Supersymmetry and Division Algebras

There's a surprising connection between supersymmetry , a hot topic in theoretical physics, and division algebras: the real, complex, quaternion and octonion number systems. Supersymmetry only works in 3,4,6 and 10 space time dimensions. That's because there's a cute little trick which allows us to represent an n+2 dimensional spacetime vector using one number from a division algebra and two additional real numbers. There are only four division algebras - which just happen to have 1,2,4 and 8 dimensions. John Baez Explains It All To You here.