Computation as a universal and fundamental concept

Thank you for your insightful answer, in reduction; "Don't fight a god, you won't win, and you'll definitely die in the process!"

The approach you describe though is brute force. I don't think (if there even is an answer to this problem) that it can be brute forced; that's where you run into the limits of hardware/computation/energy and start talking about timeframes which exceed the life of the universe.

I think brute force might be a useful tool in places to validate results, but if there _is_ an answer to this problem it's purely mathematical.

Apologies for sounding both excited and naive; these sorts of challenges make me happy in strange ways that no other thing does!

Ahhh this is fantastic thank you; it _is_ hard to reconcile whether problems come with the original topic or whether they are introduced by the abstraction that we _need_ to make in order to quantify a thing/explain it to ourselves and others.

Regarding the downcast/upcast; I think it _can_ be possible to do this successfully;

> I have a glass, I throw it at a hard surface. What will happen? Well (duh) the glass will (most likely) break.

This hypothesis completely ignores nearly 100% of all relevant physics and the laws surrounding the problem; the arrangement of air molecules, the arrangement of the molecules in the glass, the physical forces governing me, it reduces the entire equation down to some really basic napkin physics.

But; does the outcome work? Has my interpretation of the universe and its physics actually predicted what will happen?

Probably a stupid example, but I think that a lossy picture of the universe can still yield a correct answer.

I can't physically run a simulation of the entire universe in my brain, as my brain is part of that same universe. Lossy representations/models are a necessity in the thinking-ham bound world in which we exist.

There is no general solution other than brute force. That's not a terribly difficult extension of the halting problem, it just takes more paperwork to deal with the edge cases, but you'll get to that result. The same basic technique works: Your supposed solution to the problem is itself some finite program, and you can feed it the "I halt only if I don't halt" problem too. The difference is that brute force is a solution, because now instead of an infinite sequence of programs you have a bounded set of programs. So whatever concrete "I halt only if I don't halt" you pass to someone within the specified limits, there is definitely some answer, but your technique won't be able to tell what it is short of just running it.

For the same reason the halting problem doesn't even have a good heuristic, neither does this. Unpredictable chaos is not an exceptional case, it is the exponentially-normal case. You have to go the other way, and construct programs deliberately designed to have the ability to tell if they halt. The term for that if you want to learn more about it is "non-Turing complete programming language", sometimes called a "sub-Turing" programming language: https://increment.com/programming-languages/turing-incomplet...

You can read that as "this is how hard it is to construct code that we can make execution guarantees about". That focuses on code that is deliberately constructed to be finite in scope and may be something that can be strictly bounded in memory use or time or both. You'll note if you spend any time working with them how hard they are to work with. That's a reflection of the limits of generalizing any such proofs of time or space of a given program.

If there is a general algorithm that does what you think, we don't even have a clue what it would look like. And we have a lot of clues there can't be any such thing.

The somewhat abbreviated answer is that the "state" is formalized into the concept of fields. All the physical properties we can observe are from coupling with the relevant fields. The speed at which changes can propagate in fields is C, hence the speed of light being the same value.

There are a lot of long comments basically saying what I am about to say so I will try to keep this brief:

Computation is a metaphysically universal and fundamental concept, since metaphysics is (tautologically) the domain of humans and we use symbolic communication. So of course very general theories of symbolic processes (e.g. Turing machines) are pertinent to the symbolic methodology we use to understand scientific processes.

But it is a fundamental mistake to jump from that to saying computation extends to a law of the universe. Computation reflects laws of the universe, but only in the exact same way that scientific and mathematical human speech do. The mystery (still totally unsolved) is how humans are able to intuitively understand space / time / causality / etc in order to define coherent symbolic rules that reflect real processes. That computers can seemingly always implement these rules having been given the symbols is of philosophical/scientific interest, but it's solipsistic to say it's a fundamental concept of the universe.