I don't know how Sedenions fit into the picture but "Hurwitz's theorem":http://en.wikipedia.org/wiki/Hurwitz%27s_theorem_(normed_division_algebras) http://en.wi

I don't know how Sedenions fit into the picture but "Hurwitz's theorem":http://en.wikipedia.org/wiki/Hurwitz%27s_theorem_(normed_division_algebras) http://en.wikipedia.org/wiki/Hurwitz%27s_theorem_(normed_div... may be one explanation as to why there are essentially only 1,2,4, and 8 dimensional numbers.