John Baez on Octonion 📺
first time seeing the great [John Baez
https://plus.google.com/117663015413546257905/posts] 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. At http://math.ucr.edu/home/baez/octonions/ , accessed on 2014-01-12 ]
- [ Octonion ] [ https://en.wikipedia.org/wiki/Octonion ]
- [ Fano plane ] [ https://en.wikipedia.org/wiki/Fano_plane ]
- [ Spinor ] [ https://en.wikipedia.org/wiki/Spinor ]
- [ String theory ] [ https://en.wikipedia.org/wiki/String_theory ]
- [ Sphere packing ] [ https://en.wikipedia.org/wiki/Sphere_packing ]
- [ Élie Cartan ] [ https://en.wikipedia.org/wiki/Élie_Cartan ]
- [ E8 lattice ] [ https://en.wikipedia.org/wiki/E8_lattice ]