for the last few pages. Think, to begin with, of the sequence :
This, recall, was our perfect case for R: the pattern we identified holds perfectly in this data-set. What does it mean to say that R holds perfectly in light of the Dennettian compressibility constraint introduced above, though? Suppose that we wanted to communicate this string of digits to someone else—how might we go about doing that? Well, one way—the easiest way, in a sense—would just be to transmit the string verbatim: to communicate a perfect bit map of the data. That is, for each digit in the string, we can specify whether it is a 'one' or a 'zero,' and then transmit that information (since there are 28 digits in the dataset S1-2, the bit-map of S1-2 is 28 bits long). If the string we're dealing with is truly random then this is (in fact) the only way to transmit its contents: we have to record the state of each bit individually, because (if the string is random) there is no relationship at all between a given bit and the bits around it. Now we're getting somewhere. Part of what it means to have identified a pattern in some data-set, then, is to have (correctly) noticed that there is a relationship between different parts of the data-set under consideration—a relationship that can be exploited to create a more efficient encoding than the simple verbatim bit-map.
The sense of 'efficiency' here is a rather intuitive one: an encoding is more efficient just in case it is shorter than the verbatim bit map—just in case it requires fewer bits to transmit the same information. In the case of S1-2, it's pretty easy to see what this sort of encoding would look
- Citing Chaitin (1975), Dennett (op. cit.) points out that we might actually take this to be the formal definition of a random sequence: there is no way to encode the information that results in a sequence that is shorter than the "verbatim" bit map.