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*. This map is interesting largely in virtue of being valid for any point in the system: no matter where the system starts at

_{1}*t*, fundamental physics will describe the pattern in how it evolves. That is, given a list of points [

_{0}*a*,

_{0}*b*,

_{0}*c*,

_{0}*d*…

_{0}*z*], the fundamental physics give us a corresponding list of points [

_{0}*a*,

_{1}*b*,

_{1}*c*,

_{1}*d*…

_{1}*z*] that the system will occupy after a given time interval has passed. In the language of

_{1}**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*. 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

_{1}*continuous infinity*) of points that do not lie inside

*P*, and for which the pattern just described thus just has

_{0}*nothing*to say. This is not necessarily to say that the project of identifying patterns like P0 P1 isn’t one

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