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Since intelligent life is known one of its aspirations seems to be understanding of the world. Currently physics provides a pretty good explanation of the universe. There are areas that are not figured out, e.g. quantum gravity, information loss in black holes, etc. The goal of the theoretical physics seems to be to prepare a complete theory that explains everything.

So, here are some questions:

  1. Obviously, the required condition to understand the universe is that it has some kind of "simplified" rules set. E.g. Conway's Game of Life contains the rules set. But can we be sure that our universe even has something like that?
  2. Even if we sure that there are some rules, can we be sure that the "rules set" is finite? May it be the case that the rules are in fact infinite? E.g. if there is always a sublevel: we explain molecules, but molecules consist of atoms. We explain atoms but atoms consist of quarcs. We explain quarcs, but there is something else they "consist" of. And that may in fact be infinite.
  3. Even if the "rules set" exists and it is indeed finite, is there a guarantee that it can be formulated/understood from inside the system? Or may there be some fundamental limitation that makes it impossible to describe a system from inside the system?

So, do we know or can we know if the universe can be explained/formulated/understood?

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    You have to precisely define your "rule set". In logic it's common to have only finite number of inference rules to derive anything else, some systems like Hilbert system only has one such rule (modus ponens) and possibly plus another universal rule. Of course you need axioms (schemas) and laws in most math and physics theories, so maybe your "rule set" mean axioms/laws? If so, the number of axioms also depend on many other factors such as the order of your underlying logic... Dec 17, 2021 at 7:02
  • It seems that we know a lot of thing... maybe it is not "feasible" to know all. Dec 17, 2021 at 8:35
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    Literal answers to these questions are negative and uninteresting: there is no guarantee that there is a complete mathematical description of the universe, nor that it is finitely expressible, nor that it is accessible to us, if so. Proponents of the "theory of everything" hope for positive answers to all three. But what sort of answer are you looking for on a Q&A site? This topic seems more appropriate for a a forum where users can share thoughts and express opinions on controversial open-ended prompts.
    – Conifold
    Dec 17, 2021 at 9:24
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    Dec 17, 2021 at 13:07
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Cellular automata are used in physics, no less a physicist than Gerald t'Hooft proposed they can be used to interpret quantum mechanics, with the potential to unify physics and fulfil Archibald Wheeler's ambition to generate an 'It from bit' picture of the laws of physics emerging from something simple.

Stephen Hawking gave a lecture Gödel and the end of physics in which he suggested the mission of unifying physics may always have been hubris, and that there will always be unanswered questions.

We have good indications that quarks are point-particles like electrons, that lack any internal structure. But, String Theory, Quantum Spin Lattice Networks, or other structure could be hiding below what we can detect. I'd say the implicit premise of what you are asking is, can the layers go on forever, and that is called fractal cosmology, which we discussed here What would a fractal universe tell us about Time?

The basic job of a physics theory is to simplify or make more efficient our model of the world. This is why symmetry is so important, it is the core mechanism to shed unnecessary information, and by Noether's theorem we know conservation laws directly relate to this. For it to reduce to 'ultimate simplicity' of rules, requires that it has been ultimately simple at some time, and complexity emerged from there. Conformal Cyclic Cosmology is a nice proposal for cycling between simple and complicated, where we could imagine a 'random walk' selecting a set of fundamental physical constants each cycle.

We have reason to expect a fundamentally unified quality to things in our universe, because of the Big Bang. It all started in as close to one place, at one time, as it's possible to be. If the laws of physics are emergent, and causality not fully deterministic, we may not be able to get all the laws, but we will be able to understand where the ones we know come from, and tell the story of the emergence of what we have. For instance our universe could be a random fracture plane in the E8 hyperstructure.

Another possibility is the universe itself will turn out to gave a mind-like structure to it, transcending Godel Incompleteness and the halting problem in the same strange-loop way our minds are able to form tangled hierarchies and feedback. And minds involve irreducible complexity, to fully understand them you have to be them.

So the answer to all three questions is no, we can't be sure. But physics has been on a 'unification journey', as discussed here Is the idea that "Everything is energy" even coherent? which we have reasons to think will include minds Is it the job of physics to explain consciousness? linking them at least narratively with whatever the simplest state of the universe has been.

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    – CriglCragl
    Dec 17, 2021 at 22:45

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