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I wondered that for a long time myself and recently stumbled on what I believe is (or at least is a good candidate for) the correct answer: planetary orbits are

by lisper 5y ago

I wondered that for a long time myself and recently stumbled on what I believe is (or at least is a good candidate for) the correct answer: planetary orbits are stable in three dimensions, but not any other dimensions. The anthropic principle therefore selects for three-dimensional slices/subsets of the wave function.

guerrilla 5y ago
They're really not stable in two dimensions? Hmm [1], and another answer [2] (mentioned by Hawking apparently) but that's less convincing since there could be a 2D universe with intelligent organisms that just have their digestive systems on the outside... 1. https://www.reddit.com/r/askscience/comments/q8fmo/what_would_orbits_look_like_in_a_2d_universe/ https://www.reddit.com/r/askscience/comments/q8fmo/what_woul... 2. http://ion.uwinnipeg.ca/~vincent/4500.6-001/Cosmology/2-D_Digestion.gif http://ion.uwinnipeg.ca/~vincent/4500.6-001/Cosmology/2-D_Di...
- chaxor 5y ago
  Right hand rule only works in 3d and 7d
  - lordnacho 5y ago
    That is rather fascinating, where can I read about this?
    - octoberfranklin 5y ago
      In the early chapters of the Feynman Lectures on Physics (volume II) there is a really good explanation of why cross product and curl make absolutely no sense in more than three dimensions. The fact that they can be defined unambiguously is a complete accident which occurs only in three dimensions. Not sure if this is what GP was talking about. But the explanation there is excellent. It's in the chapter where curl is introduced for the first time. After you read it, you'll get annoyed whenever you see curls or cross products. Also: https://en.wikipedia.org/wiki/Seven-dimensional_cross_product https://en.wikipedia.org/wiki/Seven-dimensional_cross_produc...
    - ogogmad 5y ago
      Given a cross product in n dimensions, it's possible to construct a normed division algebra in n+1 dimensions. Hurwitz's theorem says that the only normed division algebras are the reals, complexes, quaternions and octonions. So there can be no cross products outside of 0, 1, 3 and 7 dimensions. In computing applications, if you want to find a vector perpendicular to two or more vectors outside of 3 and 7 dimensions, you would use the QR decomposition to do it. If on the other hand, you want to generalise the "directed area" properties of the cross product, you would use Exterior Algebra, or its elaborations like Clifford Algebra or the theory of differential forms.
- lisper 5y ago
  > They're really not stable in two dimensions? Stable is not really the right word. "Well behaved" is better. In 2D all orbits are stable in the sense that escape velocity is infinite, but a consequence of that is that you don't naturally get nice (nearly) circular orbits that keep planets in habitable zones. That only happens in 3D.
desmosxxx 5y ago
Actually in 2d they are but there are other problems in 2D. There are actually quite a few special properties of 3D+1 interesting reading https://en.m.wikipedia.org/wiki/Anthropic_principle#Dimensions_of_spacetime https://en.m.wikipedia.org/wiki/Anthropic_principle#Dimensio...
pontus 5y ago
Anthropic arguments only work if there's a mechanism for generating other versions besides the one you're observing. For example, you could use the anthropic argument to explain why earth is in the "goldilocks zone" because there are plenty other planets out there at varying distances from their sun. So, if you want to make the argument that 3d is preferred for some reason you need to acknowledge that there are other universes out there with 2d, 4d, etc that just can't sustain life and that therefore life only finds itself in the subset of universes that have three dimensions.
- guerrilla 5y ago
  > So, if you want to make the argument that 3d is preferred for some reason you need to acknowledge that there are other universes out there with 2d, 4d, etc that just can't sustain life and that therefore life only finds itself in the subset of universes that have three dimensions. Or you can make the argument that no other universes other than a 3D one can support life, i.e. that 3D is necessary for life. Then you can conclude if life, then 3D.
  - pontus 5y ago
    I disagree. If there really is only one universe which is 3D, this argument does not in any way explain why it is 3D. If you use Bayesian probability, you would in this case start with p(3d) = 1 since there's only one universe which is 3d and then end with p(3d | life) = 1. In other words, there's no explanatory power in the observation that there's life. If instead you say that p(3d) = 1/1000 because maybe the multiverse has all sorts universes out there but you also say that life is only possible in 3d, i.e. p(life | 3d) > 0, but p(life | not 3d) = 0, then you go from p(3d) = 1/1000 to p(3d | life) = 1. In other words, the observation of life does have explanatory power.
    - GoblinSlayer 5y ago
      When you assume 3D, there's no need to explain it, because it's assumed from the start. 3D needs to be explained if it's not assumed.

