I take a lot of inspiration from this brave philosopher. Some detractors imagined he talked so much about integrity, staging Integrity Days and so on, because he was suffering from self doubt.
I’d say it’s a bigger Self that’s in its final exam period and Fuller hoped this Self (the Self of humanity) would have the integrity to keep reprogramming and improving itself, including by taking advantage of whatever insights we were gaining through Fuller, which were mathematical in nature, not simply architectural.
Along those lines, Koski and I have been looking at the S3 + S6 = Regtet volume formula, which is our shorthand for the Synergetics S module amplified by the golden mean. S3 = S volume times phi to the third power (with each edge extended linearly by phi). S6 = S volume times phi to the sixth power, the same as S3 bumped up by phi once again.
What if we wanted to model these as apex + frustum, two pieces of a tetrahedron?
If S3 is the apex volume, the slice is around 0.57588, meaning all edges of the apex tet have that length, the 3rd root of S3. If S6 is the apex volume, the slice is at around 0.931792. The Regtet itself has unit edges, so once we know where to slice, we know the frustum’s edge lengths as well.
Remember, we always work in tetravolumes. If your math curriculum had a modicum of integrity, you’re already quite familiar with that practice.
These floating point approximations have symbolic expressions behind them. I use sympy to keep them in memory until such time as I want a decimal number output.
Fuller received a Medal of Freedom for Synergetics and many small-S selves have taken it in. I’m fortunate to have a network of folks willing to take on faculty-level duties when it comes to sharing our subculture / ethnicity. Even Fuller himself did not have this Koski Identity to play with. We have continued to pick low hanging fruit.
