip through the cracks no matter what happens re MIT. Like, I've already shared my http://www.teleport.com/~pdx4d/bworks.html with Asian concerns (and Motorola) and sparked some interest. Which ideas we attribute to Fuller, which to Jay Baldwin, which to you... that's something we can sort out at our leisure. In the meantime, lets get on with the storyboarding! Thanks for all you hard work. Keep it up. Kirby 4D Solutions PS: have you seen 'Lost in Space' yet? Good take of a 'Garden of Eden' dome home (plus that DaMert BuckyBall on Will's toy shelf -- gotta be quick to catch it). Encl: edited copy of one of my replies (I get lots of inquiries re domes, this one representative), copy of yours to MIT Building Tech. ======= At 01:12 PM 5/2/98 EDT, you wrote: >Kirby, > >I am looking into purchasing a dome home. Do you have a company that you seem >to trust more than others? Also, are they really energy efficient, as well >as more cost efficient to build? >I live in Kansas City, MO. Which company would be worth looking into for >plans, shipping, etc. Right now, I like the Geodome Woodworks Sky Gazer plan. >You can find it at www.geodomesinc.com. >Please respond. I'm not sure who to trust. > I maintain http://www.teleport.com/~pdx4d/domeman.html which presumably you've seen, but I don't get into the business of recommending this or that for reliability at this point, since I haven't done business with any of them. Sorry. In principle domes are efficient, but I also tend to view them as in their infancy. Those models on the market to day will look very primitive, even if classics in their day, is my hope. In my view, just about all of today's domes are too similar in design, materials and conception to regular box homes. I hope to live long enough to spend some time in the models which today are more likely to appear only in science fiction, like in 'Lost in Space', the newly released movie -- quick shot of a 'garden of eden' dome inside of which is a more Frank Lloyd Wright style home plus garden -- presumably the home is more like a theater prop, not needing the same kind of insulation and reinforcement against high winds, which is what the dome provides). >Also, this is my sister's e-mail address. Please don't reply via this >address. My e-mail address is [XXX] > >Thank you for your time, > >[XXX] > Kirby ======== At 07:30 PM 5/3/98 -0700, Joe S. Moore wrote: >William J. Mitchell >Dean, School of Architecture and Planning >Massachusetts Institute of Technology > >Dear Sir, > >I certainly hope that the ideas of R. Buckminster Fuller are seriously >included in MIT's "Building Technology Program" >(http://web.mit.edu/bt/www/bt.html), otherwise it would seem to appear that >a cruel hoax and intellectual fraud may being perpetrated on your students. > >Sincerely, > >**************************************** >* Joe S. Moore >* Independent Buckminster Fuller Scholar >* joemoore@cruzio.com >* Buckminster Fuller Virtual Institute >* http://www.cruzio.com/~joemoore/ >**************************************** ======== ========================================================================= Date: Mon, 4 May 1998 12:07:50 -0700 Reply-To: List for the discussion of Buckminster Fuller's works Sender: List for the discussion of Buckminster Fuller's works From: Lee Fisher Subject: geodesic greenhouse kit? Hi, If anyone has pointers to geodesic greenhouse kit manufacturers, or available designs, I would greatly appreciate it. [This is for my neighbor, an Fuller-fan and ex-hippie; her old non-geodesic greenhouse was damaged by a tree recently...] Thanks, Lee ========================================================================= Date: Mon, 4 May 1998 13:29:23 -0700 Reply-To: "P. O. Box 2321" Sender: List for the discussion of Buckminster Fuller's works From: "P. O. Box 2321" Subject: Re: geodesic greenhouse kit? Comments: To: Lee Fisher In-Reply-To: MIME-Version: 1.0 Content-Type: TEXT/PLAIN; charset=US-ASCII On Mon, 4 May 1998, Lee Fisher wrote: > If anyone has pointers to geodesic greenhouse kit manufacturers, or > available designs, I would greatly appreciate it. This from only yesterday - always a good idea to look before asking... http://w3.one.net/~monkey/geodesics/pvcstruts ... but it's also true sometimes not everything in the geodesic listserv shows up in the geodesic newsgroup. Either way, good luck to your neighbor! -- Trevor Blake box2321@teleport.com http://www.teleport.com/~box2321/ Post Office Box 2321, Portland Oregon 97208-2321, United States ========================================================================= Date: Mon, 4 May 1998 17:51:19 -0400 Reply-To: List for the discussion of Buckminster Fuller's works Sender: List for the discussion of Buckminster Fuller's works From: Robert Conroy Subject: geodesic greenhouse kit? MIME-Version: 1.0 Content-Transfer-Encoding: quoted-printable Content-Type: text/plain; charset=ISO-8859-1 Lee, You wrote: <> I have several geodesic greenhouse designs on my Greenhouse WEB pag= e along with one on my conduit page. http://ourworld.compuserve.com/homepages/robert-conroy/greenhou.htm " " " " " /conduitd.htm = I also plan to design an add-on greenhouse to my full size domes whi= ch will be comprised of used recycled double glass panels from hotel sliding= glass doors, which generally can be bought very cheaply. Hopefully it wi= ll be done by this fall. Although it will be tied in with a geodesic structure, it will not be what you could desribe as geodesic, other than the roof and floor make a triangle. = Bob ========================================================================= Date: Mon, 4 May 1998 20:16:52 EDT Reply-To: List for the discussion of Buckminster Fuller's works Sender: List for the discussion of Buckminster Fuller's works From: RINEHARTJR Subject: Re: geodesic greenhouse kit? Mime-Version: 1.0 Content-type: text/plain; charset=US-ASCII