Computational Foundations for the Second Law of Thermodynamics

There is not really any new insight in the post, though cellular automata are indeed a good way to explain entropy, coarse-graining, etc.

The breakthrough (if it exists) must be in his computational irreducibility theorem, which he alludes to in many places. Unfortunately the link is to a book chapter which doesn't render properly on mobile and seems more of a long ramble than a formal proof, so I didn't dig into it.

An effective principle along the lines of, "if the output of a sufficiently simple program 'seems random,' then it is indistinguishable from random by all other programs," would be extraordinarily powerful and would immediately close many famous open problems, such as the normality of pi (and other numbers like sqrt(2)), infinitude of primes of the form x^2+1, the twin prime conjecture (and Dickson's conjecture), etc. It's somewhat telling that these are still open problems.

I agree. My conclusion is that he is delusional. There are quite a few crazies on the internet who claims to be just on the brink of a major breakthrough. But they never actually get there. However it is much harder to tell with wolfram because he has actually achieved things in life.

He is a scientist in the finest sense: he collects lots of data and publishes that data for others to look at and think about for themselves.

His blog is priceless. He does such great deep dives on historical thinkers (Leibniz comes to mind) and travels to where they lived and worked and publishes photos of their original works.

Such a treasure.

(And the products are neat too!)

This is the usual kind of useless pedantry on this site.

It's not a misunderstanding. The entropy of a discrete probability distribution is indeed a measure of how random samples from it are. The misunderstanding is by you.

See Gibbs and Shannon entropy before commenting on this again.

You should start with his explanation of ruliad for a full understanding. But the ELI5 idea is that humans have limited mental capacity while reality is trying everything possible. So a lot of physical laws result from that interaction. In this article he does an informal explanation of how a future, formal derivation of the second law of thermodynamics could be done and what problems need to be solved in order to do that (specifically better definition of observers).

I spent ten minutes reading this and lost interest. Everything he explains in the beginning of this article is obvious or common sense (common sense for anyone who has a physics degree, that is) and I am not sure where the "new" things he discovered begin. There is a reason that academic papers are required to have an abstract, an introduction section and a conclusion section. Unfortunately Mr Wolfram seems to think that his endless rambling can convey scientific discovery better.