Inherent Unpredictability

[Robert Arvay]

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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[Eugene I]

But it also means that the Creator cannot exhaustively know the reality by his cognition (including the reality it creates), and the reality is irreducible to his ideas, because if he could exhaustively know it, then the reality (and the knowledge of it) would be entirely deterministic and there would be no free will. So, free will and omniscience are mutually exclusive.

[Robert Arvay]

by Eugene I » Sun May 09, 2021 3:33 pm

But it also means that the Creator cannot exhaustively know the reality by his cognition . . .

Unless He is infinitely beyond OUR cognition.


because if he could exhaustively know it, then the reality (and the knowledge of it) would be entirely deterministic

Unless He has created us with free will


and there would be no free will. So, free will and omniscience are mutually exclusive.

Free will and determinism are mutually exclusive. Omniscience? We cannot begin to fathom that,
much less to assign limits to it.
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[Eugene I]

because if he could exhaustively know it, then the reality (and the knowledge of it) would be entirely deterministic

Well, how is it free will if the Creator knows the result of my free choice even before I made it? If he knows the result of all our choices before we make them, that's exactly determinism, because we do not have any choice and freedom to make decisions that are different from those known to the Creator.

[Robert Arvay]

Well, how is it free will if the Creator knows the result of my free choice even before I made it? If he knows the result of all our choices before we make them, that's exactly determinism, because we do not have any choice and freedom to make decisions that are different from those known to the Creator.


That is a very common argument, but it relies on a flawed set of conceptions-- conceptions both of time and of free will.

For example, I already know of the free will choices I made yesterday. I cannot go back in time and alter them. Does that mean that at that time, I had no free will? Non sequitur.

Likewise, if God knows that in the future I will make free will choice #A, then He knows that I will make that choice by my free will.

We are so mired in thinking in terms of physical determinism that it is very difficult to mentally step outside of the space-time continuum and consider that the eternal condition does not necessarily follow our rules or our logic. We need to be humble, and to accept that we are finite creatures who cannot encompass the infinite.
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[Martin_]

Chaos is not a-causual. Indeterminism (as defined by you), is not the same as a-causuality.

The three-body problem (classiclly formulated) is fully deterministic on short time scales, and the fact that we can't predict whats going to happen in the far future does NOT suddenly open up for some kind of free will that wasn't there before.


Now if you wan't to bring up quantum indeterminism/uncertainty; that's a different matter. But chaos theory and its consequences doesn't open up for any acausuality / free will opportunity in my opinion.

[Robert Arvay]

Chaos is not a-causual. Indeterminism (as defined by you), is not the same as a-causuality.

The three-body problem (classiclly formulated) is fully deterministic on short time scales, and the fact that we can't predict whats going to happen in the far future does NOT suddenly open up for some kind of free will that wasn't there before.

Now if you wan't to bring up quantum indeterminism/uncertainty; that's a different matter. But chaos theory and its consequences doesn't open up for any acausuality / free will opportunity in my opinion.

I'm actually agreeing with all that.

I used the 3-body problem to introduce the idea that, as I said,

"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."

From there, I moved into some of the metaphysical implications of that.
I could have been more systematic and exhaustive, but I did that in my self-published book, The God Paradigm.

This forum is too constricted for that. My apologies for the contraction.
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[Jim Cross]

Robert,

You might be interested in this paper.

https://link.springer.com/chapter/10.10 ... -95972-6_3

For some reason, various people have a problem opening that link but I also provide a summary and discussion of it on my blog.

https://broadspeculations.com/2021/04/2 ... ypothesis/

The gist of it is that author argues that processes in the brain are not computable in the Turing sense so the brain must be doing simulation rather than computation.

It is thus reasonable to pit simulation as an alternative to computation and ask whether the brain, rather than computing, is simulating a model of the world in order to make predictions and guide behavior. If so, this suggests a hardware supporting dynamics more akin to a quantum many-body field theory.