Inherent Unpredictability

 --by Robert Arvay

It seems logical to many educated people that, if one knows everything about the state of a closed system, then one can, at least in principle, predict (or accurately calculate) all future states of that system. Yet, this seeming logic is provably false, as indicated by the famous three-body problem—according to which, even in principle, certain future states (or events) of finite, closed systems are incalculable. It is important to state this correctly. The unpredictability arises not because of any inadequacies of our skill in mathematics, but rather, what may be an inherent property of math and/or physics.

Quoting from Space-dot-Com (Charlie Wood), “Famed mathematician Henri Poincaré showed in 1889 that no equation could accurately predict the positions of all three bodies at all future moments, winning a competition sponsored by King Oscar II of Sweden. In this three-body case, Poincaré had discovered the first instance of chaos, a phenomenon whose outcome can effectively disconnect from how it began.”

Those last words in that quote are profound. They imply, perhaps more than merely imply, that the final state of a system might be independent of its beginning state.

If taken literally, that seems impossible from a deterministic standpoint. Even if we cannot mathematically compute an outcome, the universe, so to speak, does in fact “know” what the outcome will be, since by the chain of cause-and-effect, each step in the sequence is predetermined and inalterable. This means that the outcome is not detached from the beginning. It is inextricably connected through causation.

Computer simulations try to mimic this natural sequence of cause and effect, but achieve only limited success, because at each step, there is a slight, unavoidable inaccuracy, an approximation error. At first, such an error is so tiny as to be negligible, but after many iterations, the errors add up, until the calculations become wildly inaccurate. Supercomputers, interlocked with large numbers of processors, can keep the errors within limits, but at best, they achieve only approximations, not precise solutions.

What we are left with, is a fog of unpredictability that extends not only forward in time, but also, backward. We can use statistical methods to determine ranges of possibilities, but those ranges contain what are called, “outliers,” the improbable but still possible, extreme edges of the bell curve graph.

Note also that these imprecisions are not the same as those found in quantum mechanics, in which some theories disavow any “hidden variables,” which (if they exist at all) in principle could remove the effects of chance from physical phenomena, such as for example, nuclear decay. The inherent unpredictability of the three-body-problem is of a different sort than random chance, or randomness dissociated with physical states. What the three-body problem says is that, in effect, the universe “knows,” but will not allow us to know, the future state of certain closed systems, no matter how much we know about that present system.

What does all this mean, in metaphysics?

It reminds us of the debate between determinism and volition. If the physical universe is purely deterministic, it does not allow for free will, even if it does allow for unpredictability. This is because free will contains the principle of conscious intent. Free will is not random; it is goal-oriented.

If the universe is not deterministic, if instead there is free will, then there is an external reality, a super-nature, that governs the natural. Free will can override the chain of cause-and-effect. There is a Creator.

Life, consciousness and free will are the interlocked aspects of triunity in the physical world.

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