  Sequences of actions do not commute.. For example, the tick of a clock and
the measurement of a position do not commute with one another, since the
position will have moved to the next position after the tick. We adopt
non-commutative calculus, with derivatives represented by commutators. In the
beginning distinct derivatives do not commute with one another, providing
curvature formalism so that the form of the curvature of a gauge field appears
almost as soon as the calculus is defined. This provides context for the
Feynman-Dyson derivation of electromagnetic formalism from commutators, and
generalizations including the early appearance of the form of the Levi-Civita
connection dervived from the Jacobi identity. In this version of
non-commutative physics bare quantum mechanics (its commutation relations)
appears as the flat background for all other constructions. Ascent to classical
physics is obtained by replacing commutators with Poisson brackets that satisfy
the Leibniz rule. An appendix on matrix algebra from a discrete point of view
(Iterants) is provided. This paper will appear in the proceedings of the ANPA
conference held in Cambridge, England in the summer of 2002.
