This talk will show how discrete measurement leads to commutators and how discrete derivatives are naturally represented by commutators. We show how i, the square root of minus one, arises naturally as a time-sensitive observable for an elementary oscillator. In this sense the square root of minus one is a clock. This sheds new light on Wick rotation, which replaces t (temporal quantity) by it, the product of time with the square root of minus one.. The Wick rotation replaces numerical time with elementary temporal observation. We show how a number of aspects of physics look from this point of view including a generalization of the Feynman-Dyson derivation of electromagnetism in the context of non-commutative worlds. This generalization depends upon the definitions of derivatives via commutators and upon the way the non-commutative calculus mimics standard calculus.
*Dr. Louis H. Kauffman is a Professor at the University of Illinois at Chicago and is the featured Langenhop lecturer.