TITLE: What's wrong with this information theoretic argument for free will?
QUESTION [1 upvotes]: Forgive me if this is incredibly naive. I am an undergraduate studying mathematics and have studied almost no physics, but a friend of mine mentioned this argument and it's been bugging me since it seems to have some intuitive thrust, even if it's not rigorously set forth. In the setting of nonlinear dynamics, we know that particles in a many-body system that have a starting position even infinitesimally apart will eventually diverge in motion when subject to the laws of eg. gravitation, in classical physics. And so any predictions about the long term (asymptotic to infinitely far into the future) must have more and more detailed knowledge about their starting positions to be able to maintain accurate predictions. Mathematically, this means writing down or storing their positions to increasing degrees of numerical accuracy, manifesting as more digits to be stored in "memory" of any such system making such a prediction. To be able to use the laws of physics to predict the future in its entirety (as in Laplace's Demon), you require infinite precision, and therefore infinite amount of "memory" (in some abstract sense), which is not possible, given the universe is finite and the smallest thing that can serve as a quantum of information is a fundamental particle. "Therefore," there is structurally no way physics can be used to predict the future entirely correctly, and thus no way for any model of the universe to be deterministically correct. This was the thrust of his argument, and then he mentioned off-hand this suggests we have free will (I do not think that implication holds), which I found interesting.
My intuition says the trickery in the argument here is mostly semantic, since it's not stated formally, but I am sure physicists have something to say about this line of reasoning? Thanks!

REPLY [0 votes]: I agree with the excellent answers preceding mine. I would add the observation that a necessary requirement for free will is that thought is self-directing. Assuming thought is correlated in some way with the physical behaviour of the particles that comprise the brain, then free will requires that thought must be able to influence the physical behaviour and not simply arise from it. If all thought is a consequence of the behaviour of the physical constituents of the brain acting in accordance with the laws of physics, then it follows that thought is predetermined to the extent that any other physical process is.
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