David Ruelle is a Belgian mathematical physicist who has made original contributions to complexity theory and non-linear dynamical systems. He named the "strange attractor." Like many mathematical physicists, he leans toward deterministic physical theories, and has puzzled over the problem of free will and determinism. In his 1991 book, Chance and Chaos, Ruelle admits that it is hard to explain free will in a deterministic universe, but "the laws of physics are deterministic," he says, and this is true of both classical mechanics and quantum mechanics. Erwin Schrödinger's equations of motion for his wave function (probability amplitudes) are indeed deterministic, but the probability amplitudes moving through space are only predictions of indeterministic probabilities for finding a quantum particle somewhere. Can quantum indeterminism help with the problem of free will? Ruelle says no, citing Schrödinger's 1936 essay in Nature, Indeterminism and Free Will.
Introducing chance into the laws of physics does not help us in any way to resolve [the] contradiction [between free will and determinism]. Indeed, could we say that we engage our responsibility by making a choice at random? Our freedom of choice, actually is rather illusory.This is the randomness objection in the flawed standard argument against free will. In two-stage models of free will, randomness only helps generate alternative possibilities for action, it does not directly cause the action. Ruelle finds an adequate explanation for (our illusion of) free will in the practical lack of predictability (or computability) that is a consequence of our inability to know the initial conditions with the kind of unlimited accuracy that Pierre-Simon Laplace imagined for his intelligent demon.
In brief, what allows our free will to be a meaningful notion is the complexity of the universe or, more precisely, our own complexity.
Sensitivity to Initial ConditionsA hallmark of complexity and chaos theory is the fact that very small variations in the initial conditions can be amplified rapidly to produce extremely different end states. James Clerk Maxwell saw this in hydrodynamic flows where neighboring molecules at one instant could wind up widely separated just moments later. In an 1873 Essay on Free Will, Maxwell thought that such sensitivity to initial conditions might provide the contingency of events needed to break with determinism and explain free will. Ruelle has done the same.
The Ruelle/Berry/Borel DemonRuelle imagines a little devil (see our collection of demons and compare Harry Frankfurt's controller who manipulates our decisions in so-called Frankfurt cases) who can alter the initial conditions ever so slightly at astronomical distances (Emile Borel thought such small effects could be responsible for irreversibility) and thus change the future to spoil our plans.