Paragraph about LaTeX equation editor
This example raises a number of questions. Just what does the CM model require in the case of complex systems in which we cannot trace individual causal processes, at least at a fine-grained level? How exactly does the causal mechanical model avoid the (disastrous) conclusion that any successful explanation of the behavior of the gas must trace the trajectories of individual molecules? Does the statistical mechanical explanation described above successfully trace causal processes and interactions or specify a causal mechanism in the sense demanded by the CM model, and if so, what exactly does tracing causal processes and interactions involve or amount to in connection with such a system? As matters now stand both the CM model and Equation editor the process theories of causation that are its more recent descendants are incomplete.
There is another aspect of this example that is worthy of comment. Even if, per impossible, an account that traced individual molecular trajectories were to be produced, there are important respects in which it would not provide the sort of explanation of the macroscopic behavior of the gas that we are likely to be looking for — and not just because such an account would be far too complex to be followed by a human mind. There are a very large number of different possible trajectories of the individual molecules in addition to the trajectories actually taken that would produce the macroscopic outcome — the final pressure P2 — that we want to explain. This information is certainly explanatorily relevant to the macroscopic behavior of the gas and we would like our account of explanation to accomodate this Scientific software fact. Very roughly, given the laws governing molecular collisions, one can show that almost all (i.e., all except a set of measure zero) of the possible initial positions and momenta consistent with the initial macroscopic state of the gas, as characterized by P1, T1 , and V1, will lead to molecular trajectories such that the gas will evolve to the macroscopic outcome in which the gas diffuses to an equilibrium state of uniform density through the chamber at pressure P2. Similarly, there is a large range of different microstates of the gas compatible with each of the various other possible values for the temperature of the gas and each of these states will lead to a different final pressure P2*. If we just trace the causal processes (in the form of actual molecular trajectories) that lead to P2, as the CM model requires, we will fail to represent or capture this information about the full range of conditions under which P2 and alternatives to it will occur.