30 December 2011

The Problem of Free Will II: Limited Autonomy

Let us return to the first proposition of my friend the skeptic:

"Every human thought is in principle a pre-determined consequence of biochemical processes that are themselves determined by evolution, the course of which is pre-determined by chemistry and physics. Therefore, there is no such thing as free will."

At first, it appears that the question of Free Will is an "either/or" proposition. Either we have Free Will, or we don't. What we actually experience, however is freedom within the constraints of our abilities. For example, you may be free to desire whatever you can imagine, but you are not free to desire what you can't imagine. The limits of your own imagination are the limits of what you can want, or will. I concede that the limits on our Free Will are pre-determined by our genetic makeup combined with our experience and our situation in the world. But within those limits, determinism is dead.

Determinism is based on the notion that if we could know the positions and velocities of every particle in the Universe we could, in principle, calculate the entire future evolution of the Universe. This idea was born from the structure of Newton's equations of motion and held sway for over 200 years, until the 1920's. Then we found out that very small particles begin to exhibit behavior that is masked by the sheer size of large ones. It turns out that the process of precisely measuring a particle's position destroys information about its velocity, and vice versa. That is to say, measuring exactly where a particle is gives it such a whack that we can no longer know where it's going, and measuring exactly where it's going can only be done via interactions that "smear out" where it is. That the position and velocity of a particle cannot simultaneously take on precise values is a statement of Heisenberg's Uncertainty Principle, and seems to be a fundamental limitation on the measurability of reality.
If the Uncertainty Principle struck Determinism a mortal blow in the 1920s, nonlinear dynamics delivered the coup de grace in the 1980s. The nonlinear dynamicists finally had the desperation, the courage, and the methods to tackle some of the really hard problems of Classical Mechanics (the branch of physics that deals with the motion of ordinary sized things and is described by Newton's equations). They found that even for relatively simple systems, like three bodies moving under mutual gravitational attraction, the future motion can depend so sensitively on the given conditions at any moment (positions and velocities) that the detailed motion of the system is unpredictable (or chaotic) - not only because classical measurements are only finitely precise, but because of the limitations imposed by the Uncertainty Principle as well. In other words, the Universe is not nearly as well-behaved as a wind-up clock. The Universe is not a machine or a mechanism, as we understand machines and mechanisms. Determinism is dead.

How dead is it? Consider that three bodies moving under their mutual gravitational attraction have 6 degrees of freedom per body (their positions along any three perpendicular directions in space, and their velocities along those directions). These three bodies are a system with 18 degrees of freedom whose motion is unpredictable in principle. Now consider that the human brain has about 100 billion neurons, each with about 10,000 interconnections to other neurons, each of which is a degree of freedom for that neuron. The human brain is a system with at least a quadrillion degrees of freedom. The idea of trying to predict the state of a living human brain is ludicrous. 

And that's just classically. Quantum mechanically, the wave function of each neuron in your brain extends throughout the whole universe. True, the far reaches of that wave function have very low values. But I include it to emphasize the fundamental impossibility of knowing all the influences on the state of the brain. 

Now the three gravitating bodies will under certain circumstances, stay within some enveloping region of space. Within that region, it is impossible to predict where they will be over the long term. But they will be (almost completely) somewhere within that region. They are free within that constraint.

Similarly, you are free to think and to desire whatever you want within the constraints of your being human at a certain time and place. That is to say, you have Free Will within limits. You are free to will anything possible. You are free even to will the impossible. But you are not free to will the unimaginable, because you don't know what it is. This is Limited Freedom, rather than an Absolute Freedom. The limits are set only by human nature and physical reality. At least, until we figure out how to change them.

So the dichotomy between Absolute Freedom and being an automaton is false. There is space for freedom with the constraints of being in this Universe. It puts us in a situation that seems paradoxical to absolutists who insist on Free Will as an all-or-nothing proposition. As Isaac Bashevis Singer once said, "We have to believe in Free Will. We have no choice."