>Starting from some entirely arbitrary simple formal system and working upwards and hoping you'll bump into reality along the way is very, shall we say, optimistic.

Honestly, I think this is a great way of describing what they're trying to do. I guess I think it's a little more realistic than you do: if our universe's physics could be described by a program on the order of tens of bits (I give an argument below for why we could expect that), then it's possible for us to come up with something like it from scratch by trying to construct a simple program that could have rich dynamics. If someone came up with a tiny model that happened to have physics emerge in it resembling our own, I'd be really interested to see how much we could learn from the model. They're trying to show that they happened to bump into interesting parts of relativity and quantum mechanics.

If they really did bump into relativity and QM from a simple system, then I think this is significant enough for more attention, even if they don't have any testable results yet, because it's possible that testable results will come from it. It might be that this model deeply resembles reality and we can flesh it out further, or it might just be that there is a class of models (that includes our physics) where relativity+QM arises (but not the rest of our physics, like the standard model), and we can learn about relativity and QM by studying models where the pair of them arise. Investigating this model is hard and it makes sense they want help.

> Sure, simple elegant formal systems are enticing to our brains but why assume that of our universe? Why not even try to explain why you feel this to be true? It's a pretty huge assumption in my eyes.

>Yes, and with good reason. Because TOEs claim to be fundamental – how can they be fundamental if there's something underneath them so to speak.

I've always imagined (and given the article's talk about "rule space", I think what Wolfram believes is something roughly similar) that the true-root TOE looks like the mathematical universe hypothesis / UDASSA (http://fennetic.net/irc/finney.org/~hal/udassa/) where in some sense, every possible computation exists, and they have measure (~the probability we find ourselves in it) inversely related to the length of information describing the computation (because if every possible computation existed, then every finite-length program would be instantiated infinite times by equivalent infinite-length programs with lots of ignored garbage code, and shorter programs would be instantiated proportionately more often).

From that, you would expect at large probability that our own universe's physics is described by the shortest possible program/rules that gives dynamics as rich as we see. If we imagined some universal computational language, it seems like specific cellular automata and hypergraph-rewrite systems could maybe be specified in tens of bits, so they're prime candidates for exploring. Even if those systems specifically aren't how reality works, then if they can produce dynamics about as rich as reality, then it implies that our reality's rules might be even shorter (or else we'd be more likely to exist in a cellular automata or hypergraph-rewriting system). At such short program lengths, the strategy of guess-and-check could be realistic, though the check part is really hard since we can't directly compute a significant number of timesteps, and instead have to try to reason about what large-scale patterns must emerge from the program.

(Wolfram specifically seems to believe that the hypergraph-rewriting system is universal enough to fill the role of the universal computational language, but I don't think that's strictly critical. As long as it's sufficiently simple to represent in whatever the root-TOE computes by, then it could be a candidate for our universe's physics. Hmm, I guess it would make sense that the way the root-TOE computes would have structure in common with whatever our universe's physics program is, because then our universe's program could be specified with fewer bits.)