Suppose that instead of thinking of the special sciences as providing compressed versions of the space provided by fundamental physics, though, we take the view offered in Chapter One: we can think of a special science as defining a new configuration space for the system. What were formerly regions in the very high-dimensional configuration space defined by fundamental physics can now be treated as points in a lower dimensional space defined by the special science in question. It is tempting to think that both these representations—the special sciences as coarse-graining and the special sciences as providing entirely novel configuration spaces—are predicatively equivalent, but this is not so.
The difference is that the second way of doing things actually makes the compression—the information loss—salient; it isn’t reversible. It also (and perhaps even more importantly) emphasizes the fact that the choice of a state-space involves more than choosing which instantaneous states are functionally equivalent—it involves more than choosing which collections of points (microstates) in the original space to treat as macrostates. The choices of a state-space also constitutes a choice of dynamics: for a system with a high degree of dynamical complexity, there are a large number of state spaces which evince not only interesting static detail, but interesting dynamical detail as well. Thinking of (say) a conscious human as being at bottom a system that’s only really completely describable in the state space of atomic physics eclipses not just the presence of interesting configurations of atomic physics’ particles (interesting macrostates), but also the presence of interesting patterns in how those configurations change over time: patterns that might become obvious, given the right choice of state space. Choosing a new state space in which to describe the same system can reveal dynamical constraints which might otherwise have been invisible.