Friday, March 25, 2011

The Curse of Dimensionality

Picture this..
say you have a square.. Perfectly flat.
2D cube

Now say you take that square and make it 3D perhaps not a cube, but just a tiny bit of height too it.. maybe a paper cut out of a square.
3D Cube projected in wire lay out

That square now has more weight (relative) and mass than the 2D square.

The same happens going from 1D to 2D and 3D to 4D, every time you add a dimension. You add mass to the object.
4D cube in wire layout

5D cube in wire layout

This is problematic because when you are talking about a multidimensional existence (parallel universes and such)
Different universes will have different perceived weight due to their increased mass.
11D cube

Now say all dimensions appear universally but we cannot perceive any but 2 and 3 then the universe would have infinite mass as mass increases every time you add on a new dimension.

and it would have virtually no middle as 1D and 0D are imperceivable too the human mind.. BUT HANG ON, I hear you say.. You can perceive 1D..

Well no you can't sorry to say..

Imagine the smallest thing you can think of, thats 3D..
Tiniest flattest thing... Well its 3D too, everything we can perceive is 3D, accept when we look at something displayed upon something..

For example the image on your computer monitor is 2D.. The monitor is 3D the pixels are 3D but what you are viewing is a 2D image..
We can perceive this because it has length and height..

But if you take away either of these it would not be a straight line, because even a straight line has some height or some width, it would be an infinitly receding point in existence, being ever smaller than is capable.. Thus it is out of our knowledge to perceive it.

Thought you might find some geometry interesting on this the day of the NSW State election!

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