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 reasonable for us to say that R is informative in the former case but not in the latter, despite the fact that neither string is consistent with the hypothesis that R is the pattern underlying its generation. The intuitive way to put the point is to say that R holds approximately in the case of S$3$ but not in the case of S$0$, but we can do better than that now: given R, and a restricted set of S$3$, an observer who is asked to guess the value of some other part of the set will do far better than we’d expect him to if R was totally uninformative—that is, he will be able to make predictions about S$3$ which, more often than not, turn out to be good ones. In virtue of knowing R, and by measuring the values in one sub-set of S$3$, he can make highly successful predictions about how other value measurements in the set will turn out. The fact that he will also get things wrong occasionally should not be too troubling; while he’d certainly want to work to identify the exceptions to R—the places in the sequence where R doesn’t hold—just picking out R goes a very long way toward sustained predictive success. Contrast that case to the case in S$0$: here, knowledge of R won’t help an observer make any deductions about values of unobserved bits. He can learn as much as he wants to about the values of bits before and after a missing bit and he won’t be any closer at all to being able to make an educated guess about the missing data.

1.4 Fundamental Physics and the Special Sciences

It might be worth taking a moment to summarize the rather lengthy discussion from the last section before we move on to considering how that discussion bears on the larger issue at hand. We started by observing that science is “about the world” in a very particular sense. In exploring what that might mean, I argued that science is principally concerned with identifying patterns in how the world around us changes over time. We then spent some time examining some basic

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