Compressibility, laws of nature, initial conditions and complexity

TL;DR

This paper critically examines the idea that laws of nature function solely as data compression tools, arguing that they encompass more than just data reduction and that large data sets are not always helpful for understanding complex phenomena.

Contribution

The paper challenges the view that scientific laws are equivalent to data compression, emphasizing the importance of initial conditions and the limitations of large data in understanding complexity.

Findings

Laws of nature are more than data compression tools.

Initial conditions of phenomena are generally incompressible.

Large data sets do not necessarily aid understanding of complex systems.

Abstract

We critically analyse the point of view for which laws of nature are just a mean to compress data. Discussing some basic notions of dynamical systems and information theory, we show that the idea that the analysis of large amount of data by means of an algorithm of compression is equivalent to the knowledge one can have from scientific laws, is rather naive. In particular we discuss the subtle conceptual topic of the initial conditions of phenomena which are generally incompressible. Starting from this point, we argue that laws of nature represent more than a pure compression of data, and that the availability of large amount of data, in general, is not particularly useful to understand the behaviour of complex phenomena.