5 ms·

> And no practical amount of shaking the jar will ever return the marbles to a high order state again. This can't be true. Take the case where there's only 2 m

by soperj 4y ago

> And no practical amount of shaking the jar will ever return the marbles to a high order state again. This can't be true. Take the case where there's only 2 marbles, it's likely that at some point that shaking them will return them to the original state. For higher numbers of marbles the probability becomes lower and lower, but is never 0.

a257 4y ago
With enough marbles, the discrete distribution behaves like a continuous distribution. The point probability of a continuous distribution is infinitely improbable -- in other words it is 0. (0.00..0..1 = 0 just as 0.99 repeating equals 1)
- TechBro8615 4y ago
  > infinitely improbable -- in other words it is 0 This sounds like a rather bold statement to make, as long as we're already speaking so metaphysically.
  - a257 4y ago
    The statement is mathematically correct [0]. [0] https://stats.stackexchange.com/questions/142730/px-x-0-when-x-is-a-continuous-variable https://stats.stackexchange.com/questions/142730/px-x-0-when...
    - TechBro8615 4y ago
      We're talking about physics, not mathematics. We don't have the luxury of hand-waving away fundamental questions about the nature of the continuum. See: https://en.wikipedia.org/wiki/Continuum_hypothesis https://en.wikipedia.org/wiki/Continuum_hypothesis
      - a257 4y ago
        Please elaborate.
        TechBro8615 4y ago
        I'm neither a mathematician nor a physicist, so I'm not nearly informed enough to elaborate on the subject properly, but I would note that the axiom of choice is not proven, and while you can mathematically divide a continuum into infinitesimally small sets, you cannot do the same to physical matter. From my understanding, many of the contradictions between classical and quantum physics arise at this boundary between the discrete and the continuous, where classical physics generally assumes continuity while quantum physics is constructed around discrete quantization mostly independent of time. Again, I'm not a physicist, but I think it's telling that the validity of continuum mechanics [0] depends on a model and multiple assumptions. I have no trouble agreeing with your original statement, "with enough marbles, the discrete distribution behaves like a continuous distribution," when speaking mathematically, but mathematics by its nature is an idealized model of the world - I'm not willing to accept that it's objectively representative of physical reality. The discussion we're having here is one of metaphysics, so it feels a bit like the height of hubris to use mathematics as the tool for describing objective reality, because metaphysically, we cannot say that mathematics is anything other than a tool we've constructed for approximating the model of the world as we understand it. Considering the subject of this post is about retrocausality, we're already throwing out some pretty wild ideas, so I think it's a bit hubristic to dismiss them by citing a branch of mathematics that assumes the existence of countably infinite sets [1]. [0] https://en.wikipedia.org/wiki/Continuum_mechanics#Validity https://en.wikipedia.org/wiki/Continuum_mechanics#Validity [1] https://en.wikipedia.org/wiki/Constructivism_(philosophy_of_mathematics)#Axiom_of_choice https://en.wikipedia.org/wiki/Constructivism_(philosophy_of_...
        lupire 4y ago
        This whole thread hinges on your not giving credence to the word "practically" , as in "approximately". No countably infinity needed, and Continuum Hypothesis isn't relevant at all in any way, as it is aboit uncountable infinity. Until you explain what you are trying to say, you aren't saying anything meaningful. The one showing hubris here is you, tossing around technical terms don't admit you don't understand.
      - coldtea 4y ago
        >We're talking about physics, not mathematics. Mathematics still apply.
        TechBro8615 4y ago
        Mathematics applies insofar as it can model the subject under discussion. It's a great tool for, dare I say, 99.999999...% of practical problems. But mathematics is an imperfect model of objective reality that cannot resolve metaphysical problems like Zeno's paradoxes [0]. Any discussion of retro-causality is inherently one of the philosophy of space and time, which is the domain of metaphysics, not mathematics, so we can't necessarily apply familiar mathematical lemmas to resolve the problems it creates. [0] https://en.wikipedia.org/wiki/Zeno%27s_paradoxes#In_modern_mathematics https://en.wikipedia.org/wiki/Zeno%27s_paradoxes#In_modern_m... [1] https://en.wikipedia.org/wiki/Philosophy_of_space_and_time#Direction_of_time https://en.wikipedia.org/wiki/Philosophy_of_space_and_time#D...
