On the random character of fundamental constant expansions

We propose a theory to explain random behavior for the digits in the expans ions of fundamental mathematical constants. At the core of our approach is a general hypothesis concerning the distribution of the iterates generated by dynamical maps. On this main hypothesis, one obtains proofs of base-2 no rmality-namely bit randomness in a specific technical sense-for a collectio n of celebrated constants, including pi, log 2, zeta (3), and others. Also on the hypothesis, the number zeta (5) is either rational or normal to base 2. We indicate a research connection between our dynamical model and the t heory of pseudorandom number generators.