Synergetics in the Humanities

Excerpt from recent correspondence (email to Maurice, Apr 20, 2021, 3:02 AM ), regarding Kenneth Snelson's relationship with Bucky Fuller:

He was always trying to figure out where the narrative was going to go around Bucky.  Was the guy a genius or a crackpot and to what extent would tensegrity be tarnished or polished by the association?  Had he been victimized somehow, was the core question, e.g. by a mad man with a messiah complex?  A lot hinged on what a next generation did with the whole corpus.  He was still trying to see the future.  That's why he reached out to me, an early web guy focusing on Bucky stuff, both to warn me about what he called the Church of Bucky, and to get a sense of where said "church" might be going in future, as that would inevitably be impacting the Snelson story and reputation as well.

I don't think his question was ever fully answered, and that had been the problem all along:  an inability to reach consensus on the nature and/or level of Bucky's game.  He somewhat resented the sense that, as a Black Mountain College student, he'd been left to figure that all out for himself.  Bucky was looking at Snelson as a possible protege, and given how mission-critical the former thought his own work might be, that put Kenneth under a lot of pressure.  He just wanted to enjoy being a college kid and having a girlfriend.  That he was put in the position of needing to assess Bucky was in some ways infuriating.  Others should be helping more.  

To make a long story short, he eventually fell in with a crowd who assured him Bucky was pretty much a charlatan and he'd be doing us a service by fighting him directly and publicizing their tug-o-war over intellectual property (both were patenting).  Kenneth thought they had something like a truce, an understanding:  Bucky would stay out of the art world and leave "tensegrity as art" to Kenneth, as what could a design science guy need with pure art?  Then it appeared Bucky transgressed that line, and was moving into the art world himself, and that's when Kenneth put on his battle armor.  

But then people such as myself gave him pause. Maybe there was something to it all after all?  We discussed these matters at some length, why not?  He was a really charming guy, easy to get along with.  We both had daughters.  I took mine to New York City to visit that time, and show her some of my young adulthood haunts in Jersey City.  

We exchanged a lot of emails, Kenneth and I, none of which I've kept as if he'd wanted those kept, he'd have archived them on his end, as he was very organized.  Maybe he did, I don't know.  He was also handsome and athletic.  He didn't like old age and what it did to him.  He was having a brilliant life.  Who'd want to ever let go of such an amazing scenario?

The Algorithm

compute a tetrahedron's tetravolume given its six edge lengths

I'm pretty sure the first time I saw Gerald's algorithm it was already expressed in source code, Java no doubt. I've also implemented it in Clojure just for fun and suggest on my Youtube channel that students use whatever language currently interests them, i.e. use it as a Rosetta Stone entry.

The constant e.g. 288 or 144 (a 2nd root thereof) was already absent from Gerald's version, and returning in tetravolumes was already the goal. I don't claim that wrinkle came in with the Python.

Given Python's "duck typing" it's easy enough to use the same source code to use arbitrary precision inputs (way beyond floating points in precision) and to use such as the plane nets for A, B, T, E, S modules in Synergetics to get these volumes and to interconvert their expression with Koski's versions, involving Phi (Fuller avoided using both Phi and Pi in his invented language of Synergetics, whereas adding Phi back in simplifies a lot of the dimensions).

I've also been frequenting a certain Wayne Roberts Principles of Nature website wherein he proves how the area of what he calls a "eutrigon" (one or three angles set to 60 degrees) is A x B where A, B are the lengths including the 60 degree angle, and C is the opposite edge connecting A to B. Multiplication is a matter of specifying the two sides and "closing the lid" (adding C). Lengths 4, 3 would give area of 12 etc.

area in ETUs

Using the same volume formula and treating the unit tetrahedron as analogous to Wayne's "ETU" (equilateral triangular unit), I show the model is entirely analogous i.e. lengths A, B, C from a common corner (picture XYZ corner as analog) give A x B x C as the corresponding volume, once again with a "closing the lid" operation, this time on a tetrahedron vs. a triangle.

2 x 2 x 5 = 20

Given the fixed angle of the ABC corner (that of a regular tet), the remaining three lengths are already determined and easy to obtain, for the purpose of feeding into the 6-edge-eating formula above.

I personally don't need a whole worked out math textbook with proofs + index in order to encourage developing coding skills while imagining a reference "sculpture" namely the concentric hierarchy from Synergetics. Your typical arts and design academy, where fluency with computers is baked into the curriculum, would have reasons to include this segment.

concentric hierarchy