  This paper reviews results about discrete physics and non-commutative worlds
and explores further the structure and consequences of constraints linking
classical calculus and discrete calculus formulated via commutators. In
particular we review how the formalism of generalized non-commutative
electromagnetism follows from a first order constraint and how, via the
Kilmister equation, relationships with general relativity follow from a second
order constraint. It is remarkable that a second order constraint, based on
interlacing the commutative and non-commutative worlds, leads to an equivalent
tensor equation at the pole of geodesic coordinates for general relativity.
