26 ms·

With enough marbles, the discrete distribution behaves like a continuous distribution. The point probability of a continuous distribution is infinitely improbab

by 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.
        TechBro8615 4y ago
        > The one showing hubris here is you, tossing around technical terms don't admit you don't understand. Hence the disclaimer. I just think this stuff is fascinating. If you're interested, this is the article that originally got me thinking about these ideas as they relate to the flow of time: "Does Time Really Flow? New Clues Come From a Century-Old Approach to Math" [0]. It's effectively an appeal to intuitionist mathematics and a rejection of constructivism, where - simplified - every particle since the big bang can be assigned some "number" that describes its position on its world line, with a precision that is finite, but always increasing - and it's this increase in precision from which emerges the "flow" of time. If you ctrl+f the article for "continuum," you'll see some better constructed arguments for what I'm trying to argue, e.g.: > Moreover, the continuum can’t be cleanly divided into two parts consisting of all numbers less than ½ and all those greater than or equal to ½. “If you try to cut the continuum in half, this number x is going to stick to the knife, and it won’t be on the left or on the right,” said Posy. “The continuum is viscous; it’s sticky.” The impression I'm left with is that the difference between constructivist vs. intuitionist mathematics (which rejects the law of the excluded middle) has some parallels to the difference between eternalism (there is a past, present and future) vs. presentism (there is only the present). As a layman, I just can't help but notice the same patterns come up again and again when looking at unresolved problems between classical and quantum mechanics, namely those that lie at the boundary between the continuous and discrete. FWIW, I asked ChatGPT for some unresolved mathematical problems that might relate to this, and it came up with: The Continuum Hypothesis, The Axiom of Choice, and The Riemann Hypothesis, all of which it admitted are possibly impossible to prove because they're effectively unfalsifiable. (I also showed it this entire thread, and it agreed with your critique of my arguments, but also that every argument in the thread is unfalsifiable - and then it pointed me to the Boltzmann Brain paradox). [0] https://www.quantamagazine.org/does-time-really-flow-new-clues-come-from-a-century-old-approach-to-math-20200407/ https://www.quantamagazine.org/does-time-really-flow-new-clu...
    - 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

by a257 4y ago

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.
        TechBro8615 4y ago
        > The one showing hubris here is you, tossing around technical terms don't admit you don't understand. Hence the disclaimer. I just think this stuff is fascinating. If you're interested, this is the article that originally got me thinking about these ideas as they relate to the flow of time: "Does Time Really Flow? New Clues Come From a Century-Old Approach to Math" [0]. It's effectively an appeal to intuitionist mathematics and a rejection of constructivism, where - simplified - every particle since the big bang can be assigned some "number" that describes its position on its world line, with a precision that is finite, but always increasing - and it's this increase in precision from which emerges the "flow" of time. If you ctrl+f the article for "continuum," you'll see some better constructed arguments for what I'm trying to argue, e.g.: > Moreover, the continuum can’t be cleanly divided into two parts consisting of all numbers less than ½ and all those greater than or equal to ½. “If you try to cut the continuum in half, this number x is going to stick to the knife, and it won’t be on the left or on the right,” said Posy. “The continuum is viscous; it’s sticky.” The impression I'm left with is that the difference between constructivist vs. intuitionist mathematics (which rejects the law of the excluded middle) has some parallels to the difference between eternalism (there is a past, present and future) vs. presentism (there is only the present). As a layman, I just can't help but notice the same patterns come up again and again when looking at unresolved problems between classical and quantum mechanics, namely those that lie at the boundary between the continuous and discrete. FWIW, I asked ChatGPT for some unresolved mathematical problems that might relate to this, and it came up with: The Continuum Hypothesis, The Axiom of Choice, and The Riemann Hypothesis, all of which it admitted are possibly impossible to prove because they're effectively unfalsifiable. (I also showed it this entire thread, and it agreed with your critique of my arguments, but also that every argument in the thread is unfalsifiable - and then it pointed me to the Boltzmann Brain paradox). [0] https://www.quantamagazine.org/does-time-really-flow-new-clues-come-from-a-century-old-approach-to-math-20200407/ https://www.quantamagazine.org/does-time-really-flow-new-clu...
  - 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