StatCosmoLec_09.mp3

Tim and David begin by continuing their discussion of the 'Stosszahlansatz', the assumption that the number of particle collisions in a given subregion is just proportional to the volume of that region. They summarize the debate up to this point and attempt to clarify the nature of their disagreement about its explanatory value. Tim then takes over and gives a short primer on the mathematics of measure theory, connecting it with the purely mathematical notion of a "probability measure" and contrasting that with the physical notion of something being probabilistic in any real sense. Tim relates this discussion by example to the notion of Typicality. A behavior of a system is typical of that system iff the set of initial conditions that yield that behavior has measure 1 (on any normalized continuous measure). When a certain limit frequency is typical, then we have something very close in form and content to an objective, deterministic probability. Tim goes on to discuss how this model can be extended to adequately include finite systems or finite, and then he and David debate at length whether this extension preserves the virtues of the view as first presented.