Incredible connections

Monstrous moonshine

normed alternative algebras over R:
- R/C/H/O
- simple complex Lie algebras
- formally real Jordan algebras

More distantly:
- Bott Periodicity
- classification of finite simple groups

Basic idea:
- every basic symmetry
  (with possible rare exceptions: the 6 weird sporadic groups,
   not in the Happy family (20 sporadic simple groups subgroups of
   Monster))
  comes from the alternative algebras
- these come in 4 families: R (even/odd), C, H,
  and exceptions come from the octonions

Exceptional items:
Octonions
E_8 lattice
triality
Leech lattice (24-dimensional; comes from E_8 and triality)
Monster group
binary Golay codes
Steiner system S(5,8,24)

(there are other sporadic/Golay/Steiner connections)