Content-transfer-encoding: 7bit David Falasco, 4209 Maxwell St, Colorado Springs, CO 80906, Home (719)596-5337, Work 599-5961 has been building them for several years. Good luck! ========================================================================= Date: Mon, 4 May 1998 16:36:40 -0500 Reply-To: List for the discussion of Buckminster Fuller's works Sender: List for the discussion of Buckminster Fuller's works From: Curt Flowers Organization: University of Illinois Subject: Re: Information Mime-Version: 1.0 Content-Type: text/plain; charset=us-ascii Content-Transfer-Encoding: 7bit Patricia Goodson wrote: > > Hello, > I am a member of Unity Clear Lake Center in Lake county. We are > thinking > of building a church on the geodesic design. Any information that you can > give me I would appreciate it. I know very little about domes and I would > like to learn. Thank You and Blessings! Pat You might check out Living Word Fellowship Church, St. Joseph, IL. (217) 469-7410 Pastor: Larry Millis. Their church sanctuary is a large 3v icosa geodesic dome around which they've build classrooms. It's a beautiful sight, right next to interstate 74 between Champaign and Danville. ========================================================================= Date: Mon, 4 May 1998 23:24:14 EDT Reply-To: List for the discussion of Buckminster Fuller's works Sender: List for the discussion of Buckminster Fuller's works From: RINEHARTJR Subject: Re: Information Comments: To: Oregon@domes.com Mime-Version: 1.0 Content-type: text/plain; charset=US-ASCII Content-transfer-encoding: 7bit In a message dated 5/4/98 19:08:24, you wrote: Oregon Dome, Inc has built several domes for church use, both in 3/8th's and 1/4 sphere domes. They can be reached at Oregon@ Domes.com. Member wrote: << Hello, > I am a member of Unity Clear Lake Center in Lake county. We are > thinking > of building a church on the geodesic design. Any information that you can > give me I would appreciate it. I know very little about domes and I would > like to learn. Thank You and Blessings! Pat >> ========================================================================= Date: Tue, 5 May 1998 10:31:41 -0600 Reply-To: List for the discussion of Buckminster Fuller's works Sender: List for the discussion of Buckminster Fuller's works From: Rob Hafernik Organization: Shokwave Software, Inc Subject: Re: Discrete math In article <6i79t8$hii@b.stat.purdue.edu>, hrubin@b.stat.purdue.edu (Herman Rubin) wrote: > Part of this is that the computer does not do what it is claimed it > does. "Floating point arithmetic" is rarely the operation it is > commonly called, and the computation of square roots and transcendental > functions is not "correct", but an approximation. If this is realized, > the problems do not go away, but are better faced. The point of all this escapes me, but this statement is misleading. The values for all transcendental functions are approximations (by definition, really), so to chide computers for approximating them is misleading. I'm sure Herman knows this. The "approximation" that computers use is generally the result of a Taylor series or similar function. This may be computed on the fly or it may be stored in a table and interpolated. For the most part, it's certainly possible for a computer to use "approximations" as precise as any you would use doing the math by hand. Every time you go from a transcendental function to a value for that function, whether it's in a mathematical operation done by hand or computer, "exactness" is sacrificed. Different types of programs use different methods too. A 3D game, for example, needs sines and cosines for transformation matrices, but it doesn't need accurate ones. I've often seen games that had small look-up tables with a granularity of only a degree or half degree to speed up the calculation of trig functions. I've seen other programs that need precise values, but only over a small range, calculate a few very exact values over the range, then do high-quality interpolation within that range. Some computers (not many, anymore) do transcendentals in software, calculating them as needed from Taylor series terms. As for floating point arithmetic rarely being the operation its commonly called, I hardly know where to start. Generally speaking, ALL computation is done by the same sort of "approximation" that computers use. When you have the term "1/3" in a problem you're working out, you don't worry that 0.333333333 is just an approximation, you just go ahead. A computer may represent 0.333333333 differently, but the end result of the calculation will be the same. With today's 64 or 80 bit floating point numbers, precision is high enough that rounding errors and such can be ignored much of the time. Under some conditions, such as problems that combine very large and very small numbers or functions that are sensitive to very small errors, you have to pay extremely close attention to the way numbers are handled in the computer you're using. Truly disasterous combinations are possible. Of course, if you're representing a descrete value (such as money), you usually don't use a floating point number. On the flip side, continuous values are sometimes represented as descrete values to save computational time (in the bad old days, floating point operations were very computationaly expensive, they could take thousands of times longer than integer math). I've seen graphics programs, for example, that used fixed-point coordinate systems. Since there are only so many pixels in play (1200 to the inch being adequate for most purposes), you can represent a coordinate as a integer number of inches and an integer fraction of an inch (which gives you a coordinate space about 1/2 mile square, enough for most graphics). Thus a point midway between 5 and 6 becomes 5 and 16384/32768ths of an