Determinism - does it imply predictability?

[David B]

In theory, at least.

I don't think it does, for reasons I am prepared to go into, but not at this time of night.

David

[Jobar]

:confused:

If reality is completely determined, how can we know this, if not by its predictability (at least in theory)?

Don't worry about replying tonight; but at your leisure, I'd be interested in your view of this. And just so you know, I've long thought that determinism is a dead horse; Heisenberg and that lot killed it deader than King Tut.

[His Noodly Appendage]

A universe could be completely determined, but not predictable. It's called chaos. A set of interactions that can't be extrapolated any more efficiently than a 1:1 simulation. A system where you'd need a simulator as complex as the entire universe (at least in order to have certainty) isn't out of the realm of possibility.

It seems reasonable that down at the quantum-weirdness level, the very least-significant-bits of this universe are in fact utterly acausal. This averages out to determinism at larger scales... from which larger-scale chaos can be constructed, which averages out...

[BWE]

Schroedinger's equations are entirely determinitic. If there was no observer, the quantum stuff ought to carry right along...

of course... that raises a different set of questions. :)

[The AntiChris]

A universe could be completely determined, but not predictable. It's called chaos. A set of interactions that can't be extrapolated any more efficiently than a 1:1 simulation. A system where you'd need a simulator as complex as the entire universe (at least in order to have certainty) isn't out of the realm of possibility.
So in theory (i.e. disregarding any practical linmitations) a deterministic universe would be predictable.

I guess it depends on precisely what David B means by "In theory, at least.".

Chris

[His Noodly Appendage]

Semantics does indeed play a role.

But in a system where you just don't have room in the universe itself to store all the information and perform all the calculations necessary... I'd say that it would be necessarily impossible, even in theory.

[David B]

OK, let's see if if I can reconstruct my late night wanderings of last night.

So far people have mentioned quantum indeterminacy and chaos, which are telling, but not exactly what I was thinking at the time.

What I was thinking, as best I can briefly explain off the top of my head, was that any given moment, high energy stuff is impacting on us from cosmic events just getting into our light cone. http://en.wikipedia.org/wiki/Light_cone.

Any one of them could have macroscopic effects - like for example creating a beneficial mutation, or inducing a fatal cancer in an individual foetus.

And I don't see how the presence (or absence) of effects that start outside our light cone can be predicted.

I hope that's clear enough - it makes some sort of sense to me, anyway.

David

[Valheru]

Can you determine what a tennis ball will do if you threw it at a wall, and knew the state of all of the forces at play?

Of course you could.

The reaction of Sodium and Chlorine ions? That's deterministic. The effect of gravity on a metal sphere in a vacuum? That's pretty deterministic if you ask me.

The question is, what do you want to determine, and what CAN and CAN'T you determine?

Determinism works perfectly down to a point where our observation of the system (the act of "determining") interferes with it, or simply isn't possibly via any known means.

Does that mean that everything is indeterministic? No. At some point the individual random variations (if that's what they are) become obscured in a larger, predictable whole - much like a school of fish.

[His Noodly Appendage]

Exactly, David. In order to predict anything absolutely, you'd need to know about the state of ancient neutrinos in a quasar gajillions of light years away. You'd need to know everything.

[Valheru]

Exactly, David. In order to predict anything absolutely, you'd need to know about the state of ancient neutrinos in a quasar gajillions of light years away. You'd need to know everything.

But this is exactly the problem people introduce when thinking about this. Why should people have to think about it and test whether the system is deterministic for it to be deterministic (or otherwise) in the first place.

It's like people are placing some burden of god-like perspective on the problem and via that intractability, then conclude that determinism isn't true.

It gets my goat. Tennis ball analogy again. If you sit and spectate at Wimbledon - do the tennis players or the tennis balls act any differently whether your eyes are closed or not?

That's the point - why do we need to predict stuff in order to assume predictability? It either is or isn't, whether we observe or not.

[Barbarian]

In theory, at least.

I don't think it does, for reasons I am prepared to go into, but not at this time of night.

DavidDoes not, for a given value of 'predictability'.

The notion of predictability I would shoot after is the one of "the measures of arbitrarily many state variables of the system can be simulated for any arbitrary finite length of time with arbitrary precision in a Turing machine, assuming we have arbitrarily precise measurements of the initial conditions".

