Where it looks to me Fuller was headed was towards a “geared trig” based on what he called Scheherazade numbers. With gear teeth that fine, would we ever need something finer for physics engines (models)? Instead of trailing off indefinitely, we could stay with definite terminating numbers — as we must anyway in the real world.
When it comes to visualizations on a computer screen, the threshold is pretty low i.e. there’s no way to register a difference of higher frequency than the resolution of the monitor. Under the hood though, we can carry the overhead needed to go higher precision if we need to, which is where computer algebra systems come into play.In the world of frequencies (energy world), we come down to measurement. Even though physics formulae are redolent with pi, we learn in high school that the uncertainty in measurement trumps theoretical “infinite precision” i.e. no one in physics needs pi to a thousand places (unless working on a pi algorithm for some reason — I like Ramanujan’s). “Nature is not using pi” is akin to saying: in a discrete quantized universe, “infinite precision” is a mirage.
When I introduce Synergetics to people, one of my first moves is to talk about “namespaces”, a concept with concrete literal meaning in the Python language, but also kind of a shorthand for “subculture” (Wittgenstein: way of life). We can identify three namespaces that use the meme “4D” as in “four dimensional”.
(1) n-D, n-dimensional linear algebra, home of E8, Leech Lattices, Machine Learning and all the rest of it, very established and highly productive.
(2) 4D as 3D + Time, owing to Einstein / Minkowski. Donald Coxeter (to whom Synergetics is dedicated) is at pains, in Regular Polytopes, to distinguish Einstein’s 4D from his own n-D 4D, the 4D of extended Euclideanism (i.e. the 4D in (1)).
(3) 4D as referring to the the four directions of the tetrahedron, the most primitive polyhedron, the “ab initio” beginning for conceptuality in prefrequency (Platonic) space (Fuller’s shoptalk).
There’s a tendency to confuse (sometimes deliberately) all these different meanings of 4D, on the assumption that math is some “universal language” whereas in reality it’s an amalgam of partially overlapping namespaces, or language games as Wittgenstein calls ‘em.
Assuming an IVM ball of radius R, diameter D, I think what Synergetics does that’s both easy to understand and revolutionary is he trades in the R-edged cube of unit volume (XYZ, unit cube) in favor of a D face-diagonaled cube of volume 3. The inscribed tets have volume 1.
The payoff is the octa (same D edges) is now 4, and the rhombic dodeca (D long face diagonals) is 6.
We get more whole numbers if we let the old R-edged cube be the “odd man out” with volume 1.06066… sqrt(9/8).
That’s heresy, meaning to fight against it is to merely uphold an established dogma, not to mount a rational thought-out defense (which the orthodoxy is not prepared to do). Fuller’s system has merit, there’s no way around that fact. Even if XYZ still works, as it does.
The epithet Fuller applied to XYZ “Qyoobism” (making it sound like a cult) is not “it’s wrong” but “it’s awkward” (relatively).
