Search All of the Math Forum:

Views expressed in these public forums are not endorsed by NCTM or The Math Forum.

Notice: We are no longer accepting new posts, but the forums will continue to be readable.

Topic: Negative, Complex Dimensions
Replies: 7   Last Post: Aug 10, 2001 3:11 AM

 Messages: [ Previous | Next ]
 Earthlink News Posts: 18 Registered: 12/13/04
Re: Negative, Complex Dimensions
Posted: Aug 9, 2001 7:54 PM

"Alexander Sheppard" <alex1s1emc22@icqmail.com> wrote in message
news://2wfpuk1ecemg@forum.mathforum.com...
> Are there any definitions for negative or complex dimensions?
>

I've never seen anything involving complex dimensions but if you want you
can *sort of* extend
dimensions into the negatives, consider the following analogy:

If you take a point (0D) and extend it a finite distance in 1-space, you
find a line segment.
If you take a line segment and extend it a finite distance in 2-space,
you find a square.
If you take a square and extend it a finite distance in 3-space, you
find a cube.
If you take a cube and extend it a finite distance in 4-space, you find
a tesseract.

This process can be repeated forever. What if we look at it in the opposite
direction? In some
negative dimensional space, there must (loosely using the word "must" here)
exist some -1
dimensional that when extended a finite distance, you arrive at a point.
This is almost impossible
to visualize, even harder than high dimensions like a 15D hypercube.
However, here's the way
I would visualize it: think of a point as the basic unit for all zero and
positive dimensions. You
can form the analogy to the atom. Now, think of the
electrons/protons/neutrons as the -1 dimensional
objects (for the purposes here, I'll just call them -1-points). They're like
little strings that when
all hooked together we get a 0D point. To extend it into -2 dimensions,
think of -2-points as little
quark-like strings that hook together into a -1-point.

However, complex dimensions (as far as I can see) serve no real purpose.
Maybe in the future there
will be some field of math which grows around them.

-- Entropix

Date Subject Author
8/8/01 Alex S.
8/9/01 Twisted Topologist
8/9/01 Jonathan Hoyle
8/9/01 Russell Harper
8/9/01 Leroy Quet