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Macroscopic quantum objects cannot exist if P ≠ NP?

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Re: Macroscopic quantum objects cannot exist if P ≠ NP?

#51

Post by elektronjunge »

scott_s wrote: post #42
IanCal wrote: post #39

Earlier quoted context omitted.

With 2, are you saying there are situations in nature that can solve NP-hard problems in polynomial time? Because if so, we could just use those to solve our hard problems and therefore P=NP. P=NP is not just statement about difficult problems or big equations, it's a very particular class of problems.

There are situations in nature where our models are NP-hard. Whether or not this is the same as saying that nature itself performs those computations is, I think, tied into the question of whether or not our Universe is a simulation.

If natures models reduce to our NP-hard models which they would if our models are accurate, that is to say if and only if there is some computation that is NP-hard (which means that it is proven to not have a polynomial time solution unless P=NP) that nature can solve in polynomial time and we have proven that P must equal NP.

Re: Macroscopic quantum objects cannot exist if P ≠ NP?

#52

Post by awhitty »

Dunnorandom wrote: post #15

For anyone interested, here's Scott Aaronson's response to the paper: http://www.scottaaronson.com/blog/?p=1767#comment-103591

I understand that people get a little passionate about their fields of study, but the tone of Aaronson's response is wildly inappropriate. Phrases like "a common novice mistake" and "as if he just emerged from a cave" are unnecessary and entirely condescending. This style of discourse fosters a really awful and exclusive atmosphere, and I wish it wasn't the norm.

I don't know this guy at all, and I'm guessing he's pretty respected in his field, but at the end of the day, he doesn't have to be a jerk to get his point across.

Re: Macroscopic quantum objects cannot exist if P ≠ NP?

#53

Post by drdeca »

SnacksOnAPlane wrote: post #27
tomp wrote: post #16

Wait what? What this article is arguing is totally absurd - just because we can't model certain physical objects, they cannot exist?! That's like saying that since we can't model three gravitational objects interacting (i.e. the numerical solutions diverge, therefore to properly model the system, we would require increasing amounts of memory and time), therefore they cannot exist. I'm not saying that the physical cla…

I'm a simulationist. I believe that the universe we're experiencing is a simulation made by a far-advanced civilization. So in my reality, if something can't be modeled, it can't exist. Not saying that this is the truth, just the way I choose to understand things.

Is a reality where computers can store and process e.g. Actual real numbers, inherently inconsistent?

I'm not sure, but from what I remember from Wikipedia, doesn't that allow for computations that can not be done with turing machines?

Iirc, there are models of computation which are self consistent, and can simulate Turing machines, but are such that it seems impossible to simulate in our universe (or on a Turing machine).

If I am correct in remembering this, and if these machines can simulate things with values from a set with cardinality greater than aleph null, wouldn't the argument that we are likely to be simulations also argue that we are likely to be simulations on a machine in a reality capable of simulating with a more powerful type of computation.

Ok I'm going to say that there are many potential hole in my argument.

But I think it might be possible that machines capable of hyper computation could simulate an infinite number of Turing machines in parallel.

And if it could do that, then it should be able to simulate an infinite number of universes like our own (not like it's own probably though).

And as such, shouldn't any argument that our universe is probably a simulation due to a universe like our own containing a large (but finite) number of simulations of universes like our own, Equally validly argue that our universe is almost certainly a simulation in a universe with greater computational ability than our own?

I acknowledge that this argument has many assumptions behind it, and that many of them could be wrong. I hope this argument doesn't come off as nonsense (preferably just Misinformed)

Also I suppose the large number of simulations might not be your line of reasoning for your beliefs.

Also, I think there's supposed to be a hiarchy(spelling?) of hyper computation, so maybe the surreal numbers would be a better basis for the argument than the reals?

I'm not sure if my line of reasoning makes sense, but I thought I would mention it anyway.

Re: Macroscopic quantum objects cannot exist if P ≠ NP?

#54

Post by drdeca »

mdxn wrote: post #48
SnacksOnAPlane wrote: post #27

Earlier quoted context omitted.

I'm a simulationist. I believe that the universe we're experiencing is a simulation made by a far-advanced civilization. So in my reality, if something can't be modeled, it can't exist. Not saying that this is the truth, just the way I choose to understand things.

I think you would have to be assuming that the far-advanced civilization's simulator has the same complexity as the models of computation we can construct. I think that's a huge leap to make. We might not be able to model something due to issues with, let's say, Turing decidability. Unlike us, the advanced civilization's might be able to because their constructable models of computation are strictly more powerful.

