6 ms·

I've always liked these kinds of questions. Myself, I always wondered why specifically three dimensions. (Please don't start telling me about string theory.)

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.
cblconfederate 5y ago
you mean 4, or 11, or 26
- quickthrower2 5y ago
  Or 1 with spooky action at a distance
jiggawatts 5y ago
String theory is just intellectual wankery at this point. However, a more interesting and much simpler variation has just 5 dimensions, and was seriously studied by Einstein: https://en.wikipedia.org/wiki/Kaluza%E2%80%93Klein_theory https://en.wikipedia.org/wiki/Kaluza%E2%80%93Klein_theory
- alfiedotwtf 5y ago
  Thanks for the link, TIL. So given: > In 1926, Oskar Klein proposed that the fourth spatial dimension is curled up in a circle of a very small radius, so that a particle moving a short distance along that axis would return to where it began. The distance a particle can travel before reaching its initial position is said to be the size of the dimension. I've read many times that the shape of the universe could be a loop i.e if you traveled in one direction, over a long period you could possible loop to your starting point. From that pasted from Wikipedia, in a looped-shaped universe, would that be the size of the dimension of the universe you just traveled?
pontus 5y ago
I know you explicitly asked for non-string theory answers, but I have to give one anyway -- sorry! There's an argument in string theory called the brandenberger-vafa mechanism that I think is pretty clever: Imagine that a bunch of particles and antiparticles travel along in one dimension. Because they can't spread out, they'll eventually collide and annihilate. However in 2d that's not the case: they're more likely to just miss each other all the time. If you increase the dimension of the "particles" to strings, you can make a similar argument. In 2 (compactified) dimensions, strings will find each other but not in three. Then if you start with some compactified space of 10d with a bunch of strings wrapped around various 2d subspaces, they will naturally constrain that space so that it can't expand. However, as strings move around randomly they'll tend to collide and unravel, allowing various 2d subspaces to cease being constrained and therefore expand. If you analyze this carefully you can show that in fact three of the spatial dimensions will tend to expand while the six remaining ones will remain compactified.
- posterboy 5y ago
  > Imagine that a bunch of particles and antiparticles travel along in one dimension. Haha, thank you, hahaha, but no, thank you very much. > If you analyze this carefully you can show that in fact three of the spatial dimensions will tend to expand while the six remaining ones will remain compactified. While 1 is the domain of time, I pressume. Actually though, the universe is flat spread out, as is the surface of the earth, so the vertical axis, ie. gravity, also needs explained for the human experience to make sense. There are these types of questions like why is my right arm the left arm in the mirror but the head stays up? I forgot the canonical answer but it's evidently the case that the brain automatically creates a recibrocal to the mirror image which denies the fact that the "left" arm is still on your right side.
  - messe 5y ago
    > I forgot the canonical answer but it's evidently the case that the brain automatically creates a recibrocal to the mirror image which denies the fact that the "left" arm is still on your right side. Generally the argument goes as follows: the mirror doesn't invert left and right. The image of your right arm is still on the right hand side of the image, just like your head remains at the top of the image. Instead it just inverts front and back.
deleted 5y ago
[deleted]
platz 5y ago
Scotts question is better because it asks to explain why the universe as we see it needs QM. Your question is unbounded because you're asking us to imagine an alternative that doesn't exist; there could be infinitely many reasons because there could be infinitely many alternative possibilities you're asking us to imagine with no constaints
deleted 5y ago
[deleted]
Rury 5y ago
Seems like part of the question is missing. Why specifically three dimensions of what? Dimension means: a measurable aspect of something; and it's a conceptual tool we use for things. If we're talking space (defined as a continuous area or expanse which is free, available, or unoccupied), we can define and measure length, width, height. So 3 dimensions. If we're talking area, 2 dimensions. If we're talking universe, we can measure aspects of other phenomenon (such as relative movement of objects). You could combine it with space, and could say we live in a 4 dimensional universe, 3 comprising space, 1 time... and call it: spacetime. Do 4 dimensions accurately model all that's observable in the universe? That depends on what you consider as the necessary aspects that make up the universe. Anyhow, in short, why 3 dimensions? Because it can be modeled that way and seemingly makes for a good model.

