(2) from cases of not-(2) requires more data about the state of the system than does individuating cases of (1) from cases of not-(1).  This is a consequence of the fact that (as we saw in Chapter One) some special science compressions are more lossy (in the sense of discarding more information, or coarse-graining more heavily) than others: biology is, in general, a more lossy encoding scheme than is organic chemistry. This is (again) a feature rather than a bug: biology is lossy, but the information discarded by biologists is (ideally) information that’s irrelevant to the patterns with which biologists concern themselves. The regions of configuration space that evolve in ways that interest biologists are less precisely defined than the regions of configuration space that evolve in ways that interest chemists, but the biologists can take advantage of that fact to (in a sense) do more work with less information, but that work will only be useful in a relatively small number of systems—those with paths that remain in a particular region of configuration space during the time period of interest.
The significance of this last point is not obvious, so it is worth discussing in more detail. Note, first, that just by removing the human being from this system, we haven’t necessarily made it the case that the biology compression algorithm fails to produce a compressed encoding of the original state: even without a person standing next to the pot of water, generalizations like “that water is hot enough to burn a person severely” can still be made quite sensibly. In other words, the set of points in configuration space that a special science can compress is not necessarily identical to the set of points in configuration space that the same special science can usefully
- This does not necessarily mean that the associated measurements are operationally more difficult to perform in the case of (2), though—how difficult it is to acquire certain kinds of information depends in part on what measurement tools are available. The role of a thermometer, after all, is just to change the state of the system to one where a certain kind of information (information about temperature) is easier to discern against the “noisy” information-background of the rest of what’s going on in the system. Measurement tools work as signal-boosters for certain classes of information.