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> Random processes can appear to have meaningful structure, but that’s just because we value some outcomes more than others. No. It's because some structures a

> Random processes can appear to have meaningful structure, but that’s just because we value some outcomes more than others. No. It's because some structures are much much much less likely to form randomly than other structures. If you throw 1000 dices, is it possible to get all one? Yes. Is it likely? Not at all. Why do planets look like a sphere (approximately)? Because that's the most probable shape if things happen randomly. If a pyramid-shaped planet was found, scientists would freak out. This galaxy ring phenomenon is similar to that (but not that crazy).

moralestapia 2y ago
Finding ~50 dots arranged in a (very loosely defined) circle, from any projection, of a dense set of 2 trillion of them is very plausible. Actually, you would have a hard time producing this set in such way that no "circles" like that are found at all. It would have to be a very artificial distribution of points in space for you not to observe this, like all of them arranged in a single line, or a giant rectangle, idk.
- beltsazar 2y ago
  > Finding ~50 dots arranged in a (very loosely defined) circle, from any projection, of a dense set of 2 trillion of them is very plausible. It depends on the size of the circle, though. The smaller the size, the more likely the probability is. But that’s only for a particular combination of 50 dots. Now we have to average out of all possible circle sizes and all combinations of 50 dots. Can someone do the math (or the simulation)?
  - moralestapia 2y ago
    On a first glance it seems so, but ... could it be the opposite? I'm thinking, the larger the space, the larger the number of points contained within it, so the larger the probability of them being arrange in such way that blah blah ... We need a math guy to chime in. I have a hunch there may be a theorem about something like this already.
unusualmonkey 2y ago
> If you throw 1000 dices, is it possible to get all one? Yes. Is it likely? Not at all. That's literally as likely as any other possible outcome. Let's simplfy this to a coin toss, which is more likely: HHHHHH or HHTHTT or HTHTHT They all have the exact same odds of appearing, we might just tell ourselves one formation is more special than any other.
- beltsazar 2y ago
  Of course each instance has the same probability. But we're not talking about the probability of an instance, but rather that of a set of instances. In the dice example, it's obvious that the probability of getting at least one dice facing two is much more likely than the probability of getting all dice facing one. Similarly, in the planet shape example, I hope you don't think that a pyramid-shaped planet is as likely to form as a sphere-shaped planet.
  - unusualmonkey 2y ago
    Yes, a large set of instances is more likely than a single instance (all things being equal). However that doesn't mean that a sphere is any more or less likely than any specific other structure. It's an small but important distinction. No, a pyramid shaped planet is not as likely to form as a sphere shaped pyramid. Definitionally a pyramid shaped planet is impossible.
    - beltsazar 2y ago
      > However that doesn't mean that a sphere is any more or less likely than any specific other structure. A shape/structure doesn't have an intrinsic probability. Your sentence is underspecified. Shape of what under what process? In the context of the shape of galaxies, I think we can agree that if we found galaxies forming a shape like this sentence: "WE ARE COMING", everyone would freak out. So yeah, in this context, some shapes are more likely to form (randomly) than others.
      - unusualmonkey 2y ago
glandium 2y ago
> Why do planets look like a sphere (approximately)? Because that's the most probable shape if things happen randomly. That has actually nothing to do with randomness, and everything to do with gravity. https://spaceplace.nasa.gov/planets-round/en/ https://spaceplace.nasa.gov/planets-round/en/
- hughesjj 2y ago
  which, to be clear, is the exact point the parent comment is making. Randomness only favors something over noise if there is a non random process determining the structure

moralestapia 2y ago

Finding ~50 dots arranged in a (very loosely defined) circle, from any projection, of a dense set of 2 trillion of them is very plausible. Actually, you would have a hard time producing this set in such way that no "circles" like that are found at all. It would have to be a very artificial distribution of points in space for you not to observe this, like all of them arranged in a single line, or a giant rectangle, idk.

beltsazar 2y ago
> Finding ~50 dots arranged in a (very loosely defined) circle, from any projection, of a dense set of 2 trillion of them is very plausible. It depends on the size of the circle, though. The smaller the size, the more likely the probability is. But that’s only for a particular combination of 50 dots. Now we have to average out of all possible circle sizes and all combinations of 50 dots. Can someone do the math (or the simulation)?
- moralestapia 2y ago
  On a first glance it seems so, but ... could it be the opposite? I'm thinking, the larger the space, the larger the number of points contained within it, so the larger the probability of them being arrange in such way that blah blah ... We need a math guy to chime in. I have a hunch there may be a theorem about something like this already.

unusualmonkey 2y ago

> If you throw 1000 dices, is it possible to get all one? Yes. Is it likely? Not at all. That's literally as likely as any other possible outcome. Let's simplfy this to a coin toss, which is more likely: HHHHHH or HHTHTT or HTHTHT They all have the exact same odds of appearing, we might just tell ourselves one formation is more special than any other.

beltsazar 2y ago
Of course each instance has the same probability. But we're not talking about the probability of an instance, but rather that of a set of instances. In the dice example, it's obvious that the probability of getting at least one dice facing two is much more likely than the probability of getting all dice facing one. Similarly, in the planet shape example, I hope you don't think that a pyramid-shaped planet is as likely to form as a sphere-shaped planet.
- unusualmonkey 2y ago
  Yes, a large set of instances is more likely than a single instance (all things being equal). However that doesn't mean that a sphere is any more or less likely than any specific other structure. It's an small but important distinction. No, a pyramid shaped planet is not as likely to form as a sphere shaped pyramid. Definitionally a pyramid shaped planet is impossible.
  - beltsazar 2y ago
    > However that doesn't mean that a sphere is any more or less likely than any specific other structure. A shape/structure doesn't have an intrinsic probability. Your sentence is underspecified. Shape of what under what process? In the context of the shape of galaxies, I think we can agree that if we found galaxies forming a shape like this sentence: "WE ARE COMING", everyone would freak out. So yeah, in this context, some shapes are more likely to form (randomly) than others.
    - unusualmonkey 2y ago

glandium 2y ago

> Why do planets look like a sphere (approximately)? Because that's the most probable shape if things happen randomly. That has actually nothing to do with randomness, and everything to do with gravity. https://spaceplace.nasa.gov/planets-round/en/ https://spaceplace.nasa.gov/planets-round/en/

hughesjj 2y ago
which, to be clear, is the exact point the parent comment is making. Randomness only favors something over noise if there is a non random process determining the structure