# Physics, Topology, Logic and Computation: A Rosetta Stone

### Venue

Lecture Notes in Physics, vol. 813 (2011), pp. 95-172

### Publication Year

2011

### Authors

John Baez, Michael Stay

### BibTeX

## Abstract

In physics, Feynman diagrams are used to reason about quantum processes. In the
1980s, it became clear that underlying these diagrams is a powerful analogy between
quantum physics and topology: namely, a linear operator behaves very much like a
"cobordism". Similar diagrams can be used to reason about logic, where they
represent proofs, and computation, where they represent programs. With the rise of
interest in quantum cryptography and quantum computation, it became clear that
there is extensive network of analogies between physics, topology, logic and
computation. In this expository paper, we make some of these analogies precise
using the concept of "closed symmetric monoidal category". We assume no prior
knowledge of category theory, proof theory or computer science.