string:

*S _{0}: 00001000011111*

The numbers in *this* string are not consistent with our hypothesis that all the numbers in the sequence at large are generated by *R*. Does this mean that we’ve failed in our goal of identifying a pattern, though? Not necessarily. Why not?

There’s another important question that we’ve been glossing over in our discussion here: for a pattern in some data to be *genuine* must it also be *global ^{[1]}*? That is, for us to say reasonably that

*R*describes the sequence

*S*, must

*R*describe the sequence

*S*

*everywhere?*Here’s all the data we have now:

*S _{0-2}: 000010000111111100010101100010101100010101*

It is clear that we can no longer say that *R* (or indeed any single pattern at all) is the pattern generating all of *S*. This is not at all the same thing as saying that we have failed to identify a pattern in *S* *simpliciter*, though. Suppose that we have some reason to be particularly interested in what’s going on in a restricted *region* of *S*: the region *S _{1-2}*. If that’s the case, then the fact that

*R*turns out not to hold for the totality of

*S*might not trouble us at all; identifying a

*universal*pattern would be

*sufficient*for predicting what sequence of numbers will show up in

*S*, but it is by no means necessary. If all we’re interested in is predicting the sequence in a particular region of

_{1-2}*S*, identifying a pattern that holds

*only*in that region is no failure at all, but rather precisely

^{[2]}- ↑ The sense of 'global' here is the computer scientist's sense—a global pattern is one that holds over the entirety of the data set in question.
- ↑ Of course, it might not be true that
*R*holds only in*S*. It is consistent with everything we’ve observed about_{1-2}*S*so far to suppose that the sub-set*S*and the sub-set_{0}*S*might be manifestations of an over-arching pattern, of which_{1-2}*R*is only a kind of component, or sub-pattern.

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