Interesting bio of Heaviside, thanks. Fuller writes about Gibbs and Gibbs-Heaviside vectors is how I came to think of the vector algebra we learned in school. With the influence of Hermann Grassmann (universal algebra), and later people, we got Clifford algebra. I’ve tried to wrap my head around the latter, through Hestenes and so on, but that’s not stuff you’ll find in Bucky’s Synergetics. Quaternions either.

Bucky didn’t write about the new notations ala Hamilton’s quaternions as he wanted to pioneer a prose language, pregnant with scientific insights, accessible to humanities readers. One could daydream about science by exploring in a poetic space. C.P. Snow’s chasm would be bridged.

The absence of cryptic notations proves a turn-off for a lot of Synergetics readers even today who approach it as a STEM work only to find it pretty much bereft of notational innovations or much calculus fluency. No curl.

Instead we find long-winded explanations of the gyroscope, with pictures, aimed at bypassing vector cross products and such and making its mysterious responses seem intuitive.

Bucky talks about “nature’s coordinate system” but where is there any coordinate system in the notational sense? He suggests XYZ is “awkward” but where is the mathematical machinery for use with the IVM? Many of those interested in progressing with Synergetics considered it incomplete for this reason.

In time, a few people hit on candidate coordinate system language games, more akin to XYZ, one of which we called “quadrays”. Another was Clifford Nelson’s “synergetics coordinates”. Both are written up in Wikipedia.

Image for post
Image for post
sharing a world view on Youtube

I understand quadrays pretty well as one of their developers and use them (as implemented in Python) to generate CCP renderings (pictures of sphere packings). The mathematics is quite elementary, accessible to high schoolers. I introduce computer programming at the same time.

That’s been my approach in a lot of ways: to distill from Synergetics those aspects that one might grok with minimal mathematical training. I was a high school math teacher (geometry through calculus) right out of Princeton University (philosophy focus). Bucky was reaching an apex of visibility, and creating a sense of possibility, right around the same time. I tackled Synergetics as a high school math teacher with a philosophy background.

Image for post
Image for post
quadray coordinate system

The “concentric hierarchy” in particular is pretty traditional in that arranging polyhedrons in patterns is typical in Renaissance art (I grew up in Rome, exposed to Leonardo da Vinci). My Youtubes suggest we’re in some kind of art school, maybe dabbling in programming, but we’re just wanting the basics of spatial geometry, a way to develop fluency and hold a lot of it in our minds, without needing a lot of mathematical machinery.

Which doesn’t mean I’m “against” mathematical machinery or people using it. I’d just like an average human being to gain some more of this spatial savvy in the course of whatever studies, along with some programming skills.

volume ratios in the concentric hierarchy

At the forefront of my thinking is Bucky’s positive futurism and his message of potential success for humankind. His focus was always shelter in particular, with World Game (a meme) to follow.

A lot of people have given up and/or have only dire predictions about the future, and I believe such prophecies are self fulfilling unless diffused. So you could say I have an ulterior motive in wanting to get “the Bucky stuff” more widely shared in early schooling (say pre college for a lot of it). I want to rekindle the positive vision, which is lacking right now.

In later life, Fuller was touted by the US government as an avatar of the better safer world, with high living standards for all. Then after his death he became more of a hot potato, because he’d been so much a globalist, beyond even an internationalist, and these days the political currents are nationalist and anti-globalist. I discuss globalism in my Medium stories and Youtubes, representing myself as of this lineage. That doesn’t make me a George Soros (the stereotypical globalist everyone seems to love to hate).

One might not believe that a streamlined approach to polyhedrons could weigh in the balance in this political world, or tilt the zeitgeist at all. One might be right. The zeitgeist moves in mysterious ways. To me though, this seems to be where the trimtabs are, in curriculum development. It’s what I have the mental capacity to pursue, with a small community. I’m pretty humble about it and don’t consider myself a genius. I’m a reasonably bright guy, an intelligent layman. I do what I can.

Written by

Lots online.

Get the Medium app

A button that says 'Download on the App Store', and if clicked it will lead you to the iOS App store
A button that says 'Get it on, Google Play', and if clicked it will lead you to the Google Play store