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 pattern is “two ‘ones,’ followed by three ‘zeros’ followed by ‘one, zero, one, zero,’ and then repeat from the beginning.” This putative pattern R is empirically adequate as a theory of how this sequence of numbers behaves; it fits all the data we have been given. How do we know if this is indeed a genuine pattern, though? Here’s an answer that should occur to us immediately: we can continue to watch how the sequence of numbers behaves, and see if our predictions bear out. If we’ve succeeded in identifying the pattern underlying the generation of these numbers, then we’ll be able to predict what we should see next: we should see a ‘zero’ followed by a 'one,’ and then another ‘zero,’ and so on. Suppose the pattern continues:

S$2$: 0101100010101

Ah ha! Our prediction does indeed seem to have been born out! That is: in S$2$, the string of numbers continues to evolve in a way that is consistent with our hypothesis that the sequence at large is (1) not random and (2) is being generated by the pattern R. Of course, this is not enough for us to say with certainty that R (and only R) is the pattern behind the generation of our sequence; it is entirely possible that the next few bits of the string will be inconsistent with R; that is one way that we might come to think that our theory of how the string is being generated is in need of revision. Is this the only way, though? Certainly not: we might also try to obtain information about what numbers came before our initial data-set and see if R holds there, too; if we really have indentified the pattern underlying the generation of S, it seems reasonable to suppose that we ought to be able to “retrodict” the structure of sub-sets of S that come before our initial data-set just as well as we can predict the structure of sub-sets of S that come after our initial data-set. Suppose, for example, that we find that just before our initial set comes the 26