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?
If you're taking out the simulation you're no longer simulating the universe, only a subset of the universe.
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.
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".
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".
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.
Quote:Original post by Anonymous PosterWhile 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.
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.
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.
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.
Quote: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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