inch. Since it's easy and fast to add, subtract and multiply fixed-point numbers, this is a good solution. Of course division is hard, but it always is. For trig functions and the like, you use look-up tables with a modest amount of interpolation. Generalizing about math and computers is pretty dangerous. Just about every possible methodology has been used, both successfully and unsuccessfully, many times. ========================================================================= Date: Tue, 5 May 1998 15:01:41 -0600 Reply-To: jlawson@texnet.net Sender: List for the discussion of Buckminster Fuller's works From: james lawson Subject: America's most famous living genius MIME-Version: 1.0 Content-Type: text/plain; charset=us-ascii Content-Transfer-Encoding: 7bit Clifford J. Nelson wrote: > someone who was called "America's most famous living > genius" > Who, where, when and in what context did someone call Buckminster Fuller "America's most famous living genius"? ========================================================================= Date: Tue, 5 May 1998 14:26:43 -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: BUCKY BIO OUTLINE Comments: To: coend@geocities.com MIME-Version: 1.0 Content-Type: text/plain; charset="iso-8859-1" Content-Transfer-Encoding: 7bit Doug, I like your Bucky Fuller Biographical Outline (http://www.geocities.com/Area51/Cavern/2945/bucky.html)! I agree that some of the dates are probably off by a year. See Fuller's own chronologies in the back of _Critical Path_ (Appendixes I & II). Nice work, **************************************** * Joe S. Moore * Independent Buckminster Fuller Scholar * joemoore@cruzio.com * Buckminster Fuller Virtual Institute * http://www.cruzio.com/~joemoore/ **************************************** ========================================================================= Date: Tue, 5 May 1998 18:23:08 -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: A Simple Bolted PVC Geodesic Strut Design MIME-Version: 1.0 Content-Type: text/plain; charset=us-ascii Content-Transfer-Encoding: 7bit A slight correction to the paper - when calculating the strut lengths, add two inches to each strut. If you drill a hole one inch from each end, then the hole-to-hole distance (the number that counts) will be corrected to the calculated chord length - otherwise the dome will be slightly distorted. The paper has been changed to reflect this... David Anderson wrote: > Here's how I put together the framework for the greenhouse... > > http://w3.one.net/~monkey/geodesics/pvcstruts > > -- > > - Dave Anderson monkey@one.net http://w3.one.net/~monkey ========================================================================= Date: Tue, 5 May 1998 15:39:10 -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: SCIENTIFIC HOUSE Comments: To: tworld@bbc.co.uk MIME-Version: 1.0 Content-Type: text/plain; charset="iso-8859-1" Content-Transfer-Encoding: 7bit BBC ONLINE Staff London, England Gentlemen, If you're REALLY serious about your "Dream Home" project (http://www.bbc.co.uk/tw/dream/dream.shtml), look in R Buckminster Fuller's book _Critical Path_ (1981) on pages 310-15 for a description of the ultimate dream home. **************************************** * Joe S. Moore * Independent Buckminster Fuller Scholar * joemoore@cruzio.com * Buckminster Fuller Virtual Institute * http://www.cruzio.com/~joemoore/ **************************************** ========================================================================= Date: Tue, 5 May 1998 16:37:50 -0500 Reply-To: List for the discussion of Buckminster Fuller's works Sender: List for the discussion of Buckminster Fuller's works From: Herman Rubin Organization: Purdue University Statistics Department Subject: Re: Discrete math In article , Rob Hafernik wrote: >In article <6i79t8$hii@b.stat.purdue.edu>, hrubin@b.stat.purdue.edu >(Herman Rubin) wrote: >> Part of this is that the computer does not do what it is claimed it >> does. "Floating point arithmetic" is rarely the operation it is >> commonly called, and the computation of square roots and transcendental >> functions is not "correct", but an approximation. If this is realized, >> the problems do not go away, but are better faced. >The point of all this escapes me, but this statement is misleading. The >values for all transcendental functions are approximations (by definition, >really), so to chide computers for approximating them is misleading. I'm >sure Herman knows this. You know this, and I know this, but the typical user does not, or does not understand this. Students using calculators do not act as if they know it. Students who have learned to do decimal calculations by hand also do not seem to understand that it may or may not make a difference. In mathematics the associative law for multiplication holds. In floating-point computer arithmetic, this is not necessarily the case. Without checking, I cannot tell you if (5.0/3.0)*3.0 = 5.0 or not, using the hardware operations. A computer doing floating-point operations is not doing arithmetic, but an approximation to it. If the user does not understand this, the user may run into mistakes. In some cases, the software may be such as to make such mistakes relatively common. Instead of teaching students how to do the manipulations, we should teach them to understand the mathematics, so they will be aware of these problems. ..................... >With today's 64 or 80 bit floating point numbers, precision is high enough >that rounding errors and such can be ignored much of the time. ^^^^^^^^^^^^^^^^ Under some >conditions, such as problems that combine very large and very small >numbers or functions that are sensitive to very small errors, you have to >pay extremely close attention to the way numbers are handled in the >computer you're using. Truly disasterous combinations are possible. Of >course, if