Thursday, March 05, 2009


I've been highlighting our "new kind of geometry" on a number of math lists, making the tie to the Wolframites and their cellular automata studies, but also page 71 of Regular Polytopes, which goes back to like 1947 in print.

Loyal readers of this blog know I mention page 119 a lot, as the place where Coxeter cleaves the 4D world in two: tesseracts over here, time machines over there. He makes fun of science fiction writers who confuse these two. Well, on page 71 we get to preview yet a 3rd namespace, as Figure 4.7a depicts what later become known as the MITE, or "minimum tetrahedron", 4D in yet another sense (it's an "arrowhead").

Thanks to this minimal space-filler, we're able to anchor our tent to a "geometry for the ages" (Coxeter's), a kind of bedrock. Inside our tent: the sculpture garden we so care about, sometimes known as the concentric hierarchy with moving parts, various dances (cartoons) e.g. our Jitterbug Transformation.
Page 71
:: page 71 of Regular Polytopes ::

The MITE disassembles in two ways: as (A+, A-, B-) and as (B+, A+, A-). Bucky Fuller started researching these modules back in the 1950s, maybe earlier, and wanted to make sure they got wired into the literature within the context of their "home base" or "native context" i.e. Synergetics: Explorations in the Geometry of Thinking (1975, 1979, Scribner/Macmillan). For this reason, among others, dedicating Synergetics to H.S.M. Coxeter (with permission) was a good idea.

Other geniuses feeding into this NKG (besides Wolfram and Bucky): Alexander Graham Bell (octet truss); Karl Menger (a new non-Euclidean geometry); Kenneth Snelson (tensegrity); Jay Baldwin (materials studies) and Joe Clinton (optics). Of course I could go on and on (Isamu Noguchi, Shoji Sadao, Ashton Applewhite... Shirley Sharkey) -- just wanting to remind readers of the grand sweep of this literature.

J. Baldwin's Bucky Works might be a good place to start, if no grownup shared any of this in day care when you were small. 1900s-trained adults tended to be selfish about sharing this material, not sure why -- "Pavlovian conditioning" is the latest theory on Synergeo (i.e. "just trying to be good doobies, who can blame us for that?").