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Isn't mention of chaos theory irrelevant? Chaos is the effect you get when you can't measure something accurately enough, or you can't (don't have enough compu

Isn't mention of chaos theory irrelevant? Chaos is the effect you get when you can't measure something accurately enough, or you can't (don't have enough computational power) to run a perfect reality simulation with those measurements (even if they're good enough in theory to form the basis of an accurate prediction) in reasonable time, or both. I think the main premise rests on the same confusion about free will that shows up in Newcomb's paradox. Either there is free will that transcends anything's ability to predict, even in theory (perfect knowledge/measurement and infinite computation), or there is not. If there is not, then a demon/AI/God setting up a test/prediction based on your future decision may be possible, but your awareness of that fact will simply be an input into your future decision-making... an input that the demon/AI/God already accounted for when making the prediction. Just because something is recursive does not mean it's not deterministic. I happen to believe that Laplace's demon exists, it's called physics, but its state is the physical world, so it predicts things will happen at exactly the moment they happen (the prediction/computation being entropic decay); unfortunately that doesn't seem very useful for predictions in the practical sense. If there is free will that transcends physics, then prediction is fundamentally impossible by something bound to physics—so it's a thought experiment where some things are bound to the laws of physics and others are not. What is the purpose of conducting thought experiments about the physical world, based on supernatural axioms? "Free will exists," the claim goes, and yet "here's a thing that can collapse free will and issue arbitrarily accurate predictions on human behavior." And then, "Let's see what happens when these axioms are applied to someone in the physical world choosing whether to try to make more money or less."

alephnil 12y ago
> 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.
drcomputer 12y ago
> Chaos is the effect you get when you can't measure something accurately enough, or you can't (don't have enough computational power) to run a perfect reality simulation with those measurements (even if they're good enough in theory to form the basis of an accurate prediction) in reasonable time, or both. Chaos theory with regards to information doesn't take multiple observers into account - where the observers actually change the how the information is related and moves. If you can measure that, then it ceases to be chaotic. Whether that's possible (inferring intent), I am not sure. > If there is free will that transcends physics, then prediction is fundamentally impossible by something bound to physics—so it's a thought experiment where some things are bound to the laws of physics and others are not. What is the purpose of conducting thought experiments about the physical world, based on supernatural axioms? I think these theoretical suppositions are based more on a fear of something that people imagine to be real, and may be real. Instead of supernatural beings, suppose there are people that define the world, and people that live within the definition. The fear that the groups are mutually exclusive leads is directly analogous to the philosophical problem. > "Free will exists," the claim goes, and yet "here's a thing that can collapse free will and issue arbitrarily accurate predictions on human behavior." And then, "Let's see what happens when these axioms are applied to someone in the physical world choosing whether to try to make more money or less." The thing always depends on states of mind, explanations, the pretense of logic and maths, which ultimately convey themselves to me as rhetoric. There is mind, and there is the world. Instead of considering discrete points in which perfect knowledge is known, I'm more concerned with rates of information flow.

alephnil 12y ago

> 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.

drcomputer 12y ago

> Chaos is the effect you get when you can't measure something accurately enough, or you can't (don't have enough computational power) to run a perfect reality simulation with those measurements (even if they're good enough in theory to form the basis of an accurate prediction) in reasonable time, or both. Chaos theory with regards to information doesn't take multiple observers into account - where the observers actually change the how the information is related and moves. If you can measure that, then it ceases to be chaotic. Whether that's possible (inferring intent), I am not sure. > If there is free will that transcends physics, then prediction is fundamentally impossible by something bound to physics—so it's a thought experiment where some things are bound to the laws of physics and others are not. What is the purpose of conducting thought experiments about the physical world, based on supernatural axioms? I think these theoretical suppositions are based more on a fear of something that people imagine to be real, and may be real. Instead of supernatural beings, suppose there are people that define the world, and people that live within the definition. The fear that the groups are mutually exclusive leads is directly analogous to the philosophical problem. > "Free will exists," the claim goes, and yet "here's a thing that can collapse free will and issue arbitrarily accurate predictions on human behavior." And then, "Let's see what happens when these axioms are applied to someone in the physical world choosing whether to try to make more money or less." The thing always depends on states of mind, explanations, the pretense of logic and maths, which ultimately convey themselves to me as rhetoric. There is mind, and there is the world. Instead of considering discrete points in which perfect knowledge is known, I'm more concerned with rates of information flow.