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arithma

Computational Paradox

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Why is it a paradox for a computer to simulate the universe faster than the universe itself. Does the paradox remain if the simulation excluded itself?

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Guest Anonymous Poster
If you're taking out the simulation you're no longer simulating the universe, only a subset of the universe.

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Guest Anonymous Poster
It's a paradox because in the Universe you have a computer running a simulation of the Universe. In that computers simulation of the Universe, for it to be complete, it has to have a computer in it simulating the universe.... so on and so forth.

If it was a simulation of the Universe that excluded itself, then that paradox wouldn't exist.. but that wouldn't be an accurate model of the universe nor something interesting to even talk about.

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NOT INTERESTING?

It would be interesting since it would actually tell you the evolution of the universe faster than the universe itself.

And the deficiency of the simulator would be filled in by making it give a recursive statement about it self.

It would say: The universe excluding me will look like X. Put X in (the simulator's version in the simulation)

So although it is a recursive statement, it is a descriptive one.

In addition, this question might put a physical limit on simulation speed if the answer was "It is a paradox that the simulator can simulate the universe faster than the speed of the universe itself".

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Guest Anonymous Poster
If you're taking the simulation out of your simulation, then you're version of the universe would be different from the real one and thus you can't see in the real future with the simulation.

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Original post by Anonymous Poster
If you're taking the simulation out of your simulation, then you're version of the universe would be different from the real one and thus you can't see in the real future with the simulation.
While I mostly agree with this, I wonder if it would be a somewhat acceptable simulation in terms of making certain predictions given the margin of error that would occur without the simulated simulation within the simulated universe.

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It depends on the accuracy of the simulation. If the accuracy is low enough then you can simulate it on a normal computer now (that'd be a very, very inaccurate simulation of course). That ignores the paradox because the computers simulation of itself isn't simulating the universe.

Now for a perfect simulation, assuming that one is possible (pesky quantum mechanics), and that the universe is currently already doing those calculations in the most effect way possible, then the computer running the simulation will need more (likely much much more due to entropy) mass/energy than the section of the universe it's simulating. So if your modeling the whole universe expect the computer, you'll have to turn the (vast) majority of the universe into the computer.

Of course I'm not a physicist.

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I fail to see where the paradox is... No grand father being killed so far...

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Original post by arithma
Why is it a paradox for a computer to simulate the universe faster than the universe itself.

Does the paradox remain if the simulation excluded itself?


Think of it this way, if we can simulate the universe faster than itself, then the simulation is simulating itself faster than itself. Basically, if it's free to locate the simulation within the simulation, then you can get the entire simulation instantaneously (or at least faster than an arbitrary epsilon).

One thing to note, though, is that we're very far from making such a simulation. It takes several hours to run an ab initio relaxation (with various approximations) on a 12 atom cell. Molecular dynamics simulations using EAM potentials can start to push microsecond time scales. Even if it's not self-contradictory, I wonder if it's physically possible.

And, of course, it's "possible" if the simulation excludes itself because then you're approximating the results. Of course, any simulation will be an approximation of sorts because there's no closed form solution for N-body interactions.

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Original post by arithma
It would be interesting since it would actually tell you the evolution of the universe faster than the universe itself.


The simulator might make up a non-negligible fraction of the universe. Imagine a universe where all the universe but a single atom is dedicated to predicting the evolution of that atom, which is the only thing that remains once you exclude the simulation.

As to why the simulator itself cannot be a part of the simulation, it is simple: you can build a simulator in such a way that it always behave differently from its own predicted behaviour. For example, assume the simulator had an attached LED. If the prediction is that it is on at time T, then when time T comes around, turn the LED off, and vice-versa. Think about the Halting Problem.

"Aha!", will you tell me, "I just have to build my simulation in such a way that it doesn't contradict itself". "Fine!", will I reply: I will build my own simulation and inject a contradiction by behaving differently from what you predict it will do. After all, your simulation is part of the universe, therefore I can predict what you will predict I will do and do the opposite.

