Not perfectly predictable
Some folks worry that determinism deprives us of free will by making us perfectly predictable. Answering this worry requires asking two questions: (1) Does determinism imply perfect predictability? (2) Does perfect predictability deprive us of free will? This post will address question (1). I plan to address question (2) in my next post.
Determinism doesn’t imply perfect predictability. As I mentioned before, the deterministic laws governing our universe exhibit sensitive dependence, which means that perfect prediction requires literally zero error in one’s grasp of the prior conditions. Any finite being must carry out its measurements to finitely many decimal (or binary, or…) places. But many physical magnitudes have irrational values whose decimal (or binary, or…) expansions are infinite and nonrepeating. So the measurements will always be at least a bit off.
Imagine trying to predict perfectly the state of the balls in a game of billiards just six minutes into the future. Physicist James Crutchfield writes that your prediction will fail unless you factor in the (absurdly weak) gravitational effect of a single electron some 17 billion light years away! As nonlinear systems, human agents are sensitively dependent just like a bunch of billiard balls.
Predicting the behavior of any system requires measuring it. That measurement itself will affect the system’s future. Predicting the effect of one’s measurement requires yet more measurement, which in turn affects the system, and so on. As Crutchfield writes, “The infinite regression thus requires the storage of an infinite amount of information. Regardless of the size of the universe, this self-observation and internal self-coding is impossible.”
You might dismiss these arguments and say that determinism allows perfect prediction by a being (God, perhaps?) who can store infinite amounts of information or who needn’t interact with us in order to predict our behavior. That proposal strikes me as magical thinking, but I nevertheless plan to address it in my next post.