In this case, all we have to do is to couple the states of two predictable systems with a deterministic but non-Turing constraint and we'd have a non-predictable but deterministic system. E.g. let the two systems have natural numbers for states, and let the constraint be "for a state n of the first system, the state of the second system is p(n) where p(.) is some non-computable function".

It is my belief, held on no hard evidence whatsoever, that such constraints cannot be created in our physical reality. But that is just a side note.

One could imagine another kind of predictability, that of "for any state variable of the target system we can choose another system that replicates the evolution of the chosen state variable to any precision for any finite time interval". This is tautologically possible for universes where we can exactly clone any system (because then we clone the original system and that's that). If we have a no-cloning theorem, then we cannot do this exact trick, and the question then becomes whether we can build an infinite chain of simulator systems whose error margin converges to zero.

Chaotic behavior is merely super-hard to predict, not principially unpredictable, so if a deterministic chaotic system is non-predictable, it's not because it was chaotic.

[Valheru]

Chaotic behavior is merely super-hard to predict, not principially unpredictable, so if a deterministic chaotic system is non-predictable, it's not because it was chaotic.

Very well put. My instincts tell me it's this. My lack of verbal skills doesn't allow me to put it so succinctly though. :notworthy:

[David B]

In theory, at least.

I don't think it does, for reasons I am prepared to go into, but not at this time of night.

DavidDoes not, for a given value of 'predictability'.

The notion of predictability I would shoot after is the one of "the measures of arbitrarily many state variables of the system can be simulated for any arbitrary finite length of time with arbitrary precision in a Turing machine, assuming we have arbitrarily precise measurements of the initial conditions".

In this case, all we have to do is to couple the states of two predictable systems with a deterministic but non-Turing constraint and we'd have a non-predictable but deterministic system. E.g. let the two systems have natural numbers for states, and let the constraint be "for a state n of the first system, the state of the second system is p(n) where p(.) is some non-computable function".

It is my belief, held on no hard evidence whatsoever, that such constraints cannot be created in our physical reality. But that is just a side note.

One could imagine another kind of predictability, that of "for any state variable of the target system we can choose another system that replicates the evolution of the chosen state variable to any precision for any finite time interval". This is tautologically possible for universes where we can exactly clone any system (because then we clone the original system and that's that). If we have a no-cloning theorem, then we cannot do this exact trick, and the question then becomes whether we can build an infinite chain of simulator systems whose error margin converges to zero.

Chaotic behavior is merely super-hard to predict, not principially unpredictable, so if a deterministic chaotic system is non-predictable, it's not because it was chaotic.

I don't think this addresses the point I tried to make in my later post.

David

[Barbarian]

I don't think this addresses the point I tried to make in my later post.

DavidThat's right, it doesn't, I replied to what I perceived to be the OP question, which in my interpretation asked for predictability of closed deterministic systems. I would consider a deterministic system to be eo ipso closed, since I understand determinism to mean 'the earlier state(s) fully determine the later state(s)', i.e. the machine is ignoring the rest of the universe, does not change course due to inputs like external influences (alternatively: it cannot have inputs if we define input as something the machine state depends on). Allowing external unpredictable influences to play a role does change the game, because then the system cannot be said to be deterministic, only deterministically processing its input, and then the unpredictability of the state is really just a consequence of the unpredictability of the input, not having anything to do with determinism.

But I think I can tweak my first definition of predictability a bit: "simulation determining the state variable with arbitrary precision" should be replaced with "simulation that produces a random variable whose expected value is arbitrarily close to the value of the state variable and whose variance can be chosen to be arbitrarily small". In this case, whether the prediction/simulation is possible is dependent upon the technological advancement of the civilization doing the experiment, because the better shields they can make, the smaller the probability that something goes through and unbalances the system being measured.

I don't particularly like this latter approach, though; there is not much to figure out about particular technological possibilities short of actually conducting the experiment, and anyway what we find to be impossible could become possible as soon as tomorrow. Whenever possible, I will restrict myself to the discussion of principial, not merely technological, possibilities and impossibilities.

[Ray Moscow]

In theory, at least.

I don't think it does, for reasons I am prepared to go into, but not at this time of night.

David

I think not, for two reasons:

1. At a quantum level, events can only be stated in terms of probabilites. Although events do follow these probability equations (and are therefore "determined"), the outcome is not "predictable" in the usual sense.

