Page:Lawhead columbia 0054D 12326.pdf/54

 my apartment. Suppose (counterfactually) that we take Newtonian dynamics to be the complete fundamental physics for systems like this one. If that is the case, then fundamental physics provides a set of directions for moving from any point in the phase space to any other point—it provides a map identifying where in the space a system whose state is represented by some point at t$0$ will end up at a later time t$1$. This map is interesting largely in virtue of being valid for any point in the system: no matter where the system starts at t$0$, fundamental physics will describe the pattern in how it evolves. That is, given a list of points [a$0$,b$0$,c$0$,d$0$…z$0$], the fundamental physics give us a corresponding list of points [a$1$,b$1$,c$1$,d$1$…z$1$] that the system will occupy after a given time interval has passed. In the language of Section 1.3, we can say that fundamental physics provides a description of the patterns in the time-evolution of the room’s bit map: given a complete specification of the room’s state (in terms of its precise location in phase space) at one time, applying the algorithm of Newtonian mechanics will yield a complete specification of the room’s state at a later time (in terms of another point in phase space).

This is surely a valuable tool, but it is equally surely not the only valuable tool. It might be (and, in fact, is) the case that there are also patterns to be discerned in how certain regions of the phase space evolve over time. That is, we might be able to describe patterns of the following sort: if the room starts off in any point in region P$0$, it will, after a given interval of time, end up in another region P$1$. This is, in fact, the form of the statistical-mechanical explanation for the Second Law of Thermodynamics. This is clearly not a description of a pattern that applies to the “bit map” in general: there might be a very large number (perhaps even a continuous infinity) of points that do not lie inside P$0$, and for which the pattern just described thus just has nothing to say. This is not necessarily to say that the project of identifying patterns like P0 􏰀 [sic] P1 isn’t one 44