like—we specify R, then specify that the string we're passing consists in two iterations of R. Given a suitable way of encoding things, this will be much shorter than the verbatim bit map. For example, we might encode by first specifying a character to stand for the pattern, then specifying the pattern, then specifying the number of times that the pattern iterates. It might look something like this:
This string is 15 bits long; in just this simple encoding scheme, we've reduced the number of characters required to transmit S1-2 by almost 50%. That's a very significant efficiency improvement (and, given the right language, we could almost certainly improve on it even further).
This compressibility criterion is offered by Dennett as a necessary condition on patternhood: to be an instance of a (real) pattern, a data-set must admit of a more compact description than the bitmap. However, as a number of other authors have pointed out, this cannot be the whole story; while compressibility is surely a necessary condition on patternhood, it cannot be both necessary and sufficient, at least not if it is to help us do useful work in talking about the world (recall that the ultimate point of this discussion is to articulate what exactly it is that science is doing so that we can see if philosophy has something useful to contribute to the project). Science cannot simply be in the business of finding ways to compress data sets; if that were so, then every new algorithm—every new way of describing something—would count as a new
- All of this can be made significantly more precise given a more formal discussion of what counts as a "good" compression algorithm. Such a discussion is unnecessary for our current purposes, but we will revisit information theory in significantly more detail in Chapter Two. For now, then, let me issue a promissory note to the effect that there is a good deal more to say on the topic of information-content, compression, and patternhood. See, in particular, Section 2.1.3.
- Collier (1999) and Ladyman, Ross, Spurrett, and Collier (2007)