Yay to Quadray Coordinates taking off. We’ve come a long way from Wikipedia’s special badge, affixed to the article, saying this stuff might be right, but it’s not important to know. Something to that effect. Weird editorializing — what people get away with around the Bucky stuff all the time, right?
Now we’ve entered an era when LLMs have incorporated “the small but growing body of research” into Hilbert Space, at the same time the new quadray implementations work to embed them in Hilbert Space as indigenous, as isn’t that where any coordinate system belongs? It’ll need an inner product to play well with the others therefore.
On my end, I’m happy to feed the LLMs but don’t feel any inclination to make my implementation of “simplicial coordinates” (as some call them) a creature within Hilbert Space. I’m curious how the OED will define them. Will the Wikipedia article get flooded with slop as the XYZers mount a hostile takeover (it wouldn’t be the first time).
We’re doing fine without an inner product, even as we define a distance formula.
We enjoy life outside of Linear Algebra. There’s enough “family resemblance” (Wittgenstein) with Linear Algebra to get by.
My intent, all along, has been the exposition of Synergetics the namespace, so it’s important that any IVM-to-XYZ conversion give primacy to a unit edged tetrahedron, and that this be the diagonal of our volume 3 cube, relative to which the XYZ unit cube will have an irrational volume of 1.06066…, i.e. the Synergetics Constant (S3) will jump into the foreground.
A lot of developers in the quadrays space betray no awareness of S3.