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.

cblconfederate 5y ago

you mean 4, or 11, or 26

quickthrower2 5y ago
Or 1 with spooky action at a distance

jiggawatts 5y ago

String theory is just intellectual wankery at this point. However, a more interesting and much simpler variation has just 5 dimensions, and was seriously studied by Einstein: https://en.wikipedia.org/wiki/Kaluza%E2%80%93Klein_theory https://en.wikipedia.org/wiki/Kaluza%E2%80%93Klein_theory

alfiedotwtf 5y ago
Thanks for the link, TIL. So given: > In 1926, Oskar Klein proposed that the fourth spatial dimension is curled up in a circle of a very small radius, so that a particle moving a short distance along that axis would return to where it began. The distance a particle can travel before reaching its initial position is said to be the size of the dimension. I've read many times that the shape of the universe could be a loop i.e if you traveled in one direction, over a long period you could possible loop to your starting point. From that pasted from Wikipedia, in a looped-shaped universe, would that be the size of the dimension of the universe you just traveled?

pontus 5y ago

I know you explicitly asked for non-string theory answers, but I have to give one anyway -- sorry! There's an argument in string theory called the brandenberger-vafa mechanism that I think is pretty clever: Imagine that a bunch of particles and antiparticles travel along in one dimension. Because they can't spread out, they'll eventually collide and annihilate. However in 2d that's not the case: they're more likely to just miss each other all the time. If you increase the dimension of the "particles" to strings, you can make a similar argument. In 2 (compactified) dimensions, strings will find each other but not in three. Then if you start with some compactified space of 10d with a bunch of strings wrapped around various 2d subspaces, they will naturally constrain that space so that it can't expand. However, as strings move around randomly they'll tend to collide and unravel, allowing various 2d subspaces to cease being constrained and therefore expand. If you analyze this carefully you can show that in fact three of the spatial dimensions will tend to expand while the six remaining ones will remain compactified.

posterboy 5y ago
> Imagine that a bunch of particles and antiparticles travel along in one dimension. Haha, thank you, hahaha, but no, thank you very much. > If you analyze this carefully you can show that in fact three of the spatial dimensions will tend to expand while the six remaining ones will remain compactified. While 1 is the domain of time, I pressume. Actually though, the universe is flat spread out, as is the surface of the earth, so the vertical axis, ie. gravity, also needs explained for the human experience to make sense. There are these types of questions like why is my right arm the left arm in the mirror but the head stays up? I forgot the canonical answer but it's evidently the case that the brain automatically creates a recibrocal to the mirror image which denies the fact that the "left" arm is still on your right side.
- messe 5y ago
  > I forgot the canonical answer but it's evidently the case that the brain automatically creates a recibrocal to the mirror image which denies the fact that the "left" arm is still on your right side. Generally the argument goes as follows: the mirror doesn't invert left and right. The image of your right arm is still on the right hand side of the image, just like your head remains at the top of the image. Instead it just inverts front and back.

deleted 5y ago

[deleted]

platz 5y ago

Scotts question is better because it asks to explain why the universe as we see it needs QM. Your question is unbounded because you're asking us to imagine an alternative that doesn't exist; there could be infinitely many reasons because there could be infinitely many alternative possibilities you're asking us to imagine with no constaints

deleted 5y ago

[deleted]

Rury 5y ago

Seems like part of the question is missing. Why specifically three dimensions of what? Dimension means: a measurable aspect of something; and it's a conceptual tool we use for things. If we're talking space (defined as a continuous area or expanse which is free, available, or unoccupied), we can define and measure length, width, height. So 3 dimensions. If we're talking area, 2 dimensions. If we're talking universe, we can measure aspects of other phenomenon (such as relative movement of objects). You could combine it with space, and could say we live in a 4 dimensional universe, 3 comprising space, 1 time... and call it: spacetime. Do 4 dimensions accurately model all that's observable in the universe? That depends on what you consider as the necessary aspects that make up the universe. Anyhow, in short, why 3 dimensions? Because it can be modeled that way and seemingly makes for a good model.