Q:

I've read that our universe is thought to be flat (as opposed to spherical or saddle-shaped), but the representation of our universe as a sheet (as I've seen it in books) is spatially two-dimensional. If our universe has three spatial dimensions, then why is our universe depicted as a spatially two-dimensional sheet? Also if you were on that sheet, what would happen if you tried to move along the "z-axis" of the sheet (as opposed to along the "y-axis" or "x-axis" of the sheet), and therefore move off the sheet (i.e. below the sheet or above the sheet)?
Thank you,
Brian

- Brian F. (age 24)

Bethesda, MD, U.S.A.

- Brian F. (age 24)

Bethesda, MD, U.S.A.

A:

Those pictures use 2-D images because

1. They're printed on 2-D paper

2. In order to picture curvature to our limited Euclidean imaginations, it helps to picture a non-Euclidean space imbedded in a higher dimensional Euclidean space. So that means you use 2-D images of things in 3-D space just to convey the ideas of how our 3-D (+time) space behaves.

The only directions that really exist are within the space. The other directions are just left over from trying to picture the curvature, whose definition is really internal to the space. Only the picture involves the other dimensions, just as a somewhat misleading visual aid.

Mike W.

1. They're printed on 2-D paper

2. In order to picture curvature to our limited Euclidean imaginations, it helps to picture a non-Euclidean space imbedded in a higher dimensional Euclidean space. So that means you use 2-D images of things in 3-D space just to convey the ideas of how our 3-D (+time) space behaves.

The only directions that really exist are within the space. The other directions are just left over from trying to picture the curvature, whose definition is really internal to the space. Only the picture involves the other dimensions, just as a somewhat misleading visual aid.

Mike W.

*(published on 10/19/2011)*