you're representing a descrete value (such as money), you >usually don't use a floating pointnumber. The Pentium bug turned out to be more serious than thought, because many producers of software used what the hardware was SUPPOSED to do in such a way as to avoid many problems. These steps made the occurrence of the errors far more common. >On the flip side, continuous values are sometimes represented as descrete >values to save computational time (in the bad old days, floating point >operations were very computationaly expensive, they could take thousands >of times longer than integer math). This was never the case; it is easy to program floating operations using integer arithmetic. At this time, it is integer operations which are the far more expensive ones on most machines. -- This address is for information only. I do not claim that these views are those of the Statistics Department or of Purdue University. Herman Rubin, Dept. of Statistics, Purdue Univ., West Lafayette IN47907-1399 hrubin@stat.purdue.edu Phone: (765)494-6054 FAX: (765)494-0558 ========================================================================= Date: Tue, 5 May 1998 20:17:12 -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: geodesic greenhouse kit? Content-Type: TEXT/PLAIN; CHARSET=US-ASCII Content-Transfer-Encoding: 7BIT MIME-Version: 1.0 (WebTV) You might try Ernie's domes..... http://www.fastlane.net/~ega/wgd1.htm ========================================================================= Date: Tue, 5 May 1998 22:14:12 -0400 Reply-To: Kevin Sender: List for the discussion of Buckminster Fuller's works From: Kevin Subject: Re: geodesic greenhouse kit? MIME-Version: 1.0 Content-Type: text/plain; charset="us-ascii" Content-Transfer-Encoding: 7bit Or this link if that one below does not work: http://www.fastlane.net/~ega/ -----Original Message----- From: anthony kalenak Newsgroups: bit.listserv.geodesic To: GEODESIC@LISTSERV.ACSU.BUFFALO.EDU Date: Tuesday, May 05, 1998 9:17 PM Subject: Re: geodesic greenhouse kit? You might try Ernie's domes..... http://www.fastlane.net/~ega/wgd1.htm ========================================================================= Date: Tue, 5 May 1998 22:19:22 -0400 Reply-To: m_moy@juno.com Sender: List for the discussion of Buckminster Fuller's works From: Michael Moy Organization: None Subject: Re: Discrete math Mime-Version: 1.0 Content-Type: text/plain; charset=us-ascii Content-Transfer-Encoding: 7bit Herman Rubin wrote: > > In article , > Rob Hafernik wrote: > >In article <6i79t8$hii@b.stat.purdue.edu>, hrubin@b.stat.purdue.edu > >(Herman Rubin) wrote: > > > >> Part of this is that the computer does not do what it is claimed it > >> does. "Floating point arithmetic" is rarely the operation it is > >> commonly called, and the computation of square roots and transcendental > >> functions is not "correct", but an approximation. If this is realized, > >> the problems do not go away, but are better faced. > > >The point of all this escapes me, but this statement is misleading. The > >values for all transcendental functions are approximations (by definition, > >really), so to chide computers for approximating them is misleading. I'm > >sure Herman knows this. > > You know this, and I know this, but the typical user does not, or does > not understand this. Students using calculators do not act as if they > know it. Students who have learned to do decimal calculations by hand > also do not seem to understand that it may or may not make a > difference. > > In mathematics the associative law for multiplication holds. In > floating-point computer arithmetic, this is not necessarily the case. > Without checking, I cannot tell you if (5.0/3.0)*3.0 = 5.0 or not, > using the hardware operations. A computer doing floating-point > operations is not doing arithmetic, but an approximation to it. > If the user does not understand this, the user may run into mistakes. > In some cases, the software may be such as to make such mistakes > relatively common. You could always use a symbolic calculator instead of one that uses approximations for results. > Instead of teaching students how to do the manipulations, we should > teach them to understand the mathematics, so they will be aware of > these problems. It's not that difficult to demonstrate what goes on in floating point arithmetic though this is typically done in university courses. > ..................... > > >With today's 64 or 80 bit floating point numbers, precision is high enough > >that rounding errors and such can be ignored much of the time. > ^^^^^^^^^^^^^^^^ > > Under some > >conditions, such as problems that combine very large and very small > >numbers or functions that are sensitive to very small errors, you have to > >pay extremely close attention to the way numbers are handled in the > >computer you're using. Truly disasterous combinations are possible. Of > >course, if you're representing a descrete value (such as money), you > >usually don't use a floating pointnumber. There are two bits for four options on rounding. You may run into surprises if you have the wrong setting on or if you have a software bug that incorrectly sets these bits. These are described in one of the three Intel Pentium books at Intel's site. > The Pentium bug turned out to be more serious than thought, because many > producers of software used what the hardware was SUPPOSED to do in such > a way as to avoid many problems. These steps made the occurrence of the > errors far more common. > > >On the flip side, continuous values are sometimes represented as descrete > >values to save computational time (in the bad old days, floating point > >operations were very computationaly expensive, they could take thousands > >of times longer than integer math). > > This was never the case; it is easy to program floating operations using > integer