Re: P != NP, I would say that question assumes a certain architecture, so while it might hold for Turing machines, the real question is is a HyperTuring/Turing machine really all there is? I assume you are familiar with Real Computation? https://en.wikipedia.org/wiki/Real_computation I did note the "if real computation were physically realizable" clause, however, I'm not going to be placing bets.
> A scalable analog computer goes against some "first principles", not mere technicalities. If you want to claim that it is feasible to build it, you need a way to address those first principles.
I find your argument to rely on classical logical reasoning as opposed to constructive (intuitionistic) logical reasoning. There is quite a lot of excluded middle in all of these questions that you aren't accounting for. "First principles" are nice and all but, my fundamental problem right now is that I'm having a hard time verifying the "first principles" for myself.
> but if they are pointing out fundamental laws of nature as impediments, maybe it would be interesting for everybody if we try to learn and discuss those fundamental laws.
You are assuming that I'm not aware of those principles. I'm not saying I have solutions, I just don't feel like anyone's given it a proper shake quite yet.
>Re: P != NP, I would say that question assumes a certain architecture, so while it might hold for Turing machines, the real question is is a HyperTuring/Turing machine really all there is?
No, P and NP are defined by an architecture, there's nothing to assume about it. E.g., P is defined as "problems solvable in polynomial time on a deterministic Turing machine".
> A scalable analog computer goes against some "first principles", not mere technicalities. If you want to claim that it is feasible to build it, you need a way to address those first principles.
I find your argument to rely on classical logical reasoning as opposed to constructive (intuitionistic) logical reasoning. There is quite a lot of excluded middle in all of these questions that you aren't accounting for. "First principles" are nice and all but, my fundamental problem right now is that I'm having a hard time verifying the "first principles" for myself.
> but if they are pointing out fundamental laws of nature as impediments, maybe it would be interesting for everybody if we try to learn and discuss those fundamental laws.
You are assuming that I'm not aware of those principles. I'm not saying I have solutions, I just don't feel like anyone's given it a proper shake quite yet.