# The Mathematical Universe

## TL;DR

This paper discusses the hypothesis that our universe is a mathematical structure, exploring its implications for physics, consciousness, and the nature of reality, and suggests only computable structures exist, simplifying cosmological questions.

## Contribution

It proposes the Mathematical Universe Hypothesis based on a broad definition of mathematics, linking physical reality to abstract mathematical structures and their computability.

## Key findings

- Physical laws may be derived from underlying mathematical structures.
- Assuming only computable structures exist simplifies cosmological measure problems.
- The universe's simplicity could be explained by the decidability of its mathematical structure.

## Abstract

I explore physics implications of the External Reality Hypothesis (ERH) that there exists an external physical reality completely independent of us humans. I argue that with a sufficiently broad definition of mathematics, it implies the Mathematical Universe Hypothesis (MUH) that our physical world is an abstract mathematical structure. I discuss various implications of the ERH and MUH, ranging from standard physics topics like symmetries, irreducible representations, units, free parameters, randomness and initial conditions to broader issues like consciousness, parallel universes and Godel incompleteness. I hypothesize that only computable and decidable (in Godel's sense) structures exist, which alleviates the cosmological measure problem and help explain why our physical laws appear so simple. I also comment on the intimate relation between mathematical structures, computations, simulations and physical systems.