arithmetic. At this time, it is integer operations which are > the far more expensive ones on most machines. I find this rather hard to believe though I can check this on the Digital Alpha and Intel Pentium Processors when I'm in the office. ========================================================================= Date: Wed, 6 May 1998 07:29:39 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: Volume of geodesic "sphere" (project) MIME-Version: 1.0 Content-Type: text/plain; charset=us-ascii Content-Transfer-Encoding: 7bit Robin Chapman wrote: >Aaaaargh! I give up. What can I do against such logorrhoea? I return >after the weekend and the thread has snowballed. Clearly I'm not going >to able to read all this stuff, let alone refute every single >dubious argument. > I went off on a tangent with Cliff Nelson and then Brian Hutchings jumped into the scene (sigh). With you it's been tit for tat I think, with one extra by me to further clarify, longer than your two correctives I admit -- but then who's keeping score? :-) Anyway, I gather I'm losing the benefit of your participation. It's hard for me to track this on sci.math as well -- one of the most frenetic of the USENET newgroups (lots of "me first" people). Thanks for the chatter -- much enjoyed. >OK. But is there an easy to see reason why the regular octahedron >has 4 times the volume of the regular tetrahedron of the same edge length? Sure. First you consider that doubling the linear dimensions of any shape increases its volume 8-fold (volume goes up as a 3rd power of edge length). So our unit-volume tetrahedron, now twice as big (edge-wise) has a volume of 8. It's midpoints subdivide it into four tetrahedra of the original size (the "tips") leaving a regular octahedron once you take them away. 8 - 4 = 4. It's easier to show as an animation of course. >Can one dissect the octahedron into a finite number of smaller polyhedra >which can be reassembled to form four regular tetrahedra of the same >edge-length? You can dissect it into 48 A and 48 B modules, which have equal volume (1/24). The tetrahedron is assembled from 24 A modules, so the 4:1 relationship is pretty easy to see. >Equivalently, since a regular tetrahedron of side-length 2 >can be dissected into 4 regular tetrahedra plus an octahedron of >unit side length This is the 4 + 4 = 8 thing I was talking about. >can one dissect an edge-length 2 regular tetrahedron >into smaller polyhedra and reassemble into eight unit tetrahedra? The 2-frequency tetrahedron dissects into A and B mods -- for a total of 8 x 24 modules, we can say without hesitation. The A and B mods also assemble the cube, rhombic dodecahedron, cuboctahedron, Coupler, MITE, tetrakaidecahedron and other shapes -- cubes are not as flexible. I do have a cube to play with though, just like you do -- except its volume is 3 relative to the volume 1 tetrahedron. This is the so-called 'duo-tet' cube, formed by the 8 vertices of a tet interpenetrating its dual 'Star of David' fashion. You can show it has a volume of 3 with an animation glomming 4 eighth octahedra to a unit volume tet. We already know the octa is 4 so 4/8 = 1/2 and 1 + 4 x 1/2 = 3. Fuller did a lot of this "slice and dice" stuff in his "Synergetics Folio" (color plates reproduced at the front of Synergetics 2). No computation or coordinates required. >(Of course the corresponding problem for the CUBE is a bit easier :-)) > Try building a rhombic dodecahedron with cubes. The rh dodeca is a space-filler by the way (as I'm sure you know) and has a volume of 6 relative to the inscribed cube of volume 3 (= short face diagonals). Kids love the simplicity of all this (and I make sure to work it into my quadray papers, so even if they forget all about quadrays -- fine with me -- they might get a handle on the synergetics concentric hierarchy). >> >> There is an irregular tetrahedron which fills space by the way -- >> the MInimum TEtrahedron (or MITE), with a volume of 1/8 (depicted >> on pg. 71 of Coxeter's 'Regular Polytopes' but not dignified with >> a name, nor assembled in terms of A and B modules). > >Surley the easiest way to see this is to dissect the CUBE into six congruent >tetahedra? Divide the cube into six congruent half-octahedra. The cube's center forms their common apex and its 6 faces their bases. These are half-couplers of volume 1/2 (6 x 1/2 = 3). Half-couplers consist of 4 MITEs (draw a criss-cross on the cube's face). >For instance the cube with Cartesian coordinates... Nevermind about coordinates. >My position when faced with a geomteric problem is to solve it without >introducing coordinates if possible, or if not introduce some coordinate >system respecting as much symmetry of the problem as possible. There >may even conceivably be some problem for which quadray coordinates >might be useful, but I can't think of any at the present :-) > I enjoyed using them to represent polyhedra in a relational database (vertices in one table, edges in another), a lot of which have integer coordinates in quadrays (some do in XYZ too, I realize). Beyond that, I've found the apparatus useful in a philosophical context (cite memo to one of your peers at Exeter), but I don't push them as a replacement for XYZ, nor for any practical purpose at this point -- just another game, one of gazillions. I like the British "maths" (plural) -- synchs with my sense of it as well. The papers are clearly written I might add (I get praise from classroom teachers) so I suppose you could say I use quadrays to show off my talents as a curriculum writer involved in distance learning via the internet. Kids can pick up a lot of ideas about vectors and ways to harness ray tracing software to play with polyhedra, which ideas work in XYZ world of course -- nothing new. > >I don't know. I have read any Cantor for about 15 years... OK, thanks for racking your brains anyway. >Why