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		they will be conceived as arbitrary functions mapping finite data-sets into conjectures. This liberal attitude will allow us to separate information-theoretic from computability-theoretic aspects of scientific discovery, as will become clearer in Chapter 3.

		On the other hand, much of our attention will also be devoted to scientists drawn from narrow subsets of the class of computable processes. That is, we shall consider scientists who operate under various constraints concerning the time devoted to processing data, available memory, selection of hypotheses, ability to change hypotheses, etc. Study of such restrictions will shed light on several issues, including:

		(a) the impact of various design features on the performance of computers as scientists, for example, the feature that prevents a computer from abandoning an hypothesis that is consistent with all available data;

		(b) the prospects for success by scientists who possess human characteristics, such as time and memory limitations; and

		(c) the wisdom of conforming to "rational policies" such as never producing an hypothesis falsified by current data, or never producing an hypothesis that describes a theoretical possibility ruled out in advance.

		It will be seen that exploration of such issues sometimes leads to unexpected conclusions.

		§1.4.4 Success versus Confidence about Success

		To be successful on a list of numbers, the scientist must produce a final, correct conjecture about the contents of the entire list. She is not required, however, to "know" that any specific conjecture is final. To see what is at issue, consider the first paradigm introduced above in which C contains just the sets of positive integers with a sole exception. Upon seeing 2, 3, 4, . . ., 1000, a scientist might be confident that the list contains the set of positive integers except for 1. But her confidence does not prevent the list from continuing this way: 1, 1002, 1003, 1004 . . ., 2000. Confidence at 2000 that the list holds all positive integers except for 1001 is equally unfounded, since the list may continue: 1001, 2002, 2003, 2004, . . .. Thus, the scientist is never justified in feeling certain that her latest conjecture will be her last.

		On the other hand, Fact 1.3 does warrant a different kind of confidence, namely, that systematic application of guessing rule 1.2 will eventually lead to an accurate, last conjecture on any list generated from a member of C. The relevant distinction may be put this way: If we know that the actual world is drawn from C, then we can be certain