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> So an infinitely long but finitely thick cylinder would have one large (along) and one small (around) dimension? Exactly. The mathematical concept behind thi

> So an infinitely long but finitely thick cylinder would have one large (along) and one small (around) dimension? Exactly. The mathematical concept behind this is the idea of compactness[0, 1]. A compact manifold always has finite volume. In the same way, a compact dimension always has finite length and this is what is meant here.[2] Note that the converse does not hold: Not every dimension of finite length is necessarily compact. (The mathematical reason being that the metric tensor could become smaller and smaller ("fade out") towards the infinite ends.) But for the purposes of talking about string theory, you can usually equate the terms "finite length/volume" and "compact". > Is "small" then always finite, but large can be large-but-finite or inifinte? Yes, "small" is always finite (compact). As for "large" dimensions, I would say that's a matter of terminology and physicists tend to not be very precise with their terminology. It can both be large-but-finite (compact) or infinite (non-compact), depending on the context. [0]: https://en.wikipedia.org/wiki/Compact_space https://en.wikipedia.org/wiki/Compact_space [1]: https://mathworld.wolfram.com/CompactManifold.html https://mathworld.wolfram.com/CompactManifold.html [2]: This is also what string theorists mean when they "compactify a dimension": They take this infinite dimension and "wrap it around" a circle (of a given circumference) and end up with a cylinder or some more complicated object (depending on what they started with).

chartpath 6y ago
We live in a numpy array.
- nine_k 6y ago
  If spacetime is indeed quantized, it's even a finite-precision array.
  - fmax30 6y ago
    > spacetime is quantized. Doesn't that just adds more evidence for us living in a simulation, and not the nice kind either. Would be interesting to see when the hardware is upgraded, physcists would suddenly discover that spacetime isn't as quantized as they initially thought.
    - codethief 6y ago
      > physcists would suddenly discover that spacetime isn't as quantized as they initially thought I don't think the majority of physicists think that spacetime is quantized. Sure, something is going to happen at the Planck scale but whether that's quantization of time and space is very much an open question.
    - simiones 6y ago
      Quantizing space and time would not necessarily make simulations simpler - just like quantizing forces actually turns out to probably make the simulation exponentially harder on a classical computer - quantum computers can be simulated by classical computers in exponential time with the best algorithms that we know of, though it is still possible that Polynomial algorithms could exist. Of course, nothing at all can actually prove/disprove that we live in a simulation in the scientific sense - it's just a transcendental model for people who don't like theistic transcendental models, but no more "scientific" than "creation science" or "the gods did it" theories.
    - cheaprentalyeti 6y ago
      It wasn't until Columbus came along that they finally bothered to move us from the "flat" default starter server to the spherical one.
      - joycian 6y ago
        No, that was already patched before Erastothenes. Some simple branch predictions based on behavior patterns of the Bronze Age civilizations were enough to get the change through management.
briefcomment 6y ago
What does it mean for a dimension to sit inside our 3 dimensions? I would assume additional dimensions would be outside of our 3, but it sounds like what we’re talking about here is just a surface inside 3d space. Why isn’t my body, or anything for that matter, considered an extra dimension in 3d space?
- codethief 6y ago
  > What does it mean for a dimension to sit inside our 3 dimensions? Could you clarify where in the video/text this is said?
  - briefcomment 6y ago
    I’m probably just grossly misinterpreting this, but it sounds like the extra dimension she mentions here is just a microscopic tube. My naive question is how does that differ from, let’s say, a microscopic piece of penne. “This problem was solved few years later by Oskar Klein, who assumed that the 4th dimension of space has to be rolled up to a small radius, so you can’t get lost in it. You just wouldn’t notice if you stepped into it, it’s too small. This idea that electromagnetism is caused by a curled-up 4th dimension of space is now called Kaluza-Klein theory.”
    - codethief 6y ago
      sdwr already explained this very well in their sibling comment: The extra dimension is another direction that you can move in, apart from the three directions you're already familiar with. A piece of penne doesn't provide you with such an extra direction because movement along the penne can still be described by a tuple of 3-dimensional position + velocity vectors.
- sdwr 6y ago
  As far as I understand, the idea is that the extra dimension is everywhere, but only has a tiny bit of wiggle room, and once you get to the end of it you come back from the other side, like a circle. It's not an object in space, it's a direction that all objects can move in. If you're standing somewhere, you can move N/S, E/W, and jump up/down. The extra dimension is another direction particles can move in, except when they do they stay in the same place, and their momentum in that non-direction works out to be the same energy as electric charge. More of a magic trick than anything else.