are you scared of negative numbers? In view of your lionization >of independent discoverers of classical ideas you might like to recall >that Paul Erdos's mother claimed that he discovered the idea of negative >numbers for himself at the age of three. What age will you be when you >discover them? :-) > Nevermind about this. I'm clear you don't have the time for a prolonged discussion on this score. I've already said my piece at my website and cited the relevant pages. Negative numbers are fine, I have no problem with them. >Or you can express quadrays in terms of Cartesians. (1 1 1), (1 -1 -1), >(-1 1 -1) and (-1, -1, 1) is a Cartesian expression for a quadray base. >So Cartesians are the logical underpinning of what you take for garnted :-) > I say quadrays are more primitive because they use 4 spokes instead of 6 -- its a visual thing, all talk of coordinates or negative numbers aside. Seems an appropriate analytic gizmo to stick onto Fuller's "4D" (volume's dimensionality, using other criteria than orthogonality) even if Cliff Nelson disagrees. >Yup. Mathematics is all about getting the right numerical answers >to problems. There's no interest at all in understanding how we compute these, >as our computers will do them for us, and in these days of fast computers >who cares if the program you're running is using a complicated >and inefficient algorithm :-) > Sarcasm noted. But I get some new economies in trade for the added ops in my distance computations. And computers do have their advantages. >This university will never be able to afford to jump on the upgrade >treadmill :-( Anyway let me add, that as I know nothing of synergetics, >I am not dismissing it; I'm sure it's one of the million and one things >that I really ought to know about, but haven't got round to studying yet. >On the other hand, the inflated rhetoric of its most prominent USENET >prophet has ensured that at present it will not rise much above the >million-and-first position in my list :-( > Yeah, :-( I didn't think my rhetoric was all that inflated, but of course I'm my own blind spot. I'm trully sorry if I'm the reason you'll be putting off any further "explorations in the geometry of thinking" (Fuller's subtitle) but I suspect that was just parting hyperbole. Par for the course on USENET, where "prophets" of this and that are a dime a dozen. Kirby --------------------------------------------------------- Kirby T. Urner http://www.teleport.com/~pdx4d/kirby.html 4D Solutions http://www.teleport.com/~pdx4d/ [PGP OK] --------------------------------------------------------- ========================================================================= Date: Wed, 6 May 1998 06:12:20 -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: geodesic greenhouse kit? Content-Type: TEXT/PLAIN; CHARSET=US-ASCII Content-Transfer-Encoding: 7BIT MIME-Version: 1.0 (WebTV) Sorry about that. That url should have been: http://www.fastlane.net/~ega/WGD1.htm ========================================================================= Date: Wed, 6 May 1998 09:01:16 -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: FS: Bucky Fuller Children's Book MIME-Version: 1.0 Content-Type: TEXT/PLAIN; charset=US-ASCII Content-Transfer-Encoding: QUOTED-PRINTABLE Once in a while some of my most far-flung interests intersect. This book is a case in point: it is a children's biography of Buckminster Fuller. I am a children's book dealer by profession and Bucky scholar/collector by choice. Sometimes I sell bits of my Bucky collection - but I'm also always buying more. This is one of three Bucky books with a connection to children's literature, the others being Tetrascroll and Fuller's Earth. I hereby offer this one copy of this one out of print book... [#2751] [Fuller, R. Buckminster] Athena V. Lord: PILOT FOR SPACESHIP EARTH / R. BUCKMINSTER FULLER / ARCHITECT, INVENTOR & POET. New York: Macmillan Publishing Co. Inc, 1978. 1st ed. Cloth, 12mo, 168 pp. (Photographic illust.) Very Good in Very Good dust jacket: gift inscript, sm tear dj. One of the very few works about Fuller written for young readers, signed & inscribed by the author. Out of print. $37.50 ________________________________________________________________________ =A9 1998 Trevor Blake J. Whirler Used & Rare Children's Books P. O. Box 2321, Portland OR 97208-2321 USA telephone: 503-236-2364 / e-mail: box2321@teleport.com World Wide Web: http://www.teleport.com/~box2321/jw.htm Terms of Sale: - Postage paid in North America; outside of N. America please inquire. - Reciprocal dealer discount up to 20%, libraries accommodated. - Checks in United States currency to "Trevor Blake" only, please. - No credit cards accepted. - Two week hold with order. - See URL above for full terms of sale, returns, etc. ========================================================================= Date: Wed, 6 May 1998 10:41:51 -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: TET AND OCT DOMES Comments: To: ega@fastlane.net MIME-Version: 1.0 Content-Type: text/plain; charset="iso-8859-1" Content-Transfer-Encoding: 7bit Ernie, I like your Tet- & Oct-Based domes (http://www.fastlane.net/~ega/WGD1.htm). I don't know of anyone who is currently doing any development on them--much less actually offering them for sale. Good work! **************************************** * Joe S. Moore * Independent Buckminster Fuller Scholar * joemoore@cruzio.com * Buckminster Fuller Virtual Institute * http://www.cruzio.com/~joemoore/ **************************************** ========================================================================= Date: Wed, 6 May 1998 15:45:32 GMT Reply-To: List for the discussion of Buckminster Fuller's works Sender: List for the discussion of Buckminster Fuller's works From: mike@CITYWEBSITES.COM Organization: Citywebsites Subject: World wide directory launch Please come by and visit the internets newest world wide directory. We're hoping you'll suggest a link for us, and if there is a link you want to suggest for a place we don't have on line yet please come back and make your suggestion later. We're located at http://www.citywebsites.com ========================================================================= Date: Wed, 6 May 1998 14:00:55 +0900 Reply-To: List for the discussion of Buckminster Fuller's works Sender: List for the discussion of Buckminster Fuller's works From: tce Organization: DACOM Internet Service Subject: Re: Discrete math Herman Rubin @L(0!) <6io0re$1eco@b.stat.purdue.edu> 8^=CAv?!