- soperj 4y ago
  There can't be an infinite number of marbles in a finite amount of space.
  - a257 4y ago
    The number of possible states asymptotically approaches infinity, so we can model it as such. You can get a more "accurate" model using more math (with measure theory), but the terms will coalesce such that they are negligible.
    - soperj 4y ago
      negligible isn't zero, and time at a universe scale may be longer.
- PartiallyTyped 4y ago
  Any point is infinitely improbable when sampling with infinite precision, only because this calculation is not computable. Even if the point probability is 0 or approaching zero very fast, some event occurs with probability 1. The probability that life would evolve on a blue planet that its anthropomorphic inhabitants will come to call Gaia or Earth, has as a star Sol, in this corner of the Milky Way, in this particular local group and so on is zero even if we limit ourselves to just the observable universe. At the same time the probability that life will exist at some planet at some solar system at some galaxy at some local group and so on, is practically 1. That is to say, depending on how you categorise and count said marbles, the reordering may occur. While any individual marble will not be at its place with P=1. You can still end up in a situation where the marbles are ordered in layers. The whole thing regarding entropy is concerned with a closed system. You can very much exchange energy to decrease entropy, but said exchange is a) leaky, and b) implies that the system is not isolated.
  - a257 4y ago
    A probability of zero does not mean that the event is impossible. When we refer to probabilities we are talking about probability densities. Infinite precision is a useful modeling tool in the same way that approximations of pi are useful.
    - PartiallyTyped 4y ago
      I think I was misunderstood. My comment regarding infinite precision was mostly aiming to argue that any single point has probability zero but an event still occurs. This was then used again when mentioning earth to argue that depending on the definition of "order" here: > And no practical amount of shaking the jar will ever return the marbles to a high order state again. It is entirely possible to reach a state of higher order if you don't require that individual marbles don't hold the same arrangement relative to adjacent marbles, meaning that any permutation of marbles with identical color is acceptable. This happens because the event you are asking for is a very large subset.
      - 4y ago
dekhn 4y ago
you're correct. In stats/thermo class there's a commonly taught "what's the probability of all the molecules of air in a room spontaneously moving to <extremely small location>". The problem is that shoving all those molecules into a tiny location woudl increase the pressure tremendously, sending all the particles in directions that would eventually return to a uniform distribution. IIUC my professor right the probability is non zero but is practically impossible for a large number of incompressible spheres.
Nevermark 4y ago
> For higher numbers of marbles the probability becomes lower and lower, but is never 0. Exactly. It doesn’t take a very large jar to make a return to an original state practically impossible. But even for two marbles, shaking them to return them to their original locations costs a fair amount of organized energy. And that is organized chemical energy in your muscles, which you are dissipating as disorganized heat energy due to your efforts, increasing the total disorganization. And the marbles are microscopically wearing down, shedding compounds. The jar is also wearing down. Both becoming less organized. So even with two marbles, overall entropy continues increasing. We can locally reverse entropy, only at the cost of actually increasing entropy in total. - Organizing your day takes effort and uses up useful organized energy. - Computation uses up useful organized energy. - Your cells, maintaining their metabolism, uses up useful organized energy. No matter what we do, entropy still increases.

