Geometry of Thinking

Correctly Categorizing Chatterboxen

Kirby Urner
7 min readJan 1


Those of you who’ve seen my slide deck, perhaps with an eye to performing it yourself, per my suggestion-invitation, may recall that slide wherein I go:

4D: Coxeter (polytopes, extended Euclideanism, perpendiculars)
4D: Einstein (3D space + imaginary time)
4D: RBF (a container as a concept primitively “4-eyed”)

I’m paraphrasing, working from memory. I’ll screenshot the slide in question below. [1] RBF = R. Buckminster Fuller, grand nephew of Margaret Fuller, the New England transcendentalist (Emerson, Whitman…).

Margaret Fuller

Many a phony intellect, e.g. an AI chatter box, might not care that the “tesseract as time machine” meme comes from science fiction. Shades of Flatland (also science fiction).

Chatbots interweave namespaces, indulge in name collisions, as a means of achieving verisimilitude. How could a bot competently simulate bureaucratic talk, without an ability to deliberately obfuscate?

The tesseract belongs squarely with the Euclideans and is most often considered timeless, whereas the “time machine” meme is perennially a part of Atomic Age physics (which the hippies then saved), which includes “time-dilation” as a phenomenon.

Coxeter is at pains to point out, in Regular Polytopes (page 119, Dover edition) that whereas H.G. Wells may be an excellent science fiction writer, as a student of Euclidean polytopes, you’ll need to check your time machine hat at the door, dropping the non-Euclidean geometry of Minkowski.

I see the chatterboxen, AI pseudo-intellects, as a technology, as belonging to Coxeter.4D, i.e. extended Euclideanism, which is simply n-D linear algebra with as many mutually independent axes as you like. The deep learning paradigm goes here, with its several layers of weighted neuron-like “perceptrons”. Gradient descent.

Breakthroughs in computer power (e.g. GPUs) breathed new life into these algorithms, realizing their stellar ability to shake out these minimal predictive surfaces, these topological manifolds within some feature space, providing a basis for…



Kirby Urner