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I see, so the belief is that improved theories of physics will remove all the infinities we appear to see around us? I guess as religions go, that one is no w

I see, so the belief is that improved theories of physics will remove all the infinities we appear to see around us? I guess as religions go, that one is no worse than many, but there isn't really any evidence for it now. Space looks really infinite, the hydrogen atom spectra are very well described by infinite series.

nairboon 3y ago
> will remove all the infinities we appear to see around us? Can you actually show us one of these apparent actual infinities? All one can reasonably postulate is a potential infinity, but this is completely different from Cantors actual infinities.
- eigenket 3y ago
  The spectrum of the hydrogen atom and the volume of the universe both appear to be actually infinite based on our best physical models.
  - rolisz 3y ago
    According to the Big Bang model the universe started with a super small volume. When did it get to infinity? As far as I know, we can see/measure that the universe is about 93 billion light years across. We literally can't know what's outside, so we don't know how much bigger it is or if it's infinite.
    - eigenket 3y ago
      This is a common misconception, in standard models of big-bang cosmology the universe was always infinite. It was hotter and denser earlier, and is cooler and less dense later but always infinite. A decent mental model is to think about an infinitely long ruler or measuring tape, where I have positions marked every (e.g.) 1 meter interval. You can imagine stretching or shrinking the ruler which would move the marks further or closer to each other respectively. If you think about a "cosmology" for this ruler where I keep stretching it further and further forever then the points I have marked will ger further and further away, but the ruler itself is always infinite.
      - rolisz 3y ago
        How can you prove that? We literally can't see further than 98 billion light years. How's that not also a religion? :p
        eigenket 3y ago
        That's not how physics works. We can't prove anything. All we do is come up with worse or better models, and the best model anyone has come up with so far has the universe being infinite. Finite universe models have some problems, since the global curvature of the universe is (as best we can measure) zero the universe is either flat or pretending to be flat. Finite volume flat spaces can be characterised and they're a bit weird (1). The best we can say is that if the universe is not infinite it appears to be doing a very good job of pretending to be infinite. (1) for a good idea of what "weird" means here imagine a 2d 1km by 1km square with geometry like Pac man lives in (toroidal), so if you go off the top of the square you appear at the bottom, and if you head off east you appear on the west. Now start at the middle and leave a rock at your current position. Head due east until you cycle round and hit your rock again. You'll have walked 1km (500m to the east edge and 500m from the west edge back to the middle). Now do the same experiment but walk north-east. You'll hit your rock after sqrt(2) km of walking (1/sqrt(2) takes you to the north east corner and the same to get back to your rock). In other worlds the pac-man torus space is not isotropic some angles are special and more important than others. Essentially the same thing happens in other finite flat geometries you can invent.
        rolisz 3y ago
        It's weird to you. Who says the universe must be isotropic?
        eigenket 3y ago
        I don't say it has to be isotropic, but observationally it looks very close to isotropic. There are quite clear signals we'd expect to see in the cosmic microwave background if the universe was anisotropic and they aren't there: https://arxiv.org/abs/1605.07178 https://arxiv.org/abs/1605.07178 This study is (as far as I'm aware) the state of the art on this topic, and based on the CMB observations they use it appears the universe is incredibly close to isotropic. Note that because it is based on CMB data this sort of study is sensitive to what shape the universe was a long time ago when, if it is finite, it was a lot smaller.
  - nairboon 3y ago
    > appear to be actually infinite Was it shown that the volume in this models are actually infinite or just potentially infinite?
    - eigenket 3y ago
      Could you explain how a potentially infinite universe would be different to an actually infinite one? I'm not familiar with how you're using these terms.
      - nairboon 3y ago
        I don't know what the difference would be. That's why I'm asking. These terms regained popularity due to Cantor's work. The potential infinite, is a very old idea for a process that never terminates. Like counting, you can always find a bigger natural number, by addition. Thus, the natural numbers are potentially infinite, because they grow forever, but it will never be finished. However, Cantor popularized another notion of infinity, namely that you can treat the ever growing natural numbers as one finished big bag and started doing math with this "object". Cantor's theory requires that infinity actually exists, as a finished object. Then he starts doing interesting stuff, as in measuring how many things are in the bag, even though the bag technically grows without ever stopping.
        eigenket 3y ago
        Ok, well if you come up with a definition for what a potentially infinite universe means then let me know. Until then our best models have the universe being infinite in size in the normal sense of the word.
        nairboon 3y ago
        > being infinite in size in the normal sense of the word. Well, can you maybe define what this normal sense of this word is? This is a thread about Cantor, whose whole work is based on subtle differences in the treatment of "infinity".
- mistermann 3y ago
  One example would be the infinite number of ways there are for humans to form unsound conclusions. But of course, this is not "real" reality that can be tidily corralled with math/science so it doesn't count, but it's still interesting.

