I've often used Fred's mnemonic's "0,1,3" sequence in John Conways's mnemonic for multiplying octonions: If 7 orthonormal unit vectors perpendicular to the reals are denoted e_0, e_1, ..., e_6, then e_k * e_(k+1) = e_(k+3) (indices mod 7) (e_k)^2 = -1 e_j * e_k = -e_k * e_j These rules plus the fact that the octonions are an algebra over the reals (so additively identical to R^8) are enough to multiply any two elements —Dan
On Jun 23, 2015, at 5:45 PM, Fred Lunnon <fred.lunnon@gmail.com> wrote:
It might be appropriate to remind everyone of a canonical notation for points P_i and lines L_i of the Fano plane --- index i = 0,...,6 (mod 7) ; L_i meets { P_i, P_(i+1), P_(i+3) } ; P_i meets { L_i, L_(i-1), L_(i-3) } . Anyone cursed with memory and clerical accuracy as unreliable as my own can save substantial futile blaspheming by observing it!