[andrepd]

Correct me if I'm wrong, but it seems that it's a mathematical structure so open-ended that you can write most relevant mathematics in terms of it (as you can with e.g. set theory). And of course, if you can write math you can write physics.

[Viliam1234]

Yes. The problem is that you can write any physics in it, so you cannot use it to figure out anything about our universe.

This is a crucial part that many intelligent people somehow utterly fail to understand. If you can explain everything (including the things that are not true), you can explain nothing.

A theory that explains, is a theory that says "...therefore, X can happen, but Y can't happen". Like a mathematician who says that 2+2 is 4, but also says that 2+2 is not 5. Or a physicist who says "apples fall down from the tree, they don't fall up".

Compare that to a "genius" mathematician or physicist who simply says "yes" to everything. Is 2+2=4? Yes. Is 2+2=5? Yes. Do apples fall down? Yes. Do apples fall up? Yes. And then people on internet are deeply impressed that he can answer everything. Such an amazing skill! Ask him about gravitons, he has a clear answer. Ask him about dark matter, he has a clear answer. Ask him about time travel, he also has a clear answer. The only problem is that he can both write a physics that contains gravitons, and a physics that does not contain gravitons. Etc.

Ultimately, we want to know what is real about our universe. (Or multiverse, or whatever.) A model that says "yes" to both the things that are true and the things that are false, is useless. After you figure out what is true, you get "yeah, my model explains that". Problem is, the model explains the opposite just as well.

...then you take a step back, and remember that "can write anything" is simply a different way to say "Turing-complete". Yes, if you invent something that is Turing-complete, you can simulate a universe in it. Any universe. Both the ones that exist, and the ones that don't.

(And the idea of Turing-completeness was discovered a few decades before Wolfram was born. So we can't even credit him with inventing the concept. He just uses the concept to impress people who either never heard about it, or never connected the dots.)

[FjordWarden]

The mathematical structure is called a hyper graph, a graph where nodes and edges come from the same set. Sounds weird at first but think about it like little sentences of the form subject predicate object. The word google can be all three places, as in: Google is a company, I googled his name or I work at Google. Here Google and its conjugations is an socio-economic object, but the set can also be the different grades within a geometric algebra where the different kind of reflections can be both operator and operand.