8 - Worldly chaos

Summary

Let's take stock. We now have some idea of the kinds of behaviour in dynamical models – involving sensitive dependence on initial conditions, aperiodicity, and the like – that are thought of as typical of ‘chaos’. We have seen that models exhibiting these kinds of behaviour can at least in principle be richly predictive and that we can coherently think of them as candidates for approximate truth. We have seen too how such models can throw some explanatory light on natural phenomena (even when the models are constructed by radical idealization). So most of the main general issues about the status of chaotic dynamical models that we raised back in §1.6 have turned out to be fairly easily resolved. One major issue remains – business for Chapter 9 – concerning the claim that deterministic chaos involves a kind of randomness. But leaving that aside, chaos theory so far looks to be conceptually in good order.

But what is the state of play empirically? As remarked in §§4.6 and 7.5, the Lorenz model, our paradigm example of a model with chaotic behaviour, is in fact empirically rather unsuccessful in its intended domain. It would be good to be able to note some more robust empirical successes for chaotic models. The story, however, is a mixed one.

To repeat, it is no surprise that the Lorenz model does not work very well as an account of Rayleigh-Bénard flow, given the raft of radical simplifications involved in its construction (see §1.4).