' This short video shows the embedding of an (abstract) flat torus in 3D ambient space. Sixty years ago, John F. Nash and Nicolaas H. Kuiper demonstrated the existence of this mysterious surface without being able to visualize it. Those images were computed thanks to the convex integration theory of Misha Gromov. More information here: http://math.univ-lyon1.fr/~borrelli/Hevea.html '
Leading me to speculate that there may be some connection between the corrugations of nash embedding and the nowhere-differentiable 'zig-zaggy' components of the path integral.
raising the interesting point about the consistency of the nash embedding theorem (any Riemannian manifold can be mapped in a length preserving way to a Euclidian space) with the observation that spheres are not flat. https://math.stackexchange.com/questions/87503/isometric-embedding
terrytao's notes on the theorem: https://terrytao.wordpress.com/2016/05/11/notes-on-the-nash-embedding-theorem/
Somewhat related: https://projecteuclid.org/download/pdf_1/euclid.jdg/1214442639
THE RELATOINS OF PLÜCKLER COORDINATES TO SCHUBERT CALCULUS.
and important for my cohomology decomposition programme
"Twistors exist in any dimension. However, only in dimensionsn= 2,4,8 isthe twistor space a complex manifold. This is due to the fact that only in thisdimensions there is a “coincidence” and the real conformal group SO(1,n+ 1) islocally isomorphic to a complex group."
"In the present paper we entertain the idea of quantizing the space oftwistors. Twistors, and thus also spacetime points become operators actingin a certain Hilbert space. The algebra of functions on spacetime becomes anoperator algebra. We are therefore led to the realm of non-commutative ge-ometry. This non-commutative geometry turns out to be related to conformalfield theory and holography. Our construction sheds an interesting new lighton bulk/boundary dualities."
Could be argued that only parts of the sphere are populated: those appertaining to particular shifts of particular systems interacted via in some discrete sense but if GR is to be taken seriously then all processes are interacting with spacetime on a continous basis mediated by curvature and the stress-energy tensor. So i'd say we get total holographic distribution.
So yeah I think the observation (due to twistor theory) that holomorphic transformations of the Riemann sphere accord with Lorentz shift observer relative perspective directly introduces a kind of holography, as an event is distributed as all the possible transformations of itself across the surface of its light-cone.
That's pretty neat. Wonder if it's well-discussed in the literature...
I have no idea what my subconscious was up to last night, I got cascading images of time machines and spaceships and people betraying each other and blowing things up that didn't coalsece into anything coherent, but I remember ONE THING. A historian saying:
“ice cream is, throughout the universe, the cry of the culture on the brink of death. Only those civilizations a heartbeat away from collapse discover it. The more spectacular the collapse, the more delicious the ice cream that precedes it.”
Where the plan/project is described just as a program for a highly parallel computing system, but the execution units are the employees and contractors; and is translated into a detailed estimation of time and costs for each phase.
There is no horror, no cruelty, sacrilege, or perjury, no imposture, no infamous transaction, no cynical robbery, no bold plunder or shabby betrayal that has not been or is not daily being perpetrated by the representatives of the states, under no other pretext than those elastic words, so convenient and yet so terrible: "for reasons of state."
-- Mikhail Bakunin
New EP: Cyberpunk With Rainbows (boost please ❤️ ) https://digitalscofflaw.bandcamp.com/album/cyberpunk-with-rainbows
It’s not AI vs people
It’s not Big Data vs people
It’s not robots vs people
It’s corporations vs people.
CrimethInc.: **The Hotwire #18: February 14, 2018 : Toxic Waste in STL—Labor Struggles in the Techno Age—A Rant on Love**
just an inline audio plugin that cuts any applause and cheering would increase my quality of life noticeably.
When free TTS algorithms/systems become good enough that you can feed in podcasts etc and have them revoiced without excessive (ie, any) overt excitement or affect or enthusiasm that will be pretty amazing tbh.