I admit my objection was more specifically addressed to the question of conceiving alternative worlds that would be non-mathematical or entirely chaotic.
However, you are right that, without going that far, following the cosmological landscape hypothesis, we could seriously conceive of alternative universes where the physical laws are different. We could arguably model worlds governed by less simple and elegant physical principles.
That said, today’s standard model of physics is arguably less simple and elegant than Newtonian physics was. Simplicity, elegance, and symmetry are sometimes good guides and sometimes misleading lures. The ancient Greeks were attracted by these ideals and imagined a world with Earth at the center, perfect spheres orbiting in perfect circles, corresponding to musical harmony. Reality proved less elegant after all. We also once hoped to live in a supersymmetrical world, but unfortunately, we find ourselves in a world where symmetries are broken.
It seems that in the distribution of all possible physical worlds, we probably occupy a middle position regarding mathematical simplicity, elegance, and symmetry. This is what we might expect given the general principle that we should not postulate ourselves to occupy a privileged position. I acknowledge that a form of the anthropic principle could also explain such a position: extremely simple (crystal) or extremely complex (noise) universes might be incompatible with the existence of intelligent observers.
Regarding the intriguing fact that certain mathematical curiosities turn out to be necessary components of our physical theories, my insight is that mathematicians have, from the very beginning (Pythagoras, Euclid), been attracted to and interested in patterns exhibiting strong regularities (elegance, symmetry). The heuristic instincts of mathematicians naturally guide them toward fundamental formal truths that are more likely to be involved in the fundamental physical laws common to our world and many possible worlds (but only more likely).
Good demonstration, but I’m not convinced.
Black holes can theoretically be viewed as computers of maximum density. However, it’s highly speculative that we could exploit their computational power. From an external perspective, even if information could be retrieved from Hawking radiation, it would come at the cost of dramatic computational overhead. I also wonder how one would “program” the black hole’s state to perform the desired computation. If you inject any structured information, it would become destructured in the most random form possible (random in the sense that Kolmogorov formally defined a random sequence). General relativity also implies tremendous latencies.
To me, this is not very different from—and arguably worse than—sending a hydrogen atom to the Sun and trying to exploit the computational result from the resulting thermal radiation. Good luck with that.
Now, if you consider the problem from inside the black hole… virtually everything we could say about the interior of a black hole is almost certainly wrong. The very notion of “inside” that applies to conventional physics may itself be incorrect in this extreme case.
Edit : To offer another comparison, would a compressed Turing machine be superior to an uncompressed one ? In terms of informational density, certainly, but otherwise I doubt it.