that should be pursued, though. Suppose the generalization identified looks like this: if the room is in a region corresponding to “the kitchen contains a pot of boiling water and a normal human being who sincerely intends to put his hand in the pot[1]” at t0, then evolving the system (say) 10 seconds forward will result in the room’s being in a region corresponding to “the kitchen contains a pot of boiling water and a human being in great pain and with blistering skin.” Identifying these sorts of patterns is the business of the special sciences.
Not all regions will admit of interesting patterns in this way. This is the sense in which some ways of “carving up” a system’s space seem arbitrary in an important way. In a system with a relatively high degree of complexity—very roughly, a system with a relatively high-dimensional configuration space[2]—there will be a very large number of ways of specifying regions such that we won’t be able to identify any interesting patterns in how those regions behave over time. This is the sense in which some objects and properties seem arbitrary in problematic ways: carvings corresponding to (for example) grue-like properties (or bizarre compound objects like “the conjunction of the Queen of England’s left foot and all pennies minted after 1982”) just don’t support very many interesting patterns. Regions picked out by locutions like that don’t behave in ways that are regular enough to make them interesting targets of study. Even in cases like this, though, the patterns identified by fundamental physics will remain reliable: this (again) is the sense in which fundamental physics is fundamental. The behavior of even arbitrarily-specified regions—regions that don’t admit of any parochial patterns—will be
- ↑ We can think of the “sincerely intends to put his hand in the pot” as being an assertion about location of the system when its state is projected onto a lower-dimensional subspace consisting of the configuration space of the person’s brain. Again, this location will (obviously) be a regional rather than precise one: there are a large number of points in this lower-dimensional space corresponding to the kind of intention we have in mind here.
- ↑ This is only a very rough gesture at a definition of complexity, but we’re not yet in a position to do better than this. For a more precise discussion of the nature (and significance) of complexity, see Section 2.2.
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