"Ugh, you're only proving there cannot be two simulations of the universe, I can still have my one, self-consistent simulation!". Not so fast! There's another fundamental limiting factor. If your simulation S predicts the state of the universe at time T+dT, then it needs to be at least as big as the universe, as it has to store all that state somewhere. Then there's the question of the state S' the simulation predicts it will have at T+dT, which it must take if it is to be an accurate simulation of the universe. If that state is the same as its current state (great, you can save space by just using, say, a pointer!) then the simulation has effectively halted. Assume, therefore, that that state S' is different from S: we can go down one level of recursion and consider the state S'' that is predicted by S'... Either you stop with a finite number of recursion, and have a flawed simulation which got halted at some level, or you essentially require infinite storage: S is different from S', which is different from S'' ... and all that needs to be stored somewhere.

"So what? The universe could be infinite for all I know!". Well, even then, you're not saved: you have a countable union (the nested simulations) of distinct infinite sets (the state of the universe), which brings you to the next class of infinity (see Cantor diagonalization). Meaning that your simulation actually has to be bigger than the universe that contains it...

Either way, you lose. [smile]

NB: there may be flaws in my arguments, and I'm willing to acknowledge them if they are pointed out in a civil manner. Make sure you understand what you're getting into: I don't want any of that "NOES! 0.999 repeated can't be equal to 1" batshit nonsense.

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Ugh, you're only proving there cannot be two simulations of the universe, I can still have my one, self-consistent simulation!

READ MY MIND [smile], so we will make my simulation a black box such that no other simulation can access.

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If your simulation S predicts the state of the universe at time T+dT, then it needs to be at least as big as the universe, as it has to store all that state somewhere

I just don't understand this part.

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I cant find references right now, but as far as I know there is a theorem (or just an hypotesis) that says that a physical process cannot be simulated by a machine faster than the process itself.
The link between Physic and computation is a quite new and deep research field that was one of the main reasons that lead to the born of quantum computation (David Deutch and Richard Feynman are/were two of the most famous reasearchers in that field).

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What he means to say is that, in order to store the state of every atom in the universe, you would need every atom in the universe. Perhaps you should be simulating this universe in an entirely different one? Or even better, seeing as there are an infinite number of universes anyway, just find one you like better and move there.

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Original post by cignox1
I cant find references right now, but as far as I know there is a theorem (or just an hypotesis) that says that a physical process cannot be simulated by a machine faster than the process itself.
Yeah. Need to consider the fact that there are measurements of time infinitely small, and thus to effectively simulate that progression of time the machine doing all this would have to simulate at a speed which could process those fractions of time, which... I don't think can be done... yet.

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Suppose there were a way to describe the universe using a formula. Then, due to the universe simulation running within, there would be a recurrence relation within that formula. But what if you could find a closed form equation for that recurrence relation? oooohhhhh :-).

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simulation = do all the important parts, and then forget about the details???
Why do you need every single detail? Nobody simulates like that!

another problem with the future simulator is that once we act on the simulation, the simulation isnt valid (as long as it did not simulate us), but if it simulated us, and we acted / saved the planet because of the results from the simulation, then we would not get an "destruction of planet"-alert, and we would not act, so we would not be warned, and the simulation had to simulate that we would not do anything if we were warned by the simulator and acted (in the simulator that is), so it still had to post an "planet destruction"-alert, but when it posted this, we would act on it, and then the destruction would be prevented and then the simulation would would not rise an alert flag... :-) hehe

A simulator that simulates itselfe that simulates itselfe that simulates itselfe that simulated itselfe.

Its possible to exclude the simulator from the simulation, but then we could not watch the simulation, since it then would affect what it simulated!

Just forget it people :-) Also, its illegal do survaillence on a larg number of people here in Norway, so you also had to exclude us :-)

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Original post by arithma
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Ugh, you're only proving there cannot be two simulations of the universe, I can still have my one, self-consistent simulation!