nairboon 3y ago

> will remove all the infinities we appear to see around us? Can you actually show us one of these apparent actual infinities? All one can reasonably postulate is a potential infinity, but this is completely different from Cantors actual infinities.

eigenket 3y ago
The spectrum of the hydrogen atom and the volume of the universe both appear to be actually infinite based on our best physical models.
- rolisz 3y ago
  According to the Big Bang model the universe started with a super small volume. When did it get to infinity? As far as I know, we can see/measure that the universe is about 93 billion light years across. We literally can't know what's outside, so we don't know how much bigger it is or if it's infinite.
  - eigenket 3y ago
    This is a common misconception, in standard models of big-bang cosmology the universe was always infinite. It was hotter and denser earlier, and is cooler and less dense later but always infinite. A decent mental model is to think about an infinitely long ruler or measuring tape, where I have positions marked every (e.g.) 1 meter interval. You can imagine stretching or shrinking the ruler which would move the marks further or closer to each other respectively. If you think about a "cosmology" for this ruler where I keep stretching it further and further forever then the points I have marked will ger further and further away, but the ruler itself is always infinite.
    - rolisz 3y ago
      How can you prove that? We literally can't see further than 98 billion light years. How's that not also a religion? :p
      - eigenket 3y ago
        That's not how physics works. We can't prove anything. All we do is come up with worse or better models, and the best model anyone has come up with so far has the universe being infinite. Finite universe models have some problems, since the global curvature of the universe is (as best we can measure) zero the universe is either flat or pretending to be flat. Finite volume flat spaces can be characterised and they're a bit weird (1). The best we can say is that if the universe is not infinite it appears to be doing a very good job of pretending to be infinite. (1) for a good idea of what "weird" means here imagine a 2d 1km by 1km square with geometry like Pac man lives in (toroidal), so if you go off the top of the square you appear at the bottom, and if you head off east you appear on the west. Now start at the middle and leave a rock at your current position. Head due east until you cycle round and hit your rock again. You'll have walked 1km (500m to the east edge and 500m from the west edge back to the middle). Now do the same experiment but walk north-east. You'll hit your rock after sqrt(2) km of walking (1/sqrt(2) takes you to the north east corner and the same to get back to your rock). In other worlds the pac-man torus space is not isotropic some angles are special and more important than others. Essentially the same thing happens in other finite flat geometries you can invent.
        rolisz 3y ago
        It's weird to you. Who says the universe must be isotropic?
        eigenket 3y ago
        I don't say it has to be isotropic, but observationally it looks very close to isotropic. There are quite clear signals we'd expect to see in the cosmic microwave background if the universe was anisotropic and they aren't there: https://arxiv.org/abs/1605.07178 https://arxiv.org/abs/1605.07178 This study is (as far as I'm aware) the state of the art on this topic, and based on the CMB observations they use it appears the universe is incredibly close to isotropic. Note that because it is based on CMB data this sort of study is sensitive to what shape the universe was a long time ago when, if it is finite, it was a lot smaller.
- nairboon 3y ago
  > appear to be actually infinite Was it shown that the volume in this models are actually infinite or just potentially infinite?
  - eigenket 3y ago
    Could you explain how a potentially infinite universe would be different to an actually infinite one? I'm not familiar with how you're using these terms.
    - nairboon 3y ago
      I don't know what the difference would be. That's why I'm asking. These terms regained popularity due to Cantor's work. The potential infinite, is a very old idea for a process that never terminates. Like counting, you can always find a bigger natural number, by addition. Thus, the natural numbers are potentially infinite, because they grow forever, but it will never be finished. However, Cantor popularized another notion of infinity, namely that you can treat the ever growing natural numbers as one finished big bag and started doing math with this "object". Cantor's theory requires that infinity actually exists, as a finished object. Then he starts doing interesting stuff, as in measuring how many things are in the bag, even though the bag technically grows without ever stopping.
      - eigenket 3y ago
        Ok, well if you come up with a definition for what a potentially infinite universe means then let me know. Until then our best models have the universe being infinite in size in the normal sense of the word.
        nairboon 3y ago
        > being infinite in size in the normal sense of the word. Well, can you maybe define what this normal sense of this word is? This is a thread about Cantor, whose whole work is based on subtle differences in the treatment of "infinity".
mistermann 3y ago
One example would be the infinite number of ways there are for humans to form unsound conclusions. But of course, this is not "real" reality that can be tidily corralled with math/science so it doesn't count, but it's still interesting.