first time seeing the great John Baez in video. in first 30 min, you learn a very brief history of complex numbers, quaternions, and octonions.
at 23:00, he started to talk about octonions. I learned, octonion's connection with projective geometry! the Fano plane!
after first 30 min, you start to learn octonions, and spinor, and string theory. I'm not much a physics guy, but this brief intro showed me what spinor and string theory are! and the connection of quite a few things in math.
at 42:50 it's about packing circle and spheres, then in higher dimensions, their curious happenings in 4th and 8th dimensions, eventually culminating on the E8 lattice.
here's his paper: 〔The Octonions By John C Baez. @ http://math.ucr.edu/home/baez/octonions/〕