Reworked the 24-cell sketch, much easier to understand now.

Every one of the 12 visible #spinors has a button that brings the yellow spinor (the 1 state) to the clicked one because in 3D spinors double as rotations. (both are #quaternions so there exists a quotient between spinors, which is a rotation).

I think what's clear is that thinking in terms of a spinorial/rotational lattice makes things much easier to grasp than in terms of a vectorial/translational lattice

https://editor.p5js.org/aap/sketches/-N-Bnk_jn

This article by Simon Altman on #quaternions and rotations may be the most lucid i've seen on the topic: https://worrydream.com/refs/Altmann_1989_-_Hamilton,_Rodrigues,_and_the_Quaternion_Scandal.pdf

My beloved #spinors are also mentioned. It is rarely explicitly stressed that the quaternionic imaginaries are 180° rotations, not 90° rotations. The same *can* be said of the complex numbers too of course, but commutativity makes things special there.

> ...the university's primary task, the fundamental work upon which all the other services depend. That primary task, that fundamental work, is Scholarship. In the laboratory this is called pure science; in the study and the classroom, it is research and teaching. For teaching no less than research demands original thought, and addressing students is equally a form of publication. Whatever the form or the medium, the university's power to serve the public presupposes the continuity of scholarship; and this in turn implies its encouragement. By its policy, a university may favor or hinder the birth of new truth. This is the whole meaning of the age-old struggle for academic freedom, not to mention the age-old myth of academic retreat from the noisy world.

(Jacques Barzun, General Editor's Preface to "The Algebraic Theory of Spinors" by C. Chevalley, 1954)

#academia #publishing #university #spinors

@aap
"Never believe that the Creator didn’t have a sense of humor when she invented something as damnable as spinors to describe all the ordinary matter in the universe, including you."
--William O. Straub from "A Child’s Guide to Spinors"
http://www.weylmann.com/spinor.pdf

Ignoring the energy we radiate. ("That's me TOO", I cry!)

#Physics #Spinors #Maths

"Transdimensional Pendulum"

Another math-meditation...

A new custom operator in Tooll3 I'm currently working on allows to create very beautiful iterative animations.

This one is inspired by a video on #Spinors I watched recently... 😎

#Tooll3 #realtime #newmediaart #abstractart #generativeart #particles #livingpainting #creativecoding #hlsl #gpu #shader #generative #procedural #visualart #Zen #wuwei #dao #math #opensource #mastoart