The Descent of Math

TL;DR

This paper proposes a unified physics-based framework suggesting that the universe's comprehensibility and the existence of mathematical systems are interconnected, evolving through a causal network that favors information-rich states.

Contribution

It introduces a novel causal graph model of physical reality linking comprehenders and mathematical understanding as part of the universe's evolution.

Findings

States with information encoding are most probable in the causal graph.

Mathematics and language are highly connected states in the universe's causal structure.

The evolution of the universe favors states that include systems capable of understanding and manipulating mathematics.

Abstract

A perplexing problem in understanding physical reality is why the universe seems comprehensible, and correspondingly why there should exist physical systems capable of comprehending it. In this essay I explore the possibility that rather than being an odd coincidence arising due to our strange position as passive (and even more strangely, conscious) observers in the cosmos, these two problems might be related and could be explainable in terms of fundamental physics. The perspective presented suggests a potential unified framework where, when taken together, comprehenders and comprehensibility are part of causal structure of physical reality, which is considered as a causal graph (network) connecting states that are physically possible. I argue that in some local regions, the most probable states are those that include physical systems which contain information encodings - such as mathematics, language and art - because these are the most highly connected to other possible states in this causal graph. Such physical systems include life and - of particular interest for the discussion of the place of math in physical reality - comprehenders capable of making mathematical sense of the world. Within this framework, the descent of math is an undirected outcome of the evolution of the universe, which will tend toward states that are increasingly connected to other possible states of the universe, a process greatly facilitated if some physical systems know the rules of the game. I therefore conclude that our ability to use mathematics to describe, and more importantly manipulate, the natural world may not be an anomaly or trick, but instead could provide clues to the underlying causal structure of physical reality.