why three dimensions?

Why are there three dimensions of space?
Maybe you trust me about one dimension of time. That would follow from causality.
Now imagine: what is time to me is space to you. It's the question of the point of view. I have mine and you have yours, but both are equivalent.
Now imagine cells in time-like manner arranged, and you have only one dimension. There are neighbours that have their own arrangement of 'kids' in the same manner. The neighbouring cells are the evils and your own 'childes' are the good ones.
Now *any* direction through this arrangement must have these properties. There is only one topology with this features, the anti commutative ring of quaternions.
Those quaternion cells have three neighbours (what are our three spatial dimensions). But all those cells are of the same kind, only the definitions of time and space are different. Only quaternions you can arrange in such a way, that my time is your space.

http://docs.google.com/Presentation?id=dd8jz2tx_3gfzvqgd6

Thomas Heger

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