How can an extra dimensions have finite lengths?

Question

All other dimensions we can move through seem infinite in their respective directions, but in explaining string theory i see scientists explain how there could be other dimensions that exist curled up, but they are too small to be seen. But no matter small they are, if we can see it wouldn't that just make that dimension a very small 3 dimensional object? Also, in M theory, an 11th dimension was proposed that was a membrane just like our universe, only it had a very small length. ALl of our dimensions are infinite in their directions, so how can further dimensions by restricted?

Answer 1

First of all restricted and finite do not mean the same thing. For example, take a ruler in your hand. It is restricted (e.g. 30 cm). But it has infinite number of points on it. Therefore, something can be restricted and infinite at the same time. What are the possibilities:
a) restiricted, finite
b) restricted, infinite
c) un-restricted, infinite

Actually there are more possbilities but I do not want to go into detail. Refer to a university level mathematics book on the topic real analysis.

Answer 2

Tough question. A complete answer to this would be way beyond the scope of Yahoo Answers. I'll give the conventional "short" explanation, without tackling the difficult mathematics.

Here is an analogy: Picture the surface of a garden hose. That surface is 2-dimensional. However, it is different from the 2-dimensional space that is the subject of plane geometry. The garden hose surface has one dimension that extends for a long distance, and another dimension that is "curled" up. Consider this from the point of view of an ant crawling along the surface of the garden hose. If you crawl around the circumference of the hose, you quickly return to your starting point. But, if you crawl in a different direction, along the length of the hose, you find that you can go a long, long way without returning to the starting point.

Now, consider the garden hose from a human perspective. If you look at the hose from 100 feet away, it appears to be 1-dimensional. It looks just like a curved line, because you can't percieve it's width from that distance. The second dimension of the hose becomes insignificant when viewed on that scale.

Higher dimensional spaces can also behave in this way. They may be tightly curled in some directions, and still be quite flat in other directions. The situation can become quite complex, because a higher dimensional space has many more than just 2 orthogonal directions to worry about.

If you want to explore further, investigate the subject of differentiable manifolds. But, prepare to be confused, because it is very technical.

Answer 3

What of the thought of relativity, and of bending area? additionally, treating area and time as dimensions must be seen. Time isn't possibly countless because it exists in basic terms as a potential of explaining a circumstance of residing. additionally, if that weren't actual, time could in basic terms exist via fact the commencing up of the Universe. subsequently, at the same time as time could "circulate on" infinetly, at any given 2d that's finite - stretching from the commencing up of the Universe, until finally understand. Why no longer ask if time could exist if guy become no longer alive?