[math4wisdom] Re: Math 4 Wisdom event, April 24, Wednesday, Evolution in Biology and Physics and ...
- From: kirby urner <kirby.urner@xxxxxxxxx>
- To: math4wisdom@xxxxxxxxx
- Date: Sat, 20 Apr 2024 17:29:28 -0700
KIrby, you are likewise struggling with making sense of the Goldberg
table, as you call it, with the angles for space filling tetrahedra. If
you made a page for that at the Coda, perhaps I and others could help you
think about it. It's a good way to learn more about your math interests.
Per my postings to said M4W Coda | Knowledge Engineering, my scope of
interest, re tools, goes beyond Coda to these Jupyter Notebooks I'm always
raving about, which brings in additional tools, such as nbviewer, colab,
Github, JupyterLab, Python.
Then I'm interested in what Daniel has been doing, with Perplexity (a front
end to other AI tools), and with DallE (see the Art topic, for an example
of his USA OS series, more where that one came from).
So, the Goldberg Table: instead of buried in the Coda, it's buried waaay at
the bottom of this scroll (still M4W from my angle). There's a table from
an article published in the 1970s. Here's a picture of it in my
Photostream:
https://flic.kr/p/2pKHvb1
https://github.com/4dsolutions/m4w/blob/main/Polyhedrons.ipynb
He's summarizing all the space-filling tetrahedra known so far, showing
them as plane nets (still need to be folded) attributing them to other
researchers such as Hall and Sommerville. What he plans, in this paper, is
to introduce three new "infinite families" of space-filling tetrahedra, the
punchline of his work. But before getting to that, he wants to take stock
of where we are so far.
Aristotle (you mention admiring him) gets flak for claiming "tetrahedrons
fill space" but his defenders shoot back: he never said regular. And true
enough, some irregular tetrahedrons fill space, and not in complement with
any other shape and no chirality or handedness needed.
Then Bucky comes along doing his own independent studies and the topic of
space-filling tetrahedrons grabs his attention. Picture him in your
position with the Model of Consciousness proposal, looking for a way to
break in, to gain acceptance from academia. "Surely I'll be saluted as one
of the greats, if I make a contribution to such a fundamental question:
what polyhedrons fill space, and even more fundamentally, which
tetrahedrons, given these have the fewest faces of all!?" Synergetics would
get noticed at last.
However the name of the game in academia is priority. If someone else got
there first, no matter how buried their findings... and sure enough, the
geodesic dome turns up at Jena (was it Bauhaus? no, Zeiss), and the
isotropic vector matrix (IVM) turns out to have been Alexander Graham
Bell's darling as well. Two more reasons to call Bucky a "popularizer" of
whatever others were into, even if he was into whatever too (too bad guy,
better luck next time).
A mathematician named Michael Goldberg pops up in both research areas: how
to divide spheres (cite Popko, Divided Spheres) and how to fill space with
irregular tetrahedrons.
The Goldberg polyhedrons (see Wikipedia) and classifications got into the
nomenclature just in time, making it safer for those early virologists
studying nucleocapsids to get the geodesics lore from a "real"
mathematician instead of a self-promoting upstart (protect the guild!).
Fuller had self promoted about 10 F F + 2 in the Herald Tribune, in
connection with Kasper-Klug.
The same problem arose posthumously, when Harold Kroto, a Fuller fan, named
C60 buckminsterfullerene. That was a blow to Bucky dissing darth vader
empire for sure. You could feel it in the force, when that happened.
Applewhite wrote his appreciative article for Chemical Intelligencer (at my
website and elsewhere).
Anyway, to make a long story short, Fuller had discovered that he could
build tetrahedral space fillers from As and Bs (two of the BEAST
particles), and named them RITE, MITE and BITE. However, once again it was
too late to claim priority as Goldberg and Co. were already on it. More
power to 'em.
Yet the easy vocabulary might've been useful, not to mention the easy
fractional volumes, if we scale 'em in with the rest of the hierarchy. MITE
= 1/8. RITE = BITE = 1/4 and so on. We find lots of segues between 1900s
math and Synergetics (published 1970s), which is what Bucky was seeking all
along.
He links his Figure 950.12, about these very space filling modules, to
Coxeter's published works. He's looking for acknowledgement, for an entre.
Yet here we are, in 2024 and hardly anyone even knows Fuller cared about
space-filling tetrahedrons. From my angle, this seems a ridiculous level of
ignorance, even for an average American. Yet we claim to have "public"
schools. Go figure.
Kirby, I want to thank you in general for all of your letters these last
two years it will soon be. In your recent letters, you are very caring,
creative and simply making positive efforts. You are a glue in our
community. Sometimes I don't know how to interact with you because I find
you sticky and my fingers glue together and I can lose a bit of skin. But I
shouldn't always be so wondrously insistent, and sniffing the glue, so to
speak. Please know that I am grateful for you, and I am glad to see Daniel
and others informed by your loving example.
Hey thank you.
Kirby
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