Space--time code. II

Quantum concepts can be applied to space-time processes to make a quantum (q) theory that is free of the possibility of divergencies inherent in classical continuum theories, yet causal, Lorentz-invariant, and asymptotically Poincar\'e-invariant for large times. A general technique, algebraic quantization, is provided for going from classical (c) paradigms, typically discrete logical structures, to q analogs. Applied to the two-dimensional c checker-board, algebraic quantization gives a q theory of time and space asymptotic to the four-dimensional Minkowski c theory in the limit of large time. Applied to the simplest dynamics on such a checkerboard, a piece that makes the same move again and again, algebraic quantization gives a q dynamics asymptotic to a massless spin-\textonehalf{} two-component dynamics in the same limit. The quantum of time, if it exists, must have spin \textonehalf{}. Some features of general relativity such as curvature seem plausible consequences of a quantum theory of space-time processes.