Possible purposes [for systems]

As part of asking whether the rules for a system are somehow minimal for a given purpose, one can ask what properties the system has that could reasonably be considered a purpose at all. In general one tends to talk of purpose only when doing so allows one to give a simpler description of some aspect of behavior than just describing the behavior directly. But whether one can give a simple description can depend greatly on the framework in which one is operating. And so, for example, while the digits of π have a simple description in terms of traditional mathematics, the results in Chapter 4 suggest that outside of this framework they normally do not. And what this means is that if one saw a system that had the property of generating the digits of π one would be unlikely to think that this could represent a meaningful purpose—unless one happened to be operating in traditional mathematics. And so similarly, one would be unlikely to think that generating the center column from rule 30 could represent any sort of meaningful purpose—unless one was operating within the framework that I have developed in this book.