I think you described what I wanted to in a much better and more concise way.

Thank you for doing that.

Re: Macroscopic quantum objects cannot exist if P ≠ NP?

#55

Post by scott_s »

elektronjunge wrote: post #51
scott_s wrote: post #42

Earlier quoted context omitted.

There are situations in nature where our models are NP-hard. Whether or not this is the same as saying that nature itself performs those computations is, I think, tied into the question of whether or not our Universe is a simulation.

If natures models reduce to our NP-hard models which they would if our models are accurate, that is to say if and only if there is some computation that is NP-hard (which means that it is proven to not have a polynomial time solution unless P=NP) that nature can solve in polynomial time and we have proven that P must equal NP.

Our models are not (necessarily) nature. The map is not the territory.

Re: Macroscopic quantum objects cannot exist if P ≠ NP?

#56

Post by nanofortnight »

raverbashing wrote: post #6

I'm not buying it 1 - P=NP is a mathematical problem. It has nothing to do with Physics. Physics has to do with Mathematics but one should be very careful when extrapolating (range, constraints, etc). 2 - Nature has no problem whatsoever solving complicated equations. Our mathematical models are the ones who suffer to model simple everyday stuff in Physics. Turbulence and Navier-Stokes equations, electromagnetic prop…

> P=NP is a mathematical problem. It has nothing to do with Physics.

There are some who would disagree with you. It is quite arrogant to assert that computer science has little to do with physical reality when our constraints on computational capabilities are very much embedded in reality.

Take a look at this survey article, for instance: http://www.scottaaronson.com/papers/npcomplete.pdf

Re: Macroscopic quantum objects cannot exist if P ≠ NP?

#57

Post by baddox »

IanCal wrote: post #39
raverbashing wrote: post #6

I'm not buying it 1 - P=NP is a mathematical problem. It has nothing to do with Physics. Physics has to do with Mathematics but one should be very careful when extrapolating (range, constraints, etc). 2 - Nature has no problem whatsoever solving complicated equations. Our mathematical models are the ones who suffer to model simple everyday stuff in Physics. Turbulence and Navier-Stokes equations, electromagnetic prop…

With 2, are you saying there are situations in nature that can solve NP-hard problems in polynomial time? Because if so, we could just use those to solve our hard problems and therefore P=NP. P=NP is not just statement about difficult problems or big equations, it's a very particular class of problems.

Technically P=NP is just about Turing machines (and thus all Turing complete systems, which includes all the computers humans have produced). As far as I know there is no evidence of real super-Turing systems, but the concept has been theorized.

http://en.wikipedia.org/wiki/Hypercomputation

Re: Macroscopic quantum objects cannot exist if P ≠ NP?

#58

Post by baddox »

scott_s wrote: post #42
IanCal wrote: post #39

Earlier quoted context omitted.

With 2, are you saying there are situations in nature that can solve NP-hard problems in polynomial time? Because if so, we could just use those to solve our hard problems and therefore P=NP. P=NP is not just statement about difficult problems or big equations, it's a very particular class of problems.

There are situations in nature where our models are NP-hard. Whether or not this is the same as saying that nature itself performs those computations is, I think, tied into the question of whether or not our Universe is a simulation.

I've never read any explanation of the Universe-as-a-simulation concept that I have understood. If the Universe isn't a simulation, then what is it?

Re: Macroscopic quantum objects cannot exist if P ≠ NP?

#59

Post by scott_s »

baddox wrote: post #58
scott_s wrote: post #42

Earlier quoted context omitted.

There are situations in nature where our models are NP-hard. Whether or not this is the same as saying that nature itself performs those computations is, I think, tied into the question of whether or not our Universe is a simulation.

I've never read any explanation of the Universe-as-a-simulation concept that I have understood. If the Universe isn't a simulation, then what is it?

I don't know - but answering a question with "I don't know" does not imply that we should pick an answer just because we don't have a good answer.

Re: Macroscopic quantum objects cannot exist if P ≠ NP?

#60

Post by snake_plissken »

I thought you could observe quantum effects but only when it was the superposition of all the eigenfunctions? You never observe the ones with a low probability density because they are dominated by the others. And also does it matter if you could solve numerically all of the functions for a macroscopic group of particles if in the end all you would care about is the average value (due to Planck's constant and the uncertainty principle)?
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