"Solving" NP using in alternate metaphysics
NP is only intractable only in linear time.
If you accept, as I do, the possibility that reality is not only this physical 3d + linear time world, then NP problems are quite tractable.
The rules of our metaphysics are relatively simple:
1. Wherever you intend to be, you will be there.
2. The past does not really "exist" in the objective meaning, and is reconstructed.
To solve an (instance of an) NP problem, you just find yourself ending up in a space-time location where you have the solution in your hands. And then, you reconstruct the past by remembering that this piece of information (the solution) is somehow a solution for a NP problem.
Within the 3d+linear time world, it would look like the problem comes first, then the solution. But our metaphysics don't work that way. The present comes first, then the past is "retroactively" filled in.
Of course, it does seem like we are still living in the 3d+linear time world, so the idea that the past is a mere reconstruction *feels* wrong. But there are strong arguments (which I will not go into) for this. This does not really require much faith, but it does require thinking deeply about what we really know about the world and dropping any unsubstantiated assumptions.
The only difficult part is assumption #1, and for various reasons it is a difficult proposition. Those who have first hand knowledge of mind magic, eg. manifestation, would understand that when the conditions are right, the universe bends to our will in ways that are wholly unimaginable to the physical materialist. And thus, those having manifested things with pure intention perhaps find the proposition that the universe lets us end up wherever we intend easier to accept.
The only thing I would say to the materialist is this: if you are not where "you" intended to be, why are you here at all? Note that the question of "you" can be misleading. It is not the "you" as in only the matter confined within your skin, but more like "you" as in the point of which your awareness emanates. (That said, asking that question to the physical body is still valuable.)
Think of a simulation, an immersive MMORPG, why would you be playing the character if you didn't intend to do it? There is of course nothing within the simulation or within the game that has evidence that you were anything but the objects within the simulation, and perhaps within the game your characters were not very pleased with their situation... but the player outside the simulation is probably having a good time (if your character gets hurt in the game, are you having fun?)
And thus there is good reason, both in theory that supports the possibility, and in practice (of mind magic) that suggests the phenomena is real, for us to at least ponder the possibility that #1 is a fundamental law.
Once we accept #1 and #2, we must accept that we could end up in a world where we somehow hold the solution to some instance of a NP problem in our hands (the past does not exist, so *how* we get there is irrelevant, the mechanism is simply intention per #1). Perhaps the solution is written on a sheet of paper, or in a file in the computer's trash folder. You can rationalize and reconstruct the timeline of the events that led up to this moment afterwards. The nature of NP problems admit a "random" solution process where you can say you found the solution by pure luck. Or maybe, really, this instance just happened to be super easy in retrospect (it's always easy in retrospect, that's by definition). It's really a loophole. Truly hard problems that cannot be verified are fundamentally different in that you can't even prove whether you have a solution or not.
So why don't people wake up with other people's bitcoin wallet keys on their desktop? Well, the answer is that *in general*, "you" don't really want it. The world we live in is not really one where these kinds of things happen, and you're in this world, so by rule #1 that implies you don't really want this to happen.
There are exceptions, which we call "magic", which kind of feel like glitches to the stable 3d-linear-time world that we live in. Psychics are sometimes able to glean information that they supposed have no access to. It's probably possible in theory to "steal" a bitcoin wallet's keys, but according to rumors there are safeguards to maintain apparent stability in the world, and to keep the glitches outside of the attention of the general public.
So does that mean there's a way to solve some instance of NP problem using the theory above? Not really, not within the 3d-linear-time world. It's only when "you", the transcendent "you" outside of this physical world, intend to do it, then the magic will work. The physical body will have no recollection of the non-linear "timeline" (if it can be so described), and all that the physical bodies remember are the reconstructed past. All that is observed within the simulation is that we live in a world where the configuration is so amazingly improbable, and we have no explanation why (I started writing this exposition because I saw some youtube video discussing why evolution is extremely improbable and thus there must be intelligent design involved...).
That perhaps leave one question remaining: how do we know there's anything outside the simulation? The simulation can be as perfect as it can be, but the "glitch" (I'd rather call it the "link") is the "self". The simulation is posited to be created by the transcendent self (i.e. "me"), and the transcendent self's purpose is to experience the simulation. So the transcendent self and the simulated self shares similarities that cannot be explained purely in terms of objects within the simulation. Some may call this phenomenon "resonance", but in recent computing terms it can also be called "emulation". This is how the information "outside" can "leak into" the simulation, and is how the transcendental self experiences the simulation. There is no other guaranteed way for those within the simulation to know what is beyond it. (That said, the simulated self is also greater than the stuff enclosed within the skin, so do not take this to mean that you cannot find relevant information outside your physical body -- anything that the simulated you perceive is also part of the simulated self)
