peter_m1

We can still test the theory that computation describes physical reality with experiment (presumably it makes predictions). The scientific method still holds.

Here is a brief history of computability I wrote as a blog a few months ago, https://deeplp.com/blogs/f/the-birth-of-computability-theory. Hope it's helpful to the conversation.

Your intuition could also be dead wrong.

The computational view of the universe and the nature of reality has provided us with some new insights.

Theoretical computer science is where it's at.

Attention is all we need.

The theory of general relativity answers this exact question. It has been tested experimentally and has been found to be correct in the classical regime. By correct I mean that the experimental data agrees with theoretical prediction.

Yes, these are all our attempts at explaining the nature of reality. A kind of reaching into the unknown. A desire to understand the universe and our place in it.

The universe as a computer/computation has been explored by many (e.g., see John Wheeler and Seth Lloyd). However, the laws of physics give us a lot more predictions, so their explanatory power tend to be greater. For example, the nature of space and time.

In this case quantum thermo.

No, you can prove things hold in the abstract mathematically, don't need to resort to physical systems.

A related question might be, what's the difference between mathematical (Godel), computational (Turing,) and physical (Yang-Mills) undecideabilty/computability?

Quantum mechanics is intrinsically probabilistic.

In physics we don't talk about decidability, but solvability.

There is such thing as a quantum Turing machine you know (Deutsch 1985).

Also, correct me if I'm wrong, the mass gap problem involves quantum physics, not classical, so the underlying math/logic is different.

A quantum Turing machine would be needed to simulate a truly quantum process. Stochasticity exists in classical systems, but that's an entirely different type of randomness.

That would be a quantum Turing Machine as radioactivity is a quantum process.