by soperj 4y ago

a257 4y ago

With enough marbles, the discrete distribution behaves like a continuous distribution. The point probability of a continuous distribution is infinitely improbable -- in other words it is 0. (0.00..0..1 = 0 just as 0.99 repeating equals 1)

TechBro8615 4y ago
> infinitely improbable -- in other words it is 0 This sounds like a rather bold statement to make, as long as we're already speaking so metaphysically.
- a257 4y ago
  The statement is mathematically correct [0]. [0] https://stats.stackexchange.com/questions/142730/px-x-0-when-x-is-a-continuous-variable https://stats.stackexchange.com/questions/142730/px-x-0-when...
  - TechBro8615 4y ago
    We're talking about physics, not mathematics. We don't have the luxury of hand-waving away fundamental questions about the nature of the continuum. See: https://en.wikipedia.org/wiki/Continuum_hypothesis https://en.wikipedia.org/wiki/Continuum_hypothesis
    - a257 4y ago
      Please elaborate.
      - TechBro8615 4y ago
        I'm neither a mathematician nor a physicist, so I'm not nearly informed enough to elaborate on the subject properly, but I would note that the axiom of choice is not proven, and while you can mathematically divide a continuum into infinitesimally small sets, you cannot do the same to physical matter. From my understanding, many of the contradictions between classical and quantum physics arise at this boundary between the discrete and the continuous, where classical physics generally assumes continuity while quantum physics is constructed around discrete quantization mostly independent of time. Again, I'm not a physicist, but I think it's telling that the validity of continuum mechanics [0] depends on a model and multiple assumptions. I have no trouble agreeing with your original statement, "with enough marbles, the discrete distribution behaves like a continuous distribution," when speaking mathematically, but mathematics by its nature is an idealized model of the world - I'm not willing to accept that it's objectively representative of physical reality. The discussion we're having here is one of metaphysics, so it feels a bit like the height of hubris to use mathematics as the tool for describing objective reality, because metaphysically, we cannot say that mathematics is anything other than a tool we've constructed for approximating the model of the world as we understand it. Considering the subject of this post is about retrocausality, we're already throwing out some pretty wild ideas, so I think it's a bit hubristic to dismiss them by citing a branch of mathematics that assumes the existence of countably infinite sets [1]. [0] https://en.wikipedia.org/wiki/Continuum_mechanics#Validity https://en.wikipedia.org/wiki/Continuum_mechanics#Validity [1] https://en.wikipedia.org/wiki/Constructivism_(philosophy_of_mathematics)#Axiom_of_choice https://en.wikipedia.org/wiki/Constructivism_(philosophy_of_...
        lupire 4y ago
        This whole thread hinges on your not giving credence to the word "practically" , as in "approximately". No countably infinity needed, and Continuum Hypothesis isn't relevant at all in any way, as it is aboit uncountable infinity. Until you explain what you are trying to say, you aren't saying anything meaningful. The one showing hubris here is you, tossing around technical terms don't admit you don't understand.
    - coldtea 4y ago
      >We're talking about physics, not mathematics. Mathematics still apply.
      - TechBro8615 4y ago
        Mathematics applies insofar as it can model the subject under discussion. It's a great tool for, dare I say, 99.999999...% of practical problems. But mathematics is an imperfect model of objective reality that cannot resolve metaphysical problems like Zeno's paradoxes [0]. Any discussion of retro-causality is inherently one of the philosophy of space and time, which is the domain of metaphysics, not mathematics, so we can't necessarily apply familiar mathematical lemmas to resolve the problems it creates. [0] https://en.wikipedia.org/wiki/Zeno%27s_paradoxes#In_modern_mathematics https://en.wikipedia.org/wiki/Zeno%27s_paradoxes#In_modern_m... [1] https://en.wikipedia.org/wiki/Philosophy_of_space_and_time#Direction_of_time https://en.wikipedia.org/wiki/Philosophy_of_space_and_time#D...
soperj 4y ago
There can't be an infinite number of marbles in a finite amount of space.
- a257 4y ago
  The number of possible states asymptotically approaches infinity, so we can model it as such. You can get a more "accurate" model using more math (with measure theory), but the terms will coalesce such that they are negligible.
  - soperj 4y ago
    negligible isn't zero, and time at a universe scale may be longer.
PartiallyTyped 4y ago
Any point is infinitely improbable when sampling with infinite precision, only because this calculation is not computable. Even if the point probability is 0 or approaching zero very fast, some event occurs with probability 1. The probability that life would evolve on a blue planet that its anthropomorphic inhabitants will come to call Gaia or Earth, has as a star Sol, in this corner of the Milky Way, in this particular local group and so on is zero even if we limit ourselves to just the observable universe. At the same time the probability that life will exist at some planet at some solar system at some galaxy at some local group and so on, is practically 1. That is to say, depending on how you categorise and count said marbles, the reordering may occur. While any individual marble will not be at its place with P=1. You can still end up in a situation where the marbles are ordered in layers. The whole thing regarding entropy is concerned with a closed system. You can very much exchange energy to decrease entropy, but said exchange is a) leaky, and b) implies that the system is not isolated.
- a257 4y ago
  A probability of zero does not mean that the event is impossible. When we refer to probabilities we are talking about probability densities. Infinite precision is a useful modeling tool in the same way that approximations of pi are useful.
  - PartiallyTyped 4y ago
    I think I was misunderstood. My comment regarding infinite precision was mostly aiming to argue that any single point has probability zero but an event still occurs. This was then used again when mentioning earth to argue that depending on the definition of "order" here: > And no practical amount of shaking the jar will ever return the marbles to a high order state again. It is entirely possible to reach a state of higher order if you don't require that individual marbles don't hold the same arrangement relative to adjacent marbles, meaning that any permutation of marbles with identical color is acceptable. This happens because the event you are asking for is a very large subset.
    - 4y ago

dekhn 4y ago

you're correct. In stats/thermo class there's a commonly taught "what's the probability of all the molecules of air in a room spontaneously moving to <extremely small location>". The problem is that shoving all those molecules into a tiny location woudl increase the pressure tremendously, sending all the particles in directions that would eventually return to a uniform distribution. IIUC my professor right the probability is non zero but is practically impossible for a large number of incompressible spheres.

Nevermark 4y ago

> For higher numbers of marbles the probability becomes lower and lower, but is never 0. Exactly. It doesn’t take a very large jar to make a return to an original state practically impossible. But even for two marbles, shaking them to return them to their original locations costs a fair amount of organized energy. And that is organized chemical energy in your muscles, which you are dissipating as disorganized heat energy due to your efforts, increasing the total disorganization. And the marbles are microscopically wearing down, shedding compounds. The jar is also wearing down. Both becoming less organized. So even with two marbles, overall entropy continues increasing. We can locally reverse entropy, only at the cost of actually increasing entropy in total. - Organizing your day takes effort and uses up useful organized energy. - Computation uses up useful organized energy. - Your cells, maintaining their metabolism, uses up useful organized energy. No matter what we do, entropy still increases.