zero ought to be a one if R is to hold)—but still, it seems clear that it is not an instance of the pattern. Still, does this mean that we have failed to identify any useful regularities in S3? I will argue that it most certainly does not mean that, but the point is by no means an obvious one. What's the difference between S3 and S0 such that we can say meaningfully that, in picking out R, we've identified something important about the former but not the latter? To say why, we'll have to be a bit more specific about what counts as a pattern, and what counts as successful identification of a pattern.
Following Dennett[1] and Ladyman et. al.[2], we might begin by thinking of patterns as being (at the very least) the kinds of things that are "candidates for pattern recognition.[3]" But what does that mean? Surely we don't want to tie the notion of a pattern to particular observers—whether or not a pattern is in evidence in some dataset (say S3) shouldn't depend on how dull or clever the person looking at the dataset is. We want to say that there at least can be cases where there is in fact a pattern present in some set of data even if no one has yet (or perhaps even ever will) picked it out. As Dennett notes, though, there is a standard way of making these considerations more precise: we can appeal to information theoretic notions of compressibility. A pattern exists in some data if and only if there is some algorithm by which the data can be significantly compressed.
This is a bit better, but still somewhat imprecise. What counts as compression? More urgently, what counts as significant compression? Why should we tie our definition of a pattern to those notions? Let's think through these questions using the examples we've been looking at
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