Why 5, 8 and 24 Are The Most Interesting Numbers

Warning, this is beyond me, but interesting none the less (via Mark Thoma):

In the May 2011 issue of Scientific American mathematician John Baez co-authors "The Strangest Numbers in String Theory," an article about the octonions, an eight-dimensional number system that was discovered in the mid–19th century but that has been largely ignored until quite recently. As the name of the article implies, interest in the octonions has been rekindled by their surprising relationship to recent developments in theoretical physics, including supersymmetry, string theory and M-theory. Baez and his co-author John Huerta wrote, "If string theory is right, the octonions are not a useless curiosity; on the contrary, they provide the deep reason why the universe must have 10 dimensions: in 10 dimensions, matter and force particles are embodied in the same type of numbers—the octonions."

There's more there, including references to sphere stacking and the golden ratio.  I'm sure I can't understand much any of this, but when I get a spare hour, I'll try to watch the lecture.