# Compression is Comprehension, and the Unreasonable Effectiveness of Digital Computation in the Natural World

## TL;DR

This paper explores the deep connection between compression and understanding in science, emphasizing the role of algorithmic randomness and computation in modeling the natural world, inspired by Chaitin's work.

## Contribution

It introduces novel bounds on algorithmic randomness for cellular automata and discusses how compression relates to scientific modeling and understanding.

## Key findings

- Established new upper bounds of algorithmic randomness for cellular automata
- Linked the concept of compression directly to scientific comprehension and modeling
- Highlighted the importance of algorithmic approaches in scientific prediction and explanation

## Abstract

Chaitin's work, in its depth and breadth, encompasses many areas of scientific and philosophical interest. It helped establish the accepted mathematical concept of randomness, which in turn is the basis of tools that I have developed to justify and quantify what I think is clear evidence of the algorithmic nature of the world. To illustrate the concept I will establish novel upper bounds of algorithmic randomness for elementary cellular automata. I will discuss how the practice of science consists in conceiving a model that starts from certain initial values, running a computable instantiation, and awaiting a result in order to determine where the system may be in a future state--in a shorter time than the time taken by the actual unfolding of the phenomenon in question. If a model does not comply with all or some of these requirements it is traditionally considered useless or even unscientific, so the more precise and faster the better. A model is thus better if it can explain more with less, which is at the core of Chaitin's "compression is comprehension". I will pursue these questions related to the random versus possibly algorithmic nature of the world in two directions, drawing heavily on the work of Chaitin. I will also discuss how the algorithmic approach is related to the success of science at producing models of the world, allowing computer simulations to better understand it and make more accurate predictions and interventions.