<- @[<:GO?4=@4O4Y... Well you know, a lot depends on the MIPS programming and the structure of ALU's involved. As long as computers calculate and store in 0 and 1's timely accuracy will be limited. 32 bits isn't a big word no matter how fast one clocks the CPU. ========================================================================= Date: Wed, 6 May 1998 10:39:33 -0600 Reply-To: List for the discussion of Buckminster Fuller's works Sender: List for the discussion of Buckminster Fuller's works From: Rob Hafernik Organization: Shokwave Software, Inc Subject: Re: Discrete math In article <6io0re$1eco@b.stat.purdue.edu>, hrubin@b.stat.purdue.edu (Herman Rubin) wrote: > >On the flip side, continuous values are sometimes represented as descrete > >values to save computational time (in the bad old days, floating point > >operations were very computationaly expensive, they could take thousands > >of times longer than integer math). > > This was never the case; it is easy to program floating operations using > integer arithmetic. At this time, it is integer operations which are > the far more expensive ones on most machines. Herman, you are absolutely, flatly, unquestionably wrong on this. Go to ANY computer newsgroup and post this and you will be laughed at, flamed and made the butt of crude techie jokes that you may not understand. It has only been in the last few years that programmers had access to cheap floating point. Before that, all SORTS of work-arounds were used, as I said. Everyone knows this. Most of us who have been in the business for any length of time have an ingrained, automatic aversion to floating point. Floats were so slow to use for so long that it takes an act of will to use them today, even though they are much better. It is NOT "easy" to program "floating operations" using integer arithmetic. Even stating the question this way shows you don't know how it's done. EVERY operation done by a computer CPU is "integer" in the sense that all operations are done on small chunks of bits. Floating point ops are VERY expensive to do in software. Since every floating point op requres MANY integer operations, they were ALWAYS much slower than integer operations when emulated in software. Floating point divides in integer software take DOZENS of instructions. Integer operations are still as fast or faster than floating point ops today on all CPUs that I know of. Certainly, this is true for the Pentium or PowerPC CPUs in most desktops (and the DEC Alpha). At the very best, some recent CPU's have floating point ops that are as fast as integer ops, but this is not the case for most CPUs in use today. Herman, please stick to subjects you actually know something about. ========================================================================= Date: Wed, 6 May 1998 13:57:50 -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: NEW GAZEBO DOME MANUF MIME-Version: 1.0 Content-Type: text/plain; charset="iso-8859-1" Content-Transfer-Encoding: 7bit The GeoGazebo Manufactured By DynaTek Corp. P.O. Box 5662 Knoxville, TN, 37928 USA (423) 689-8800 1-888-689-8809 Orders Only http://www.geogazebo.com **************************************** * Joe S. Moore * Independent Buckminster Fuller Scholar * joemoore@cruzio.com * Buckminster Fuller Virtual Institute * http://www.cruzio.com/~joemoore/ **************************************** ========================================================================= Date: Wed, 6 May 1998 14:31:55 -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: Dome (http://topia.simplenet.com/dome.htm) MIME-Version: 1.0 Content-Type: text/plain; charset="iso-8859-1" Content-Transfer-Encoding: 7bit Another dome manufacturer! "Ready made steel connectors for making Knocked Down Geodesic Domes" Topia Co, Ltd. 310/165 Songprapa Rd. Donmuang, Bangkok 10210, Thailand Tel. (662)566-3114, 566-1219 Fax (662) 566-1219 Web Site : http://topia.simplenet.com/dome.htm E-Mail : topia@samart.co.th **************************************** * Joe S. Moore * Independent Buckminster Fuller Scholar * joemoore@cruzio.com * Buckminster Fuller Virtual Institute * http://www.cruzio.com/~joemoore/ **************************************** ========================================================================= Date: Wed, 6 May 1998 13:47:57 -0400 Reply-To: m_moy@juno.com Sender: List for the discussion of Buckminster Fuller's works From: Michael Moy Organization: None Subject: Re: Discrete math Mime-Version: 1.0 Content-Type: text/plain; charset=us-ascii Content-Transfer-Encoding: 7bit Michael Moy wrote: > > Herman Rubin wrote: > > > > In article , > > Rob Hafernik wrote: > > >In article <6i79t8$hii@b.stat.purdue.edu>, hrubin@b.stat.purdue.edu > > >(Herman Rubin) wrote: > > > > > > >> Part of this is that the computer does not do what it is claimed it > > >> does. "Floating point arithmetic" is rarely the operation it is > > >> commonly called, and the computation of square roots and transcendental > > >> functions is not "correct", but an approximation. If this is realized, > > >> the problems do not go away, but are better faced. > > > > >The point of all this escapes me, but this statement is misleading. The > > >values for all transcendental functions