On Fri, Jul 19, 2013 at 12:17 PM, Joe Niederberger <email@example.com > wrote:
> > On the dark side, his dismissal of large parts of accumulated knowledge > (such as cartesian coordinates), > while allowing him the freedom to seek new territories to explore, also > was a testament to a hugely over-inflated ego, which continues to attract > reality-divorced types. >
I don't think "dismissal" is the right word, more a concerted attempt to clear a space for something different to take root.
We send mixed messages when we encourage "constructing one's own reality" in the sense of being willing to question age-old assumptions, and then level a charge of "ego-mania" if anyone actually follows this advise too avidly.
> > (I also saw the 2008 Whitney exhibition. Hope you were able to.) >
I caught the similar exhibit in Chicago, 2009. Missed the San Francisco one. Caught 'Best of Friends' at Noguchi Museum, right near Fuller, Noguchi and Sadao's old skunk works in Queens.
I took my daughter to that one, her first time in NYC and environs. We met up with Kenneth Snelson for lunch and visited his studio. He was working on Sleeping Dragon at the time, soon to show up in the Louvre (outdoor area). I'd hung out with him before. I developed his first web site, out of respect and pleased as punch for the honor. I developed the first BFI website as well (bfi.org), back when the web was brand new.
> >Alexander Graham Bell was another pioneer, with those octet truss kites. > > Well, there's another very interesting guy, with some very nice work to > his credit. He doesn't get the "guru" treatment and hyperbolic fawning, > but, he wasn't around in the 60s. >
All talk of personalities aside, the so-called "octet truss" (for which Fuller held a patent, now expired) is worth some focus in K-12 for its relationship to sphere packing, architecture, crystallography.
Here in Portland we have a 'World Trade Center' (no relation) where the escalators rise through such a truss, to an over-street bridge connecting WTC1 and WTC2.
Students don't get to connect any of these dots if no one helps them do so. At Winterhaven PPS, I help connect them.
In mathematics books this "octet truss" is isomorphic to the CCP and/or FCC.
Why not integrate these topics earlier? They're not that hard. I'm not talking "TAG" or "gifted" really.
One may compare this skeleton / scaffolding / matrix to the XYZ one, sure, which is of course all cubes.
> > >See a branch yet? > We probably think of the term "branch" differently. > > I think Popko's book 'The Divided Spheres' adds a lot of glue between traditional spherical trig and more recent explorations. He calls it a primer.
Edward Popko is a retired dome engineer who worked on the front lines (in the trenches). He lived through the computerization period, when dome computations went form manual to electronic.
Then I cite 'King of Infinite Space' (the one about Coxeter, not Euclid) because it gets into more of the soap opera and rivalry. Coxeter, the quintessential professorial type (went to Cambridge, studied with Wittgenstein for awhile -- though found himself more cut out for geometry than philosophy), shares the academic distrust for "gurus" and "big egos" (aka "charlatans" and "snake oil salesmen").
Coxeter didn't like Fuller's hyperbole (what he considered it to be) either, but granted him respect anyway, on the basis on his concrete contributions. One of those contributions was the simple formula 10*F^2 + 2 from whence this 1, 12, 42, 92... series I keep repeating (a growth pattern in the CCP, but also Icosahedral numbers, so related to domes / spheres). When you look that up on OEIS, you'll see the Fuller references (appropriate).
Coxeter also didn't like the idea of people "patenting" solutions clearly found in nature, such as the geodesic sphere. His first encounter with Fuller's patents enraged him. He felt any "geometry in nature" should be open source.
His anger was somewhat personal as a friend of his (M.C. Escher's son), like himself a fellow Canadian, was trying to break into the geodesic dome business and getting push-back from the DoD, because of its loyalty to Fuller's US-based companies and patents.
But lets remember that Coxeter ended up, years later, giving permission for the dedication, of Fuller's 'Synergetics' to him. In that dedication, Fuller is giving up any thought of being 'the great geometer of our time' and bestowing that honor on someone who operated well within the mathematical mainstream.
My own approach to STEM is highly historical. We remember the "Z axis" i.e. Time, meaning lots of timelines, lots of getting an overview / map of how the artifacts and personalities of a day & age connect to its mathematics / metaphysics / philosophy. I look at Vienna quite a bit, as in Vienna Circle. More interesting books that young people might read, like 'Wittgenstein's Poker'.
For me, it's a no-brainer that more from the unit-tetrahedron school should be phased in, not because it's supposed to replace or dismiss anything, but because, in providing contrasts / differences that are accessible / clear, we have more opportunities to understand the morphing / branching development of language games we collectively lump under "math" (and / or "logic" and / or "coding" or whatever). It's also a way to carve out a niche, by advertising obvious differences with the Common Core, which stops short in so many ways.
As students, we become more sophisticated, more fluent, more open minded, to the degree that we allow these different branches to thrive and inter-twine. It's not either / or.
We have ample room and ample time to look from many angles.