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> Isn't mention of chaos theory irrelevant? That was my first thought as well, but consider a chaotic system in a Newtonian universe. Laplace' demon must then

> Isn't mention of chaos theory irrelevant? That was my first thought as well, but consider a chaotic system in a Newtonian universe. Laplace' demon must then have the capability to simulate the universe to be able to predict it. What chaos theory brings is that this simulation would require infinite precision to be done without diverging from reality at some point (and sooner rather than later as the error grows exponentially). Then you could use Cantor's diagonalization theorem to prove that no such simulator could exist, even for a finite system, because even a finite system would require an infinitely large state to represent it, and no finitely sized simulator could represent it.

harshreality 12y ago
The universe represents itself. Doesn't that imply either that the universe is capable of infinite computation within a finite (though increasing) space, or that it doesn't require infinite state? There's Planck length and Planck time (entropic decay resolution?) to consider. If those are the basis for physical laws, isn't everything finite?
- alephnil 12y ago
  The universe represents itself, but no part of the universe is able to predicts its own future in detail, and is as such no simulation, at least not of itself. It just exists. The reason I said "a Newtonian universe", is precisely because quantum physics represents a discretization, which Newtonian physics does not, and the Planck length is a part of this discretization. The simulator would have to be bigger than the system it simulates to be able to represent its state, but the Cantor diagonalization argument would no longer apply.
  - harshreality 12y ago
    But we don't live in a Newtonian universe, do we? If the universe requires infinite computation to "go", it's doing that computation somehow, isn't it? If the universe at perceivable scale is not capable of infinite computation, but infinite computation is required, perhaps it's spawning infinite universes that do computations instantly with respect to our universe's arrow of time? I don't understand the difference in computational requirements between predicting (in "advance") a future (entropic future) state of the universe, and predicting it JIT. A functioning Newtonian universe must be capable of infinite computation, therefore Laplace's demon can exist (for that universe), even if only by being a copy of the universe, right?
    - seabee 12y ago
      There are two outcomes of your argument: 1) a functioning Newtonian universe is impossible 2) functioning Newtonian universes are infinitely complex The laws of physics already established 1, making 2 a moot point.
      - deleted 12y ago
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    - d--b 12y ago
      That's exactly the point of the metaphysical problem. And you could rephrase as: if we could make an exact replica of the universe, would it behave just as ours or would it diverge away? Laplace says it would behave just as ours, but it's not obvious. It's not a question about chaos or the computability of the universe, it's a question about whether true randomness exists in the laws of nature.
- roblev 12y ago
  I'm not sure Planck time has much to do with this. The universe is not thought to be quantized in time, i.e. there is no requirement that the time period between two events is a multiple of the Planck time.
- frozenport 12y ago
  Planck lengths arent the smallest increments of length, this is rather a scale under which we have serious questions about quantum mechanics, chief among these is gravity. Similiar limits exist to frustrate metrologists, for example the famous visible light diffraction limit at around 200nm >>In some forms of quantum gravity, the Planck length is the length scale at which the structure of spacetime becomes dominated by quantum effects, and it is impossible to determine the difference between two locations less than one Planck length apart.

harshreality 12y ago

The universe represents itself. Doesn't that imply either that the universe is capable of infinite computation within a finite (though increasing) space, or that it doesn't require infinite state? There's Planck length and Planck time (entropic decay resolution?) to consider. If those are the basis for physical laws, isn't everything finite?

alephnil 12y ago
The universe represents itself, but no part of the universe is able to predicts its own future in detail, and is as such no simulation, at least not of itself. It just exists. The reason I said "a Newtonian universe", is precisely because quantum physics represents a discretization, which Newtonian physics does not, and the Planck length is a part of this discretization. The simulator would have to be bigger than the system it simulates to be able to represent its state, but the Cantor diagonalization argument would no longer apply.
- harshreality 12y ago
  But we don't live in a Newtonian universe, do we? If the universe requires infinite computation to "go", it's doing that computation somehow, isn't it? If the universe at perceivable scale is not capable of infinite computation, but infinite computation is required, perhaps it's spawning infinite universes that do computations instantly with respect to our universe's arrow of time? I don't understand the difference in computational requirements between predicting (in "advance") a future (entropic future) state of the universe, and predicting it JIT. A functioning Newtonian universe must be capable of infinite computation, therefore Laplace's demon can exist (for that universe), even if only by being a copy of the universe, right?
  - seabee 12y ago
    There are two outcomes of your argument: 1) a functioning Newtonian universe is impossible 2) functioning Newtonian universes are infinitely complex The laws of physics already established 1, making 2 a moot point.
    - deleted 12y ago
      [deleted]
  - d--b 12y ago
    That's exactly the point of the metaphysical problem. And you could rephrase as: if we could make an exact replica of the universe, would it behave just as ours or would it diverge away? Laplace says it would behave just as ours, but it's not obvious. It's not a question about chaos or the computability of the universe, it's a question about whether true randomness exists in the laws of nature.
roblev 12y ago
I'm not sure Planck time has much to do with this. The universe is not thought to be quantized in time, i.e. there is no requirement that the time period between two events is a multiple of the Planck time.
frozenport 12y ago
Planck lengths arent the smallest increments of length, this is rather a scale under which we have serious questions about quantum mechanics, chief among these is gravity. Similiar limits exist to frustrate metrologists, for example the famous visible light diffraction limit at around 200nm >>In some forms of quantum gravity, the Planck length is the length scale at which the structure of spacetime becomes dominated by quantum effects, and it is impossible to determine the difference between two locations less than one Planck length apart.