Two typos fixed. Plus "Arthur Goldberg" changed to "[Michael]
Goldberg" (a mistake I fixed on
Microarchitecture of the Virus as well -- thanks to Gregory
J. Morgan for pointing out my error). Italics added. Original in
archives. Date: Wed, 26 Nov 1997 12:01:48 -0800 To: ip@sciserv.org From: Kirby Urner <pdx4d@teleport.com> Subject: 'Jungles of Randomness' re Fuller & viruses Cc: synergetics-l@teleport.com MEMORANDUM November 26, 1997 TO: Ivars Peterson, Science News, science writer FR: Kirby Urner, 4D Solutions, curriculum writer RE: 'Jungles of Randomness' re Fuller & viruses Dear Sir -- I've just been browsing your Jungles of Randomness, the section on viruses and R. Buckminster Fuller, and wanted to relay my own understanding of the events in question. First, I congratulate you for bringing Fuller back into the narrative. After his contribution got some front page press in the New York Herald Tribune, his name got dropped from subsequent accounts, ostensibly because Dr. Goldberg's mathematics had priority, but more accurately because Fuller was too much the maverick and his thinking too alien for the times, and therefore including him with tie-backs to Synergetics seemed more problematic than just wiring him out -- something of a relief that Coxeter helped uncover that Goldberg stuff I'm sure. This decision to wire Fuller out was taken by Scientific American which ran that article by Dr. Robert Horne, despite archived correspondence between Fuller and Horne in which Fuller takes great pains to show that his and Goldberg's thinking were not along the same lines at all i.e. both deserved mention in Horne's account (but by this time it was too late -- the damage had already been done). So to see Fuller wired back into the narrative is heartening, as it shows we've overcome at least some of the initial prejudice. This is an especially positive development in light of the hatchet job re Fuller's Synergetics we find in Hugh Aldersey-Williams' The Most Beautiful Molecule, wherein he implies in the conclusion of his chapter "A Fuller View" that we should feel no more compunctions about bleeping over synergetics in the fullerene chapter than we did in the virus chapter -- the fullerene chapter being a deja vu experience in a lot of ways, with science writers steadfastly ignoring the option to tie back to synergetics in any coherent manner, preferring to stick to safely superficial chatter about the geodesic domes. What I found confusing in your account is you seem to suggest it was these 'magical' T numbers and the expression 10T + 2 which Fuller was going on about in that quote of his you provide, whereas he was actually writing about 10F^2+2, which expression gives the number of spheres in successive shells of a cuboctahedron. If you dense-pack 12 spheres around a nuclear sphere, that's F=1. A second layer retains the cuboctahedral conformation (as do all subsequent layers) and contains 42, 92, 162 spheres (F=2,3,4...) and so on. What Fuller realized, and made use of when computing his domes, is that the cuboctahedron's shell count expression works equally well for the icosahedron, because of a transformation of the cuboctahedron into the icosahedron which does not alter the count, but merely the arrangement of the spheres in the outer layer (a transformation he calls the Jitterbug, though it was known to other mathematicians previously, at least in some aspects -- no others that in my awareness made it so central to their thinking as Fuller's synergetics did). I think by keeping Fuller's precise contribution in view, while giving credit to others for their own respective inputs to the virus thing, we keep the link back to synergetics unobstructed by irrelevancies -- makes things easier from a pedagogical point of view. Fuller was on his own track with the sphere packing investigations, doing something quite different from [Michael] Goldberg (what he was trying to communicate to Horne), and it makes sense that we tell the story with this in mind, neither giving Fuller more nor less than his due vis-a-vis the virus chapter. In the case of fullerenes, my line is that the name is apt, even though Leonardo and others knew of the truncated icosa, because fullerenes come in multiple frequencies, just like the domes (and cuboctahedral sphere packings), and because we have correspondence on file showing Fuller was on the lookout for the fullerene hexa-pent pattern in chemistry in particular.[1] This is not to say that Fuller specifically anticipated fullerene (others before Kroto, Smalley et al did that, including in Japan), but that 'fullerene' makes more sense than 'Leonardoene' or 'Archimedesene' for example, for the reasons just given. Thanks for helping to make our math curriculum a fun and interesting one for ourselves and those who come after us. I'm looking forward to studying more of your Jungles of Randomness plus other writings of yours, both past and future. Relevant citation: http://www.teleport.com/~pdx4d/virus.html (which now links to this memo). [1] "...I am greatly intrigued by your discovery of the two purines whose elementary components are hexagons and pentagons and the pyramidines which have a hexagonal configuration only... the pentagon occurs only as a consequence of its being a component of a polyhedral system." Fuller to Petr Jandacek, Los Alamos, NM, 15 Dec 76 as included in the Synergetics Dictionary, compiled and edited by E.J. Applewhite (Garland Press, 1986), Vol 2., pg. 219, card 8. |
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