An Invitation to Universality in Physics, Computer Science, and Beyond
Abstract
A universal Turing machine is a powerful concept - a single device can compute any function that is computable. A universal spin model, similarly, is a class of physical systems whose low energy behavior simulates that of any spin system. Our categorical framework for universality (arXiv:2307.06851) captures these and other examples of universality as instances. In this article, we present an accessible account thereof with a focus on its basic ingredients and ways to use it. Specifically, we show how to identify necessary conditions for universality, compare types of universality within each instance, and establish that universality and negation give rise to unreachability (such as uncomputability).
Cite
@article{arxiv.2406.16607,
title = {An Invitation to Universality in Physics, Computer Science, and Beyond},
author = {Tomáš Gonda and Gemma De les Coves},
journal= {arXiv preprint arXiv:2406.16607},
year = {2024}
}
Comments
10 pages, 1 figure + string diagrams. This article summarizes the framework for universality from arXiv:2307.06851. It is submitted as a contribution to "Fundamental Structures in Computational and Pure Mathematics, Volume 2"