3 ms·

You deal with 4 dimensions all the time -- up-down, left-right, forward-back, future-past. In reality, you deal with high dimensional objets all the time: the

You deal with 4 dimensions all the time -- up-down, left-right, forward-back, future-past. In reality, you deal with high dimensional objets all the time: the position you're in is composed of dozens to hundreds of muscles rotating a few dozen joints. We're fascinated by vision, but proprioception is where it's at if you want to think in high dimensions.

thaumasiotes 9y ago
An easy way to imagine a 4-dimensional structure is to associate every point in 3-space with a color or a temperature. Your mental visualization processes should have no trouble with that. But the system quickly breaks down; the imitation fourth dimension is not in the same class as the other three. You can easily visualize a three-dimensional object rotating around a line in 3-space, or a two-dimensional object rotating around a point in 2-space, or a two-dimensional object rotating around a line in 3-space. Try applying that process to a "three spatial dimensions plus one color dimension" model and you'll notice you have no idea what color a point should be in the rotated object. (You might think it should be the same color as it was before the rotation, but that's just as wrong as saying that if you rotate a point in 2-space 30 degrees around the origin, it should end up with the same x-coordinate that it started with.) Proprioception is deeply tied to a three-dimensional conception of space -- that is how you perceive its output. And the evidence is not strong that it is a function of muscle activation, since it will work just as well if you relax while someone else moves your hand around.
- SomeStupidPoint 9y ago
  That's why I used time not color: you have an inherent notion of what it means to move things along that axis. Your point about color also doesn't quite hold -- it's easy enough to map the rainbow colors to rotation. It obviously takes practice, but it's not hard. (Helps to start with two spatial and a color.) And of course it's tied to 3 dimensional space -- the whole point is to couple the correspondence between a high dimensional phase space and a blob in 3 dimensions. But you do have an awareness of the phase space, not just the 3D location -- and you can use it to think about higher dimensional objects.
  - thaumasiotes 9y ago
    I don't think my inherent sense of what it means for a point to move forward or backward in time is much different from my inherent sense of what it means for a point to get lighter or darker. Neither will help with a spatial rotation.

thaumasiotes 9y ago

An easy way to imagine a 4-dimensional structure is to associate every point in 3-space with a color or a temperature. Your mental visualization processes should have no trouble with that. But the system quickly breaks down; the imitation fourth dimension is not in the same class as the other three. You can easily visualize a three-dimensional object rotating around a line in 3-space, or a two-dimensional object rotating around a point in 2-space, or a two-dimensional object rotating around a line in 3-space. Try applying that process to a "three spatial dimensions plus one color dimension" model and you'll notice you have no idea what color a point should be in the rotated object. (You might think it should be the same color as it was before the rotation, but that's just as wrong as saying that if you rotate a point in 2-space 30 degrees around the origin, it should end up with the same x-coordinate that it started with.) Proprioception is deeply tied to a three-dimensional conception of space -- that is how you perceive its output. And the evidence is not strong that it is a function of muscle activation, since it will work just as well if you relax while someone else moves your hand around.

SomeStupidPoint 9y ago
That's why I used time not color: you have an inherent notion of what it means to move things along that axis. Your point about color also doesn't quite hold -- it's easy enough to map the rainbow colors to rotation. It obviously takes practice, but it's not hard. (Helps to start with two spatial and a color.) And of course it's tied to 3 dimensional space -- the whole point is to couple the correspondence between a high dimensional phase space and a blob in 3 dimensions. But you do have an awareness of the phase space, not just the 3D location -- and you can use it to think about higher dimensional objects.
- thaumasiotes 9y ago
  I don't think my inherent sense of what it means for a point to move forward or backward in time is much different from my inherent sense of what it means for a point to get lighter or darker. Neither will help with a spatial rotation.