## Friday, February 02, 2007

### I thought this one goes up to eleven

One of the more intelligent sorts of mathematical questions I've been asked are those on the nature of higher dimensions. Somewhere in our pop history it was decided that since we lived in the third dimension, there should be others, like so many arrondissement. These are usually just three-dimensional spaces where things are wacky, not the fundamentally larger spaces they ought to be. In fact, some authors believed they could exchange dimensions for vowels.

It's at once refreshing and disappointing to see an exposition such as this. The animation and sound are lovely, and a rather decent volley is made at the concepts of "splits" and "folds", even if the subtle beauty in the relationship and differences between these is largely ignored. However, the narrator suggests that each "dimension" has some inherent parameters defining it, such as "the seventh dimension" being the space of all possible outcomes from the origin of the universe, and similarly pinning the notion of "split" and "fold" only to certain dimensions.

Do you want to see ten-dimensional space? Here it is:

$(x_0,x_1,x_2,x_3,x_4,x_5,x_6,x_7,x_8,x_9)\;:\;x_i\in\mathbb{F}$

Anyway, isn't supersymmetry supposed to be eleven-dimensional? Or does 11-D SUSY refer to a women named Susan with an impossibly small ribcage?