Sunday, October 26, 2014

Determinism and Predictability

Determinism doesn't entail predictability, even in principle, unless you are going to help yourself to some principles so outlandish that you might as well invoke the supernatural.

To a first approximation, a system is deterministic if every event necessarily follows as a result of prior events. Or, to put it another way, every future state of the system is completely determined by the initial conditions of that system. 

It would seem to follow that every future state of such a system could be predicted, albeit perhaps only in principle. For example, imagine a snooker table at the beginning of a game and suppose the precise location, mass and other physical variables of all the balls are known. Then, given the laws of physics and the momentum and path of the cue ball after cueing off, we might think that some supercomputer could show us a picture of where every ball would be on the table at any future time.

So if the natural world as a whole is considered to be a deterministic system, we might conclude that the future is completely predictable. But there seem to be limits on predictability by any known methods of computation yet devised. 

First, we'd need precise measurements of all of the physical variables, or the error in our predictions would grow so fast as to make them uselessly inaccurate. Suppose that one such measurement had a value that turned out to be a non-computable irrational number? If it is truncated anywhere, that introduces error. But if it is not truncated, we have an infinite amount of information.

Second, even if the supercomputer is as computationally powerful as we like, it is still part of the natural world, so the information state of the computer is manifest physically, which itself would perturb the system leading to an infinite regress. Supposing the computer to be outside the natural world doesn't help either, as we then have the classic dualist problem of how it could interact with the world to take measurements whilst remaining completely separate. 

These reasons suggest that, although we might intuit that with enough information, time and computing power, every subsequent state of a deterministic system can be precisely specified within a given margin of error, this is not the case. Even given a classical deterministic physics model of the world, a precise prediction of the future state of the system is not possible, even in principle. 

This thought experiment predates modern computing by a long way. As far back as 1814 Pierre-Simon LaPlace, in his introduction to Essai philosophique sur les probabilit├ęs, postulated what would later be known as LaPlace's Demon: an intellect with enough calculating ability and knowledge to predict the future. 

Perhaps a demon is more apt a characterization than a supercomputer. Given the arguments considered above, any such entity looks like it would have to be a supernatural agent, able to flout the physical laws which both limit how much information it can store and prevent measurement without interaction. There is an irony here given this is one thought experiment that some hard determinists use to deny free will.

Their argument is that free will is incompatible with a predictable future, unless it is somehow supernatural and able to escape the constraints of a deterministic universe. Since the supernatural is anathema to them, these hard determinists conclude that free will does not exist. Yet in order to establish predictability they have invoked the very thing they deny, something supernatural.  

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