This article is surprisingly short on actual applications.

For some interesting applications one might look at the the Wikipedia article for the normalized compression distance: https://en.wikipedia.org/wiki/Normalized_compression_distanc...

This paper here shows some interesting applications - it is not the first one, but the first non-paywalled one that I found: https://arxiv.org/pdf/cs/0312044.pdf

There is also a book by Paul Vitanyi - it has been a while since I looked at it, but if I remember correctly it also discusses some of these applications: https://www.amazon.com/Introduction-Kolmogorov-Complexity-Ap...

Sipser's undergraduate textbook on the theory of computation[1] has a single, very nice, introductory chapter on the topic.

If you want to get technical and deep, you probably want [2] (An introduction to Kolmogorov complexity and its applications). It's pretty hard, though. Not for the faint of heart.

[1] http://www.amazon.com/Introduction-Theory-Computation-Michae...

[2] http://www.amazon.com/Introduction-Kolmogorov-Complexity-App...

do you have any resources that are more rigorous?

For light bedtime reading, there's An Introduction to Kolmogorov Complexity and Its Applications: http://www.amazon.com/Introduction-Kolmogorov-Complexity-App...

That is, the laws of thermodynamics concisely phrase the increasing entropy of the universe with a low Komolgorov complexity, suggesting that the mechanics of the universe operate with a low Komolgorov complexity.

I'd agree with that.