There is a long-cherished hope, which has its origins in the work of Boltzmann, that all that we are going to need to do, in order to account for all the differences there are between the past and the future, is to add to the fundamental time-reversal-symmetric dynamical laws, and to the standard statistical-mechanical probability-measure over the space of possible fundamental physical states, a simple postulate – a so-called “past hypothesis” – about the initial microstate of the universe as a whole. And there are various widespread and and perennial sorts of puzzlement about how a hope like that can even seriously be entertained – puzzlements (that is) about how it is that the macrocondition of the universe 15 billion years ago, all by itself, can even imaginably be up to the job of explaining so much about the feel, today and on earth, of the passing of time. I want to try to alleviate those puzzlements here. I will begin with a number of very general observations – and then, by way of illustration, I will present a new and detailed analysis of how it is that a simple pendulum clock invariably arranges to turn its hands clockwise in the temporal direction that points away from the Big Bang.