The first programs he wrote for the Atlas and the Mark II ("the Baby"), seem to have been focused on a theory he had around how animals got their markings.
They look a little to me (as a non-expert in these areas, and reading them in a museum over about 15 minutes, not doing a deep analysis), like a primitive form of cellular automata algorithm. From the scrawls on the print outs, it's possible that he was playing with the space of algorithms not just the algorithms themselves.
It might be worth going back and looking at that early work he did and seeing it through this lens.
https://en.wikipedia.org/wiki/Reaction%E2%80%93diffusion_sys...
The idea iiuc, is that pattern formation in animals depends on molecules diffusing through the growing system (the body) and reacting where the waves of molecules overlap.
More recently I've gotten into all sorts of debates on HN by people who like Searle. Often the argument goes "Turing is all wrong, he knows nothing about biology."
Turns out towards the end of his life he was applying his knowledge to biology. Most of which experimentally verified, besides!
(ps. just to be sure: Never wondered how DNA encodes the trick? You started out as a clump of cells, all the same. How did one part decide to become the tip of your nose, and the other the tips of your toes? Segmentation controlled by Turing patterns all the way down!)
The rest of his stuff tagged ruliology is more interesting though. Here's one connecting ML and cellular automata: https://writings.stephenwolfram.com/2024/08/whats-really-goi...
https://en.wikipedia.org/wiki/A_New_Kind_of_Science
But exactly what is the problem here? Other than perhaps a very mechanical view of the universe (which he shares with many other authors) where it is hard to explain things like consciousness and other complex behaviors.
This makes ruliology an invaluable cartography of the computational landscape, but not a foundation. It maps the territory without explaining what the territory is made of.
https://en.wikipedia.org/wiki/Chomsky_hierarchy
But maybe it is more like fractals and emerging complex systems?
Wolfram Mathematica (the Jupyter Notebook-like development environment) is paid, but there are free and open source alternatives like https://github.com/WLJSTeam/wolfram-js-frontend.
> WLJS Notebook ... [is] A lightweight, cross-platform alternative to Mathematica, built using open-source tools and the free Wolfram Engine.
Didn't find anything on falsifiable criteria -- any new theory should be able, at least in theory, to be tested for being not true.
As for falsifiability:
> You have some particular kind of rule. And it looks as if it’s only going to behave in some particular way. But no, eventually you find a case where it does something completely different, and unexpected.
So I guess to falsify a theory about some rule you just have to run the rule long enough to see something the theory doesn't predict.
You judge them by how useful they are.
Ruliology is a bit like that.
https://nedbatchelder.com/blog/200207/stephen_wolframs_unfor...