  Connes' notion of non-commutative geometry (NCG) generalizes Riemannian
geometry and yields a striking reinterepretation of the standard model of
particle physics, coupled to Einstein gravity. We suggest a simple
reformulation with two key mathematical advantages: (i) it unifies many of the
traditional NCG axioms into a single one; and (ii) it immediately generalizes
from non-commutative to non-associative geometry. Remarkably, it also resolves
a long-standing problem plaguing the NCG construction of the standard model, by
precisely eliminating from the action the collection of 7 unwanted terms that
previously had to be removed by an extra, non-geometric, assumption. With this
problem solved, the NCG algorithm for constructing the standard model action is
tighter and more explanatory than the traditional one based on effective field
theory.
