I think that determinism doesn't entail predictability, even in principle, unless you
are going to help yourself to some principles that are so outlandish
that you might as well invoke the supernatural.
Roughly speaking, 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.
I think intuitively, it seems 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 suppose that some supercomputer could show us a picture of where every ball would be on the table for any future time.
So if the whole natural world were considered as a deterministic system, we might conclude that the future is completely predictable. But there seem to be limits on
predictability by any methods of computation conceived of so far.
First, we'd need precise measurements, 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 is 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 are reasons why, although we might have a strong intuition 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 probabilités, 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, which is
ironic given this is one thought experiment that hard determinists use
to deny free will.
I have reposted this as the previous version was appearing as a draft on my dashboard, so apologies if it appears to duplicate!
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10 comments:
All of your arguments seem to be arguments for why determinism does not entail predictability in practice, but you say it isn't even possible in principle. But even the arguments you give for why determinism doesn't entail predictability in practice only show that the future can't be predicted with infinite precision indefinitely into the future.
Thanks, I see what you mean, but I think the situation in terms of predictability is drastically worse in practice than you imply. It isn't that we will get most things mostly correct for ages. This might be true for very large stable systems like the solar system, but not for, to take an example, the weather. this is because that's a chaotic system which is very sensitive to small perturbations. Such chaotic systems confound predictions of the very things determinists are interested in, like future decisions or states of human affairs.
My other point was to critique the 'in practice' versus 'in principle' distinction in this case. We can imagine a situation where this distinction is valid, maybe in principle you could sequence somebody's DNA as a diagnostic aid but this would be impossible in practice. That was true 25 years ago, but not any more. However, what would it mean to say that in principle you could predict the weather? Which principles that govern the weather will you ignore while helping yourself to the stability to other principles of physics, computation or logic?
It might be that you and I are taking "in principle" to mean different things. I take "in principle" to mean that if you knew all the initial conditions, and if you had some way to process that information with precision, then you'd be able to make accurate predictions. So you'd have to know the precise condition of every particle, and all the laws of nature, and have a computer capable of calculating it and all. It may never be possible to do that, but the impossibility is a practical impossibility. But if determinism is true, then it strikes me as being possible in principle to predict the future since the future is determined by the initial conditions plus the laws of nature.
What makes the weather practically impossible to predict with any precision is the fact that there are so many variables. Have you ever heard of the three body problem? It's the problem of calculating the path of three objects that are orbiting each other. It's easy to do with two objects, but it becomes a nightmare when it's three objects. But in the case of the weather, it's more like 10 raised to the big number problem. So it's likely we'll never be able to predict the weather with very much precision, but it's still possible in principle to predict the weather with precision, at least the way I am understanding what it means for something to be possible in principle.
Yes, I have heard of the three body problem, and way back when I did my undergraduate studies, the course in numerical methods opened our eyes to what a tiny proportion of mathematical problems are amenable to analytic solutions!
I think you are using 'in principle' in the standard way, but this usage is what I try to critique in the post. I think there is a difference between the example of DNA sequencing I gave above and the equating of determinism and predictability.
I think the in principle/in practice distinction makes sense if the limitation is practical. So computers got faster and the problem became tractable. It was clear in the problem that no fundamental aspects of the scenario needed to be changed or ignored, no laws of logic or physics needed to be broken to invoke the 'in principle' scenario.
By contrast, predictability entails that in principle, an agent could know in advance. A supercomputer by the very act of doing the calculation would alter the result, meaning it would have to redo the calculation ad infinitum. Unless it were completely outside the universe, in which case there would be no way to get the result!
To summarise, the only agent who could know in advance would be god. But goddunnit isn't a legitimate principle to invoke. Hence the in practice/in principle distinction doesn't work.
You're not allowing for chaos theory, which is what guarantees phenomena to be unpredictable. Chaotic phenomena are dependent on the sensitivity of the initial conditions which require calculating to infinite decimal places, which is why a supercomputer won't cut it. It's also why weather prediction is limited (refer link below).
Someone mentioned the 3 body problem and I think it was Poincare who realised it was indeterminable. Poincare is arguably the 'father' of chaos theory. There are a number of good books on chaos theory, but the best I've read is Does God Play Dice? by Ian Stewart. I wrote a review here.
I am not sure whether you are replying to me or Sam, but my original post does address the issues you raise. For example "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."
I am arguing that deterministic systems are not predictable, even in principle and chaos is one of the reasons.
You are, in effect, describing chaos theory in your original post, but you don’t say so. You mention Laplace’s famous claim that he could predict the future, if given enough information, but chaos theory (discovered after him) says it’s impossible.
Chaos theory is usually defined as ‘deterministic but unpredictable’, but, in practice, chaos theory could be defined by saying that if you ‘rerun’ a chaotic phenomenon you’ll get a different result. And that applies to everything from tossing a coin to the evolution of the entire universe. Even the orbits of the planets are unpredictable (extremely long term, about 100 million years) and that’s a consequence of the 3 body problem. The point about chaos is that it’s not random and it is predictable short term, including the weather. But 'short term' can mean different periods for different phenomena, as explained above for planets.
Thanks for clarifying Paul, yes I agree that chaos theory is implicit in my post, perhaps I should have referred to it by name. That isn't really my main point though, which was to critique the in practice/in principle distinction. I suspect that you put 'rerun' in quotes, not just that you can't step into the same river twice, as Heraclitus would have it (or once, thanks Cratylus).
I would agree that with a chaotic system, it is the sensitivity to arbitrarily small perturbations in the initial conditions that ensures that a rerun will be different. I have sometimes wondered whether, if I went back in a time machine with last week's winning lottery numbers, the draw would come out differently due to the effect of me going back (ignoring time paradoxes, timelines and so on).
But surely it is then open to the Demon's advocate to say, what if we started with exactly the same initial conditions? Then that it would unfold the same way is entailed by determinism. Some people draw from this that in principle, if they had perfect information about the state S of a chaotic but deterministic system, they could predict a future state S'. This is what my post rejects.
Thanks for responding to my comment. Some physicists still claim that the Universe is 'deterministic' because we know that QM (Schrodinger's equation and all its derivatives) is deterministic and chaos is defined as 'deterministic but unpredictable'. So I would call it 'indeterminable' to make the distinction, because it's mathematically impossible to predict long term. Regarding QM, it becomes indeterminable once decoherence of the wave function occurs. It's the interface between QM and classical physics that makes it unpredictable. So unpredictability is built-into the Universe at 2 levels: QM and Chaos.
So what they are saying is that the Universe is deterministic but we just can't work it out. I reject this, as I believe you do, as well.
Yes, I think we agree on that.
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