7 ms·

Technically, a lava lamp is deterministic. Still, I'd say that it's "close enough" to be considered a real RNG. There's almost no way to see a pattern in it, a

Technically, a lava lamp is deterministic. Still, I'd say that it's "close enough" to be considered a real RNG. There's almost no way to see a pattern in it, and I'm pretty sure that it would be completely impractical to simulate the contents inside, even if you knew all the initial conditions.

baddox 12y ago
Yeah, I meant "deterministic" as in "generated using standard computations starting from a simple seed." Whether the lava lamp itself is deterministic, or the Universe moreover, is another issue.
PhantomGremlin 12y ago
> Technically, a lava lamp is deterministic. Technically, it's only "deterministic" if you can fully establish the initial state. That's not possible, if for no other reason than the Uncertainty Principle [1] prevents you from measuring the initial conditions carefully enough. Plus you're not really dealing with a closed system, so basically the entire Universe can influence your system going forward. Chaos theory [2] says that you're fighting a losing game if you think it's deterministic. [1] http://en.wikipedia.org/wiki/Uncertainty_principle http://en.wikipedia.org/wiki/Uncertainty_principle [2] http://en.wikipedia.org/wiki/Chaos_theory http://en.wikipedia.org/wiki/Chaos_theory
- sopooneo 12y ago
  Even if you could determine the initial state, wouldn't quantum effects, aggregating over time, make it non-deterministic?
  - PhantomGremlin 12y ago
    That's a really good question. I'd love to hear the answer from a physicist in the know. Assume you could overcome the uncertainty principle or observer effect and you could fully determine the initial conditions of the entire system. You knew the position and momentum of every atom. You knew the spin of every electron. Etc. Etc. Etc. Doesn't the inherent nature of quantum mechanics say that it's still impossible to predict the state of that system at some future time? Interactions only occur probabilistically, and there is no way to predict them a priori.
    - rprospero 12y ago
      Physicist here. In terms of predicting the "future state", it depends on what you want to call the "state". If I know the complete wave function of the system, then knowing the wave function at a future point in time is trivial. Just apply the time evolution operator. However, knowing the wave function at a given point in time doesn't tell me the position or momentum - it just tells me the probability with which I'll measure a given position or momentum. So knowing the "state" still means that my measurements will have random components. On a slightly different note, when you talk about knowing the exact position and momentum of every particle, you're not talking about overcoming a physical limitation, but a mathematical one. To put it differently, if I know that the momentum is exactly zero, I do know that the position is. The problem is that the position is NaN. If the position isn't NaN, then I know longer know the momentum isn't precisely defined.
      - claudius 12y ago
        > If I know the complete wave function of the system, then knowing the wave function at a future point in time is trivial. Just apply the time evolution operator. But wouldn't the regular measurement cause a collapse onto a randomly-chosen eigenstate of the measured operator? That is, if we have a PRNG based on a regularly measuring the lava lamp, then to predict the state after N steps, we not only have the issue of the randomly chosen N-th measurement but also have to take into account the random results of the N-1 previous measurements, which can potentially evolve into entirely new directions. Overall, it's difficult to place a lava lamp over human time scales, as both are far from the usual quantum/classical limits: We know that even in thousands of years’ time, Earth will still revolve mostly deterministically (in the classical sense) around the sun. Similarly, electrons will hardly ever behave deterministically. Lava lamps and a couple of years are oddly in between.
        rprospero 12y ago
        You're a couple of abstraction levels lower than where I aimed my post :-) You're absolutely right that everything breaks down after a measurement. However, I'd begun my hypothetical by assuming that we had some magical technique for getting the complete wave function. If our measurements again give us the complete wave function, then we just use the time evolution operator on that again. I guess what I'm trying to say is that we should be okay after N-1 measurements, as long as we're allowed to see the result of that final measurement. You're right, though, that we rapidly lose the ability to make any predictions if some jerk keeps measuring the system. I think that there's also an Everettian argument that, if you haven't given me the complete wave function for the jerk making the measurements, then you didn't really give me the the complete wave function of the system. However, that's pushing outside my area of expertise.

baddox 12y ago

Yeah, I meant "deterministic" as in "generated using standard computations starting from a simple seed." Whether the lava lamp itself is deterministic, or the Universe moreover, is another issue.

