Non-Commutative Worlds -- A Summary

This paper summarizes the contents of the paper "Non-Commutative Worlds" by the author (published in New Journal of Physics Vol. 6, November 2004, pp. 2 - 46; quant-ph/0403012) and gives a new derivation of our generalization of electromagnetism in a non-commutative context. This generalization extends the Feynman-Dyson derivation and it admits discrete models. The methods of the present paper are diagrammatic. In this form, the theory is entirely a consequence of the choice of definition of space and time derivatives as commutators.