[krastanov]

Certainly, this is a good point. However would you use that expression if what I said was "you can not make a perpetual motion machine"? Or if I had said "NP probably does not equal P"?

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.

For instance, the existence of scalable analog computers implies that we can solve NP-complete problems easily. This is a claim as crazy as "perpetual motion machines". It would be great if either of those claims actually become feasible, but there is a gigantic wall of "first principles" that have to be addressed - mere optimism is not enough.

This is what I want to stress - do not trust people when they rely on technicalities to shoot down your argument, 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.

[adamnemecek]

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.

[kamilner]

>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".

[adamnemecek]

I think that you misunderstood what I meant by assumed. If I replaced it with implies would that clear the confusion?