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You could build a hypercube in 3D, so why is it in 4D?

I thought the fourth dimension was time.

2007-07-31 06:18:35 · 4 answers · asked by M.strom 3 in Science & Mathematics Physics

4 answers

The hypercube is a 4 dimensional object which means that it's geometry requires 4 dimensions to exist. The hypercube in 3D is just a projection of this 4 dimensional object (like a 2D picture of a 3D cube would be).

The order of the dimensions doesn't matter. There isn't a particular dimension that's Number 4. We live in 3D space which means we have length, breadth & depth (as you know). These 3 dimensions, call them dimensions 1, 2 & 3, can be taken in any order. For example, if we're looking at a cube there is no Dimension Number 1, Number 2, and Number 3; they just all muck in together.

If we have a 2D sheet (a plane) and want to make it into a cube we need to add things to it in the 3rd dimension to give it depth. In just the same way we can (theoretically) add things to the cube in the 4th dimension to make it into a hypercube. When we're talking about a hypercube then the next dimension that it makes sense to refer to is a further dimension of space. If we're talking about the way we experience the world then the next dimension that it makes sense to refer to is a dimension of time.

I don't think that the dimensions of space & time are different from each other. We're just limited in the way we can move through the dimension we call time. (Someone once suggested to me that in Einstein's equations the time dimension was expressed slightly differently but I don't know if this is true.)

I suppose, theoretically, a hypercube could exist which used time as it's 4th dimension (length, breadth, depth, and "hyperdepth" where "hyperdepth" stretched out through time). We'd see cross sections of it as we passed through it on our journey through time (at a speed of one second per second), then it would disappear into the past forever!

Hope all that helps (and makes sense)!

2007-07-31 06:59:22 · answer #1 · answered by SolarFlare 6 · 2 0

You can't really build a hypercube in the 3-D world. You can build a sort of model of it, or a crude representation of it, but not an actual hypercube.

The same holds for a Klein bottle and other impossible objects.

2007-07-31 13:43:42 · answer #2 · answered by mikeburns55 5 · 0 0

A hypercube is 4 dimensional because that's how it is defined. You can draw a cube and a hypercube on a piece of paper, but they're not really cubes or hypercubes because the pictures are two-dimensional.

2007-07-31 13:45:01 · answer #3 · answered by Benjamin K 2 · 1 0

There are theoretically more than 4 dimensions. So it doesnt really matter which one you call #4. IF theres 23 dimensions and we typically observe only 3, then you add in movemnt in the 17th dimension, you would still only observe 4 dimensions even though all 23 were there, just the value of the rest would be zero.

2007-07-31 13:26:38 · answer #4 · answered by billgoats79 5 · 0 0

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