> Assuming we can do new stuff now that we couldn't before, this opens the table to new variation, new problems, and new plausible solutions.
Right, but that's circular reasoning. Closed systems exist, there are things that can be understood so fully that you can't think of any new questions to ask about them that you don't already understand. What if we really did solve everything?
> So even though we might say we've solved NP hard problems, that allows us to define new problems of which are going to be more difficult to solve (unless the universe just stops forever or approaches an information uniformity). All that new variation is the new NP hard.
NP is a specific, well-defined category of things. It isn't remotely the class of the hardest problems we can think of. If NP=P that doesn't mean we can solve every problem easily. But it does mean we can solve a lot of important problems easily.
> Closed systems exist, there are things that can be understood so fully that you can't think of any new questions to ask about them that you don't already understand.
The existence of closed systems does not imply all systems are closed. Also, you can think you understand things so well that you have to revisit things you think you know in order to find new questions.
> It isn't remotely the class of the hardest problems we can think of. If NP=P that doesn't mean we can solve every problem easily. But it does mean we can solve a lot of important problems easily.
That's fine to you, but there's obviously some communication and definition of terms problems going on, and I don't think that's entirely surprising considering how lost everyone tends to get in the language of it.
P=NP means you can get computers to write their own math proofs. Tell that to a mathematician who would rather compare his process and functionality to that of Picasso or Rembrandt painting, Mozart composing, than that of the self serve pay station at your local grocers. Maybe we can start birthing mechanical babies, I don't really know.
> The existence of closed systems does not imply all systems are closed
I never said they were. Just that we don't know one way or the other.
> P=NP means you can get computers to write their own math proofs.
Yes and no. It means the computer can fill in the technical details of a proposition you've already formalized. But mathematicians only ever sketched those parts in papers anyway.
> Maybe we can start birthing mechanical babies, I don't really know.
You're not making any sense. Try starting with more concrete things before waxing philosophical.
I've read from mathematicians who consider their computer to be a tool, and from others who see the computer as a partner. As a hobbyist who studies automated theorem provers (like coq), there is so much elegance that goes into the computational proofs in order to even construct such a program that allows a mathematician to do their work.
Can you honestly say that it doesn't take an extreme amount of effort to construct the perfect typing system that allows you to even begin to be able to write a proof with a machine? People have to prove that theorem provers are correct with respect to that which what they define. This is no trivial task, it's an entirely different domain of knowledge.
Right, but that's circular reasoning. Closed systems exist, there are things that can be understood so fully that you can't think of any new questions to ask about them that you don't already understand. What if we really did solve everything?
> So even though we might say we've solved NP hard problems, that allows us to define new problems of which are going to be more difficult to solve (unless the universe just stops forever or approaches an information uniformity). All that new variation is the new NP hard.
NP is a specific, well-defined category of things. It isn't remotely the class of the hardest problems we can think of. If NP=P that doesn't mean we can solve every problem easily. But it does mean we can solve a lot of important problems easily.