Our Mathematical Universe: My Quest for the Ultimate Nature of Reality

by Max Tegmark

Whereas the particles that constitute the Moon are stuck together in a rather static arrangement, many of your particles are in constant motion relative to one another.

an atomhög, Swedish for “atom heap,” in an attempt to insult him. However, if someone says, “I can’t believe I’m just a heap of atoms!” I object to the use of the word just:

This pattern is part of the mathematical structure that is our Universe, and the relations between different parts of the pattern are encoded in mathematical equations.

I think that consciousness is the way information feels when being processed in certain complex ways.

Why do we perceive the world as stable and ourselves as local and unique? Here’s my guess: because it’s useful.

Nobody knows for sure where the root of the problem lies, but I have my suspicions. Here’s my prime suspect: ∞.

In fact, I have two suspects: “infinitely big” and “infinitely small.” By infinitely big, I mean the idea that space can have infinite volume, that time can continue forever, and that there can be infinitely many physical objects. By infinitely small, I mean the continuum: the idea that even a liter of space contains an infinite number of points, that space can be stretched out indefinitely without anything bad happening, and that there are quantities in nature that can vary continuously. The two are closely related: we saw in Chapter 5 that inflation created an infinite volume by stretching continuous space indefinitely.

Are infinities undecidability, potential insistency, and the measure problem really inherent in the ultimate physical reality, or are they merely mirages, artifacts of our playing with fire and using powerful mathematical tools that are more convenient to work with than those that actually describe our Universe?

The mathematical structure that is our external physical reality is defined by computable functions.

According to the finitist school of mathematicians, which included Leopold Kronecker, Hermann Weyl and Reuben Goodstein, a mathematical object doesn’t exist unless it can be constructed from