READ MY MIND [smile], so we will make my simulation a black box such that no other simulation can access.


And I'll use the exact same method to prevent you from simulating what's going on in my house, meaning that your simulation cannot actually simulate the whole universe.

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If your simulation S predicts the state of the universe at time T+dT, then it needs to be at least as big as the universe, as it has to store all that state somewhere

I just don't understand this part.


You're simulating the universe, right? So your simulation system holds a copy of its simulation results, which represent an identical amount of data as the thing you are simulating, namely the universe. The problem is that you need to carry an infinite number of such copies, since the simulation recursively includes itself along with the rest of the universe. It can't just include itself by reference, because that implies that the simulation isn't running.

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I think that I understand now what am asking about [smile].

To describe the universe (store its state), do we have to have exactly the same universe, assuming it is stored in a larger superuniverse where the same laws [as that of the describted] apply?

Forget about interactions between the description and the actual.
However if that is true, then description and actuality are the same!

I think we need something more simplified here to continue the discussion. But I don't think I am the one that should propose the suggestion.

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To describe the universe (store its state), do we have to have exactly the same universe

We need at least an amount of matter equal to the mass of the universe, I think. But the exact amount depends by the actual harware we are using to run the simulation: if we need more than an atom to store the data associated to a simulated atom, then our simulation would require far much more matter than the universe.
That's why universe performance cannot be outperformed.

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Original post by Fruny
"Aha!", will you tell me, "I just have to build my simulation in such a way that it doesn't contradict itself". "Fine!", will I reply: I will build my own simulation and inject a contradiction by behaving differently from what you predict it will do. After all, your simulation is part of the universe, therefore I can predict what you will predict I will do and do the opposite.


How can you be so sure we have a free will? Your statement implies that the universe isn't deterministic. If it were deterministic I believe it would be possible to simulate the universe, but of course you would need at least the same amount of matter, in another universe.

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Original post by CTar
Quote:
Original post by Fruny
"Aha!", will you tell me, "I just have to build my simulation in such a way that it doesn't contradict itself". "Fine!", will I reply: I will build my own simulation and inject a contradiction by behaving differently from what you predict it will do. After all, your simulation is part of the universe, therefore I can predict what you will predict I will do and do the opposite.


How can you be so sure we have a free will? Your statement implies that the universe isn't deterministic. If it were deterministic I believe it would be possible to simulate the universe, but of course you would need at least the same amount of matter, in another universe.


You don't need freewill for that - I can easily do the opposite once someone makes a prediction about my behavior, even if the prediction was perfect up until the moment it was told to me.

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Original post by wild_pointer
You don't need freewill for that - I can easily do the opposite once someone makes a prediction about my behavior, even if the prediction was perfect up until the moment it was told to me.


Also if the prediction took into consideration that you were told? (It was a perfect prediction, everything was taken into consideration)

Also since it would have to be in another universe (of more matter), how could someone find out about the simulation?

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Guest Anonymous Poster
Not to mention that the uncertainty principal makes it impossible to know the entire state of anything in complete detail. I think this is important and why quantum mechanics is my friend.

Einstein said that "God doesn't play dice with the universe", but I think he was wrong. The fact that we cannot determine the exact state of something, means that we cannot simulate it. Even a little itty bitty peice of it. This uncertainty makes all of our realty non-deterministic.

And I for one am all for free-will ;)

If the soul lives anywhere, it is in that fuzzy continuum between position and speed :P

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And who is to say all of the atoms in the universe actually exist? Perhaps they do not exist until they enter a state in which they can be observed.

As gamemakers we use geometry culling, and statistical approximation for things that are out of scope. We do not have to have a computer that will store every digit of pi if we want to find the bazillionith number. we do that algorithmically.

who's to say that anything not observed in the universe isn't being algorithmically and statistically approximated, and only perfectly simulated when being directly observed.

Particle / Wave duality certainly sounds a lot like this process to me :)

Perhaps we are just AI in a 6th dimensional game of galactic civilization.



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