PhantomGremlin 12y ago

> Technically, a lava lamp is deterministic. Technically, it's only "deterministic" if you can fully establish the initial state. That's not possible, if for no other reason than the Uncertainty Principle [1] prevents you from measuring the initial conditions carefully enough. Plus you're not really dealing with a closed system, so basically the entire Universe can influence your system going forward. Chaos theory [2] says that you're fighting a losing game if you think it's deterministic. [1] http://en.wikipedia.org/wiki/Uncertainty_principle http://en.wikipedia.org/wiki/Uncertainty_principle [2] http://en.wikipedia.org/wiki/Chaos_theory http://en.wikipedia.org/wiki/Chaos_theory

sopooneo 12y ago
Even if you could determine the initial state, wouldn't quantum effects, aggregating over time, make it non-deterministic?
- PhantomGremlin 12y ago
  That's a really good question. I'd love to hear the answer from a physicist in the know. Assume you could overcome the uncertainty principle or observer effect and you could fully determine the initial conditions of the entire system. You knew the position and momentum of every atom. You knew the spin of every electron. Etc. Etc. Etc. Doesn't the inherent nature of quantum mechanics say that it's still impossible to predict the state of that system at some future time? Interactions only occur probabilistically, and there is no way to predict them a priori.
  - rprospero 12y ago
    Physicist here. In terms of predicting the "future state", it depends on what you want to call the "state". If I know the complete wave function of the system, then knowing the wave function at a future point in time is trivial. Just apply the time evolution operator. However, knowing the wave function at a given point in time doesn't tell me the position or momentum - it just tells me the probability with which I'll measure a given position or momentum. So knowing the "state" still means that my measurements will have random components. On a slightly different note, when you talk about knowing the exact position and momentum of every particle, you're not talking about overcoming a physical limitation, but a mathematical one. To put it differently, if I know that the momentum is exactly zero, I do know that the position is. The problem is that the position is NaN. If the position isn't NaN, then I know longer know the momentum isn't precisely defined.
    - claudius 12y ago
      > If I know the complete wave function of the system, then knowing the wave function at a future point in time is trivial. Just apply the time evolution operator. But wouldn't the regular measurement cause a collapse onto a randomly-chosen eigenstate of the measured operator? That is, if we have a PRNG based on a regularly measuring the lava lamp, then to predict the state after N steps, we not only have the issue of the randomly chosen N-th measurement but also have to take into account the random results of the N-1 previous measurements, which can potentially evolve into entirely new directions. Overall, it's difficult to place a lava lamp over human time scales, as both are far from the usual quantum/classical limits: We know that even in thousands of years’ time, Earth will still revolve mostly deterministically (in the classical sense) around the sun. Similarly, electrons will hardly ever behave deterministically. Lava lamps and a couple of years are oddly in between.
      - rprospero 12y ago
        You're a couple of abstraction levels lower than where I aimed my post :-) You're absolutely right that everything breaks down after a measurement. However, I'd begun my hypothetical by assuming that we had some magical technique for getting the complete wave function. If our measurements again give us the complete wave function, then we just use the time evolution operator on that again. I guess what I'm trying to say is that we should be okay after N-1 measurements, as long as we're allowed to see the result of that final measurement. You're right, though, that we rapidly lose the ability to make any predictions if some jerk keeps measuring the system. I think that there's also an Everettian argument that, if you haven't given me the complete wave function for the jerk making the measurements, then you didn't really give me the the complete wave function of the system. However, that's pushing outside my area of expertise.