Chaos and Friction in Theory Evolution

Our theories about the world are a part of the world. The dynamic evolution of the world includes the dynamic evolution of our theories about the world. The "standard modern" picture of the pattern of the evolution of theories is that, at least once the world-system has crossed over into the scientific attractor basin, that theories gradually and steadily approach some fixed point. This fixed point can serve as an effective notion of truth. Perhaps my main theme in this essay is that this picture of the dynamic evolution of theories is an inadequate picture. As an analogy, in the past the standard model for thermodynamic systems was an isolated system gradually approaching equilibrium. Since at least the 1960's, scientists have been exploring the behavior of open systems and systems far from equilibrium. It looks now like the isolated system gradually approaching equilibrium is very much a special case.

What is the actual pattern of the dynamic evolution of scientific theories? The question is not exactly historical. It is not a matter of the path that science actually takes, but of all the various paths it might take. If in fact all paths eventually settle within some small neighborhood of a single fixed point, then this fixed point could well serve as truth. But if the various possible trajectories of theory evolution actually wander into very diverse regions, then the question of truth gets more complicated. Perhaps one trajectory indeed settles for a very long time in one neighborhood, and a different trajectory also settles in a neighborhood, but the two neighborhoods are very different. The modern theories of chaotic dynamics have charted out an amazing menagerie of patterns of trajectories.

What I propose is that the actual dynamics of theory evolution is chaotic. Proving this to be true may be very difficult, impossible, or paradoxical. Wouldn't any purported proof need to hold itself up as some sort of universal fixed point in a dynamic space of theories about theories, which as part of the actual evolution of the entire world is coupled into the dynamics of the first order theory evolution and therefore subject to the chaos that it intends merely to be about rather than itself subjected to?

Here we have two competing theories. The standard modern philosophy of science holds that the dynamic system of theory evolution is non-chaotic, that essentially the entire space of theories constitutes one big basin of attraction with a simple fixed point. The alternative proposed here (and by many others) is that the dynamic system of theory evolution is chaotic, with the full panorama of attractor types etc. How can we decide which of these theories is better?

In my discussions on this subject, one friend proposed that since the standard modern philosophy of science is the established dominant view, the burden of proof is on the newcomer chaotic theory. It occurs to me that this argument puts a very nice wrinkle into the problem. This wrinkle relies on a feature of general system dynamics. Static friction leads to chaos! When a system wants to stay where it is and resists movement, that tendency leads to multiple basins of attraction. This observation doesn't prove that theory evolution is indeed chaotic, but it does encourage an examination of the issue based on the merits of the different positions rather than the history of the power of their various advocates. Arguing for the standard view on the basis of its standardness undermines that very view itself!