chimp
Member
Member # 333
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posted 09. February 2004 03:31
Any smooth connected 1 dimensional manifold is diffeomorphic either to the circle, or to some interval of real numbers.
Take a line segment of length 1. It is one dimensional.
A-------B
Find the midpoint of the line segment and rotate it into 2 dimensions
A
|
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|------B
Each leg is 1/2
Rotate into 3 dimensions, and each leg is 1/3
A
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|
|------C
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B
rotate into N dimensions and each leg is 1/N
Continue this process as a limit
N---->oo
By the above process, an infinite dimensional universe is a point.
[ 09. February 2004, 03:32: Message edited by: Russell E. Rierson ]
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