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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

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.

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.