by lisper 5y ago

guerrilla 5y ago

They're really not stable in two dimensions? Hmm [1], and another answer [2] (mentioned by Hawking apparently) but that's less convincing since there could be a 2D universe with intelligent organisms that just have their digestive systems on the outside... 1. https://www.reddit.com/r/askscience/comments/q8fmo/what_would_orbits_look_like_in_a_2d_universe/ https://www.reddit.com/r/askscience/comments/q8fmo/what_woul... 2. http://ion.uwinnipeg.ca/~vincent/4500.6-001/Cosmology/2-D_Digestion.gif http://ion.uwinnipeg.ca/~vincent/4500.6-001/Cosmology/2-D_Di...

chaxor 5y ago
Right hand rule only works in 3d and 7d
- lordnacho 5y ago
  That is rather fascinating, where can I read about this?
  - octoberfranklin 5y ago
    In the early chapters of the Feynman Lectures on Physics (volume II) there is a really good explanation of why cross product and curl make absolutely no sense in more than three dimensions. The fact that they can be defined unambiguously is a complete accident which occurs only in three dimensions. Not sure if this is what GP was talking about. But the explanation there is excellent. It's in the chapter where curl is introduced for the first time. After you read it, you'll get annoyed whenever you see curls or cross products. Also: https://en.wikipedia.org/wiki/Seven-dimensional_cross_product https://en.wikipedia.org/wiki/Seven-dimensional_cross_produc...
  - ogogmad 5y ago
    Given a cross product in n dimensions, it's possible to construct a normed division algebra in n+1 dimensions. Hurwitz's theorem says that the only normed division algebras are the reals, complexes, quaternions and octonions. So there can be no cross products outside of 0, 1, 3 and 7 dimensions. In computing applications, if you want to find a vector perpendicular to two or more vectors outside of 3 and 7 dimensions, you would use the QR decomposition to do it. If on the other hand, you want to generalise the "directed area" properties of the cross product, you would use Exterior Algebra, or its elaborations like Clifford Algebra or the theory of differential forms.
lisper 5y ago
> They're really not stable in two dimensions? Stable is not really the right word. "Well behaved" is better. In 2D all orbits are stable in the sense that escape velocity is infinite, but a consequence of that is that you don't naturally get nice (nearly) circular orbits that keep planets in habitable zones. That only happens in 3D.

desmosxxx 5y ago

Actually in 2d they are but there are other problems in 2D. There are actually quite a few special properties of 3D+1 interesting reading https://en.m.wikipedia.org/wiki/Anthropic_principle#Dimensions_of_spacetime https://en.m.wikipedia.org/wiki/Anthropic_principle#Dimensio...

pontus 5y ago

Anthropic arguments only work if there's a mechanism for generating other versions besides the one you're observing. For example, you could use the anthropic argument to explain why earth is in the "goldilocks zone" because there are plenty other planets out there at varying distances from their sun. So, if you want to make the argument that 3d is preferred for some reason you need to acknowledge that there are other universes out there with 2d, 4d, etc that just can't sustain life and that therefore life only finds itself in the subset of universes that have three dimensions.

guerrilla 5y ago
> So, if you want to make the argument that 3d is preferred for some reason you need to acknowledge that there are other universes out there with 2d, 4d, etc that just can't sustain life and that therefore life only finds itself in the subset of universes that have three dimensions. Or you can make the argument that no other universes other than a 3D one can support life, i.e. that 3D is necessary for life. Then you can conclude if life, then 3D.
- pontus 5y ago
  I disagree. If there really is only one universe which is 3D, this argument does not in any way explain why it is 3D. If you use Bayesian probability, you would in this case start with p(3d) = 1 since there's only one universe which is 3d and then end with p(3d | life) = 1. In other words, there's no explanatory power in the observation that there's life. If instead you say that p(3d) = 1/1000 because maybe the multiverse has all sorts universes out there but you also say that life is only possible in 3d, i.e. p(life | 3d) > 0, but p(life | not 3d) = 0, then you go from p(3d) = 1/1000 to p(3d | life) = 1. In other words, the observation of life does have explanatory power.
  - GoblinSlayer 5y ago
    When you assume 3D, there's no need to explain it, because it's assumed from the start. 3D needs to be explained if it's not assumed.