Abstract: The lecturer will describe a theory intended to "explain" the random character of the digits of various fundamental constants. The theory---developed jointly with the computationalist David Bailey--- has, at its very core, what is called "Hypothesis A." That hypothesis connects dynamical iterative maps with the notions of normality (to given integer bases), and in so doing also creates new connections between areas such as: ergodic theory, pseudorandom generators, and irrationality proof methods.