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Jordan, Wigner and von Neumann classified the possible algebras of quantummechanical observables, and found they fell into 4 "ordinary" families, plusone remarkable outlier: the exceptional Jordan algebra. We point out anintriguing relationship between the complexification of this algebra and thestandard model of particle physics, its minimal left-right-symmetric$SU(3)\times SU(2)_{L}\times SU(2)_{R}\times U(1)$ extension, and $Spin(10)$unification. This suggests a geometric interpretation, where a singlegeneration of standard model fermions is described by the tangent space$(\mathbb{C}\otimes\mathbb{O})^{2}$ of the complex octonionic projective plane,and the existence of three generations is related to $SO(8)$ triality.

The Standard Model, The Exceptional Jordan Algebra, and Triality