The Arrow of Time through the Lens of Computing

Abstract

The concepts of temporal logic were introduced by Amir Pnueli [1] into the realm of computer science in general and programs in particular, to great effect. Given a program specification, a crucial element of reasoning through temporal logic is our ability to assert that one program event occurs before or after the other, with an order intuitively rooted in our notion of “time”. In the realm of temporal logic, such assertions are abstracted as pure mathematical facts. An alternative is to consider the physical realization by executing the specified program through, for example, a microprocessor-based system. In such a case, a mechanism is used to ensure that the desired temporal relationships from the program specification are obeyed, and quite often this mechanism takes the form of a clock. In physical instantiations however clocks and similar mechanisms have an associated energy cost. They are guided by the laws of physics in general and thermodynamics in particular, with which the arrow of time and the associated irreversibility are intimately intertwined. Viewed through this lens, a key question arises of whether the need for ensuring that the temporal norms needed for program correctness accrue an inevitable energy cost. In this paper, I sketch some of the intricacies underlying this question. I will hint at the subtle interactions between models of computing, time as it is represented in them, and the associated thermodynamic cost. In his early work, Amir relied as much on the philosophy of reasoning about time [2-4] as on the technical intricacies of mathematical logic. In recognition of the richness of his intellectual endeavor, I have developed this exposition in a philosophical style mimicking that of the ancient greek philosopher Zeno [5,6].

This work was supported in part by a visit to the Nanyang Technological University as a Canon Visiting Professor, and to the California Institute of Technology as a Moore Distinguished Scholar, 2006-07.