Author's 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 Gödel incompleteness.
- I hypothesize that only computable and decidable (in Gödel’s sense) structures exist, which alleviates the cosmological measure problem and may help explain why our physical laws appear so simple.
- I also comment on the intimate relation between mathematical structures, computations, simulations and physical systems.
Author's Introduction
- The idea that our universe is in some sense mathematical goes back at least to the Pythagoreans, and has been extensively discussed in the literature (see, e.g., [2–25]). Galileo Galilei stated that the Universe is a grand book written in the language of mathematics, and Wigner reflected on the “unreasonable effectiveness of mathematics in the natural sciences” [3].
- In this essay, I will push this idea to its extreme and argue that our universe is mathematics in a well-defined sense.
- After elaborating on this hypothesis and underlying assumptions in Section II, I discuss a variety of its implications in Sections III-VII. This paper can be thought of as the sequel to one I wrote in 1996 [12], clarifying and extending the ideas described therein.
Comment:
See Tegmark - The Mathematical Universe
Text Colour Conventions (see disclaimer)
- Blue: Text by me; © Theo Todman, 2025
- Mauve: Text by correspondent(s) or other author(s); © the author(s)