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Wolfram Summer School

June 24–July 14, 2018
Bentley University, Waltham, MA


Raymond Aschheim

Class of 2011


RAYMOND'S THREE is the sculpture recently exhibited in Madrid during LOOPS 11, the conference on quantum gravity. It was inspired by Ray's theory—an attempt to prove Stephen Wolfram's NKS physics fundamental statement that all is just a trivalent network—by building it in the strong framework of loop quantum gravity, where the little loops, three triangles, encode just a one-valued bit.

Binary trees are connected together in a beautiful structure, named hyperdiamond and symbolized by the floating diamond-shaped marble stone, exhibiting Hurwitz non-commutative quaternion integers from which arise a flat empty Minkowsky spacetime. Moreover, non-associative Cayley integers structure all the matter in an e8 extended standard model, curving this space in ultra-local non-associative geometry.

Project: Hyperdiamond Spinfoam

Space as a network is more sound that space as not a network. Loop quantum gravity is an official but emergent branch of physics. Its framework deals with spaces as networks. Since last year, I have built a good understanding of this framework, and my project is to design a space as network and get computable physical observables in a theory unifying quantum physics and general relativity. How to build this network from space? Just triangulate the space and create a node for each triangle, linked to each adjacent. But we will do this in 4D. The fundamental 4D element is the simplex—the total graph of 5 nodes—and is bounded by 5 tetrahedrons, each shared with a neighbor. The graph of simplices glued together with a node for each simplex is then pentavalent. It is a spinfoam in LQG. We will first tesselate the 4D space as 24-cells, then divide each 24-cell in 96 or 192 simplices. This is hyperdiamond spinfoam. We can then apply standard LQG computation, but also study emerging symmetries in their relation with the standard model extended by gravitation to e8 instead of u(1)su(2)su(3).

Favorite Four-Color Totalistic Cellular Automaton

Rule 1468