are approximations (by definition, > > >really), so to chide computers for approximating them is misleading. I'm > > >sure Herman knows this. > > > > You know this, and I know this, but the typical user does not, or does > > not understand this. Students using calculators do not act as if they > > know it. Students who have learned to do decimal calculations by hand > > also do not seem to understand that it may or may not make a > > difference. > > > > In mathematics the associative law for multiplication holds. In > > floating-point computer arithmetic, this is not necessarily the case. > > Without checking, I cannot tell you if (5.0/3.0)*3.0 = 5.0 or not, > > using the hardware operations. A computer doing floating-point > > operations is not doing arithmetic, but an approximation to it. > > If the user does not understand this, the user may run into mistakes. > > In some cases, the software may be such as to make such mistakes > > relatively common. > > You could always use a symbolic calculator instead of one that > uses approximations for results. > > > Instead of teaching students how to do the manipulations, we should > > teach them to understand the mathematics, so they will be aware of > > these problems. > > It's not that difficult to demonstrate what goes on in floating > point arithmetic though this is typically done in university courses. > > > ..................... > > > > >With today's 64 or 80 bit floating point numbers, precision is high enough > > >that rounding errors and such can be ignored much of the time. > > ^^^^^^^^^^^^^^^^ > > > > Under some > > >conditions, such as problems that combine very large and very small > > >numbers or functions that are sensitive to very small errors, you have to > > >pay extremely close attention to the way numbers are handled in the > > >computer you're using. Truly disasterous combinations are possible. Of > > >course, if you're representing a descrete value (such as money), you > > >usually don't use a floating pointnumber. > > There are two bits for four options on rounding. You may run into > surprises > if you have the wrong setting on or if you have a software bug that > incorrectly sets these bits. These are described in one of the three > Intel Pentium books at Intel's site. > > > The Pentium bug turned out to be more serious than thought, because many > > producers of software used what the hardware was SUPPOSED to do in such > > a way as to avoid many problems. These steps made the occurrence of the > > errors far more common. > > > > >On the flip side, continuous values are sometimes represented as descrete > > >values to save computational time (in the bad old days, floating point > > >operations were very computationaly expensive, they could take thousands > > >of times longer than integer math). > > > > This was never the case; it is easy to program floating operations using > > integer arithmetic. At this time, it is integer operations which are > > the far more expensive ones on most machines. > > I find this rather hard to believe though I can check this on the > Digital Alpha and Intel Pentium Processors when I'm in the office. I don't have the book with the timing for instructions but am pretty sure that just about anything emulated in software is slower than an integer instruction in hardware and the processors that I've seen generally have one instruction integer operations. A good book on computer organization should be able to show you how integer and FP math is done with circuitry examples showing the relative complexities. ========================================================================= Date: Wed, 6 May 1998 14:37:51 -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: DOME MANUF NUMBER 3 MIME-Version: 1.0 Content-Type: text/plain; charset="iso-8859-1" Content-Transfer-Encoding: 7bit ANOTHER dome manuf (#3)!! ALPINE DOMES P.O. Box 191 Monroe, OR 97456 (541) 847-5545 Contact: Bryce & Sandy Halonen Email: info@alpinedomes.com http://www.alpinedomes.com/ **************************************** * Joe S. Moore * Independent Buckminster Fuller Scholar * joemoore@cruzio.com * Buckminster Fuller Virtual Institute * http://www.cruzio.com/~joemoore/ **************************************** ========================================================================= Date: Wed, 6 May 1998 15:05:42 -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: DOME MANUF NUMBER 4 MIME-Version: 1.0 Content-Type: text/plain; charset="iso-8859-1" Content-Transfer-Encoding: 7bit Littlewood Geodesic Domes 7208 80 Ave, Edmonton, Alberta, Canada T6B 0C6 Phone; (403) 463-3004 or 970-3802 geodome@freenet.edmonton.ab.ca http://www.freenet.edmonton.ab.ca/domes/domes.html **************************************** * Joe S. Moore * Independent Buckminster Fuller Scholar * joemoore@cruzio.com * Buckminster Fuller Virtual Institute * http://www.cruzio.com/~joemoore/ **************************************** ========================================================================= Date: Wed, 6 May 1998 15:49:35 -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: ASPENSION TENSEGRITY MODEL Comments: To: marc@umr.edu MIME-Version: 1.0 Content-Type: text/plain; charset="iso-8859-1" Content-Transfer-Encoding: 7bit Marc, I like your Aspension Tensegrity model--very nice! http://www.umr.edu/~marc/bwdome.htm I built one once. It was 6 feet across. It's still clutering up my storeroom. (The spiders love it.) **************************************** * Joe S. Moore * Independent Buckminster Fuller Scholar * joemoore@cruzio.com * Buckminster Fuller Virtual Institute * http://www.cruzio.com/~joemoore/ **************************************** ========================================================================= Date: Wed, 6 May 1998 15:06:33 -0500 Reply-To: List for the discussion of Buckminster Fuller's works Sender: List f