Math Object: Fractal What exists, is uncaused, eternal, doesn’t cause anything and never changes? Logic, math and the patterns of information. For example numbers like π or e. Or patterns like the Fibonacci sequence: f(n) = f(n - 1) + f(n - 2) = 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, …

While we express them in human symbols, in the human choice of base-10, or while for π we chose circumference divided by diameter instead of radius. Those choices don’t define these numbers, instead something real and objective is reflected in these numbers. On far away worlds, aliens would have discovered the same underlying numbers.

A Universe

There is a strange hypothesis that goes back all the way to plato and is closely related to the ideas of Tegmark’s. It might sound strange, but it’s quite plausible and reasonable. Namely that the universe might be a mathematical pattern. That there is a plane of existence where all possible mathematical objects exist, like frozen crystals, uncaused, never changing, never causing anything, just existing.

Some of those objects have internal causality. Meaning that one state is computed from previous states, like how 21 is computed from 8 and 13 in the Fibonacci sequence. And for patterns like Rule 110 this internal causality is Turing complete, which means in principle it’s able to represent any computer program.

This hypothesis posits that outside of the universe there is no causality, only eternal and frozen existence. That causality is an internal property of some of these patterns. In stark contrast with the deistic first cause argument which posits a god has set everything else in motion, while lacking any satisfying explanation for what sets this god in motion.

Experiencing Time

How can there be time, or the experience of time, if these objects are completely frozen? Because on the inside these patterns can represent computation. And in the patterns with that property we might be able to find many interesting semi-stable sub-patterns of closely interacting states. If we trace one, highlighting its path through this frozen crystal, we might see it is learning, picking up changes, and interacting with other traces.

If it were possible to take this outside perspective, we could look at the beginning, middle or end of such a trace. It is completely frozen after all. But from the inside, step by step, this small sub-pattern is learning, maybe even imagining futures and making choices. A mechanistic and fully fixed universe, but it doesn’t feel that way to these learning entities who cannot experience the outside, only the inside, one step at the time.

Computation in Rule 110