chartpath 6y ago

We live in a numpy array.

nine_k 6y ago
If spacetime is indeed quantized, it's even a finite-precision array.
- fmax30 6y ago
  > spacetime is quantized. Doesn't that just adds more evidence for us living in a simulation, and not the nice kind either. Would be interesting to see when the hardware is upgraded, physcists would suddenly discover that spacetime isn't as quantized as they initially thought.
  - codethief 6y ago
    > physcists would suddenly discover that spacetime isn't as quantized as they initially thought I don't think the majority of physicists think that spacetime is quantized. Sure, something is going to happen at the Planck scale but whether that's quantization of time and space is very much an open question.
  - simiones 6y ago
    Quantizing space and time would not necessarily make simulations simpler - just like quantizing forces actually turns out to probably make the simulation exponentially harder on a classical computer - quantum computers can be simulated by classical computers in exponential time with the best algorithms that we know of, though it is still possible that Polynomial algorithms could exist. Of course, nothing at all can actually prove/disprove that we live in a simulation in the scientific sense - it's just a transcendental model for people who don't like theistic transcendental models, but no more "scientific" than "creation science" or "the gods did it" theories.
  - cheaprentalyeti 6y ago
    It wasn't until Columbus came along that they finally bothered to move us from the "flat" default starter server to the spherical one.
    - joycian 6y ago
      No, that was already patched before Erastothenes. Some simple branch predictions based on behavior patterns of the Bronze Age civilizations were enough to get the change through management.

briefcomment 6y ago

What does it mean for a dimension to sit inside our 3 dimensions? I would assume additional dimensions would be outside of our 3, but it sounds like what we’re talking about here is just a surface inside 3d space. Why isn’t my body, or anything for that matter, considered an extra dimension in 3d space?

codethief 6y ago
> What does it mean for a dimension to sit inside our 3 dimensions? Could you clarify where in the video/text this is said?
- briefcomment 6y ago
  I’m probably just grossly misinterpreting this, but it sounds like the extra dimension she mentions here is just a microscopic tube. My naive question is how does that differ from, let’s say, a microscopic piece of penne. “This problem was solved few years later by Oskar Klein, who assumed that the 4th dimension of space has to be rolled up to a small radius, so you can’t get lost in it. You just wouldn’t notice if you stepped into it, it’s too small. This idea that electromagnetism is caused by a curled-up 4th dimension of space is now called Kaluza-Klein theory.”
  - codethief 6y ago
    sdwr already explained this very well in their sibling comment: The extra dimension is another direction that you can move in, apart from the three directions you're already familiar with. A piece of penne doesn't provide you with such an extra direction because movement along the penne can still be described by a tuple of 3-dimensional position + velocity vectors.
sdwr 6y ago
As far as I understand, the idea is that the extra dimension is everywhere, but only has a tiny bit of wiggle room, and once you get to the end of it you come back from the other side, like a circle. It's not an object in space, it's a direction that all objects can move in. If you're standing somewhere, you can move N/S, E/W, and jump up/down. The extra dimension is another direction particles can move in, except when they do they stay in the same place, and their momentum in that non-direction works out to be the same energy as electric charge. More of a magic trick than anything else.