# Pregeometric Spaces from Wolfram Model Rewriting Systems as Homotopy Types

@article{Arsiwalla2021PregeometricSF, title={Pregeometric Spaces from Wolfram Model Rewriting Systems as Homotopy Types}, author={Xerxes D. Arsiwalla and Jonathan Gorard}, journal={ArXiv}, year={2021}, volume={abs/2111.03460} }

How do spaces in physics emerge from pregeometric discrete building blocks governed by computational rules? To address this question we investigate non-deterministic rewriting systems (so-called multiway systems) of the Wolfram model. We formalize these rewriting systems as homotopy types. Using this new formulation of the model, we outline how spatial structures can be functorially inherited starting from pregeometric type-theoretic constructions. We show how higher homotopy types are…

## 5 Citations

### Homotopies in Multiway (Non-Deterministic) Rewriting Systems as n-Fold Categories

- MathematicsComplex Syst.
- 2022

It is shown that a multiway rewriting system with homotopies up to order n may naturally be formalized as an n-fold category, such that (upon inclusion of appropriate inverse morphisms via invertible rewriting relations) the infinite limit of this structure yields an∞-groupoid.

### On the Operator Origins of Classical and Quantum Wave Functions

- Physics, Mathematics
- 2022

We investigate operator algebraic origins of the classical Koopman-von Neumann wave function ψ KvN as well as the quantum mechanical one ψ QM . We introduce a formalism of Operator Mechanics (OM)…

### On the Emergence of Spacetime and Matter from Model Sets

- Mathematics
- 2021

Starting from first principles and the mathematics of model sets we propose a framework where emergence of spacetime and matter can be addressed.

### Toward a Formalization of OpenCog Hyperon’s MeTTa Language in Terms of Algebraic Metagraph Rewriting

- 2021

### An Invitation to Higher Arity Science

- Mathematics
- 2022

Analytical thinking is dominated by binary ideas. From pair-wise interactions, to algebraic operations, to compositions of processes, to network models, binary structures are deeply ingrained in the…

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