The concept of typicality is nowadays a widely discussed way to deal with philosophical problems in statistical mechanics. Roughly said, it elucidates the coming about of equilibrium by showing that it is the “typical” outcome given normal mechanical conditions on the systems. In other words, it works as a high-probability argument to explain the observed behavior.
Historically, this was also the most popular use of statistical tools in mechanics at the end of the 19th century. Although Ludwig Boltzmann proved that the reach of thermal equilibrium is not an exceptions-free process (1872), he nevertheless claimed that its probability was overwhelmingly high. In so doing, he was sharply separating indeterministic processes from well understood probabilistic events. But, contrary to current philosophical reflections, typicality and high probability also showed up in mechanics with descriptive aims. In his ground-breaking work on the three-body problem, Henri Poincaré combined qualitative topological techniques with probabilistic tools to describe motions more complicate than the usual periodic trajectories deployed in celestial mechanics. This research led him to define typical trajectories as those that occur for all initial states with the possible exception of a set of states with measure equal to zero.
This tension between explanatory and descriptive functions of high probability arguments continued into the 20th century in the context of George Birkhoff’s theory of dynamical systems and in his later ergodic theory (1931). This paper explores the use of high probability arguments in statistical and general mechanics and compares it with the modern philosophical concept of typicality.