complete account of the patterns in how the world evolves over time via collaboration between different branches of science, which consider different ways of carving up the same world. Individual sciences are concerned with identifying patterns that obtain in certain subsets of the world, while the scientific project in general is concerned with the overarching goal of pattern-based prediction of the world's behavior. Success or failure in this project is not absolute; rather, the identification of parochial or "weak" patterns can often be just as useful (if not more useful) as the identification of universal patterns. Scientists identify patterns both by making novel measurements on accessible regions of the world and by creating models that attempt to accurately retrodict past measurements. The scientific project is unified in the sense that all branches of science are concerned with the goal of identifying patterns in how the physical world changes over time, and fundamental physics is fundamental in the sense that it is the most general of the sciences—it is the one concerned with identifying patterns that will generate accurate predictions for any and all regions of the world that we choose to consider. Patterns discovered in one branch of the scientific project might inform work in another branch, and (at least occasionally) entirely novel problems will precipitate a novel way of carving up the world, potentially facilitating the discovery of novel patterns; a new special science is born.
We might synthesize the discussions in Section 1.3 and Section 1.4 as follows. Consider the configuration space D of some system T—say, the phase space corresponding to the kitchen in
- That is, consider the abstract space in which every degree of freedom in T is represented as a dimension in a particular space D (allowing us to represent the complete state of T at any given time by specifying a single point in D), and where the evolution of T can be represented as a set of transformations in D. The phase space of classical statistical mechanics (which has a dimensionality equal to six times the number of classical particles in the system), the Hilbert space of standard non-relativistic quantum mechanics, and the Fock space of quantum field theory (which is the direct sum of the tensor products of standard quantum mechanical Hilbert spaces) are all prime examples of spaces of this sort, but are by no means the only ones. Though I will couch the discussion in terms of phase space for the sake of concreteness, this is not strictly necessary: the point I am trying to make is abstract enough that it should stand for any of these cases.