2. Even at a macro level, complexity is often too great for us to predict events beyond a certain point. I suppose one can consult "chaos" theory for a detailed explanation.

[Jobar]

Even at the macro level, multi-body gravitational interactions can only be approximated. They are not determinable, in theory.

And at the quantum level, the equations we use only "predict" probabilities of outcomes, not the actual outcomes. The exact path and timing of some complex nuclear decay is unpredictable. We can say it will take one of several known paths, but which one it *will* take we can never say.

[Barbarian]

Even at the macro level, multi-body gravitational interactions can only be approximated. They are not determinable, in theory.A long time ago, in a country far, far away I was taught (or so I remember) that the many-body (many = more than two) problem does not allow solutions in closed form, for a certain value of "closed form". (Actually it's slightly worse than that, but that does not matter here.) So there is no finite formula using the usual operations that would give the position vector of every single object involved at any particular time, but the many-body problem is still (1) solvable via straightforward numeric integration which is approximate but then so is the numeric evaluation of a finite formula and (2) perfectly deterministic, just not accessible via finite formulae.

Theoretical mechanics curricula are creating the impression that this is an exotic state of affairs, but it's in fact the other way around: mechanical problems solvable in closed form are the exceptional minority, and lots of work goes into choosing examples and exercise problems from this minority. In that sense, the three-body problem is just more mainstream than the exercises in the book.

[Preno]

Even at the macro level, multi-body gravitational interactions can only be approximated. They are not determinable, in theory.A long time ago, in a country far, far away I was taught (or so I remember) that the many-body (many = more than two) problem does not allow solutions in closed form, for a certain value of "closed form".Just to correct that slightly, it does allow for closed-form solutions, it's just that in general the solutions aren't that nice.

[Apostate1970]

The answer to the OP question is "Definitely no.".

If knowing about a system requires causally interacting with it then a system can be completely causally deterministic without being completely predictable, that is, without the details of its future states being completely knowable.

Recognizing this doesn't require any special knowledge about physics, mathematics, or any other such thing and requires nothing more than an ability to deal with very simple concepts like sameness vs. difference (ex. qualitative and temporal difference).

[Jobar]

If we hypothesize that reality (or some specific system within reality) is determinate, but we cannot predict or demonstrate this is so- then we cannot say certainly that the system is determinate. In fact, because we can't prove determinacy or indeterminacy, our own knowledge of the system is indeterminate as well as unpredicted. We can fairly call it neither determinable nor indeterminable; neither predictable nor unpredictable.

All we can say is that reality is both unpredicted and undetermined.

[Apostate1970]

If we hypothesize that reality (or some specific system within reality) is determinate, but we cannot predict or demonstrate this is so- then we cannot say certainly that the system is determinate. In fact, because we can't prove determinacy or indeterminacy, our own knowledge of the system is indeterminate as well as unpredicted. We can fairly call it neither determinable nor indeterminable; neither predictable nor unpredictable.

All we can say is that reality is both unpredicted and undetermined.

Your final sentence doesn't follow from the previous ones.

[Jobar]

OK, to expand:

All we can say is that, if we hypothesize that reality (or some specific system within reality) is determinate, *and* there are aspects of reality which are unpredictable even in theory, then reality is both unpredicted and undetermined.

I think there are major semantic difficulties here. In a determinate system, who or what does the determining? It sounds like one or more conscious observers is needed for that. And if the system is determinate, then it would seem that the determining consciousness must be able to predict all aspects of the system, or else how can it be said to be truly determinate? Mustn't a truly determined universe be observed by a fully omniscient awareness? And such an awareness can predict all states and events in that universe.

[Jobar]

Look at it this way. Think of a system within our universe that is, to a good approximation, determinate- say two masses so far away from any other masses that they can be treated as the ideal two-body problem. Can't we predict all states and events for this system, given knowledge of the system state at any one time? If we can't do that, then how are we to claim the system is determinate?

Maybe I'm not using the same definitions of 'determine' and 'predict' the rest of you are using. If so, I await any clarifications with interest.

[Garrett]

Chaotic behavior is merely super-hard to predict, not principially unpredictable, so if a deterministic chaotic system is non-predictable, it's not because it was chaotic.

Very well put. My instincts tell me it's this. My lack of verbal skills doesn't allow me to put it so succinctly though. :notworthy:
I agree also. However, reality is inherently unpredictable, and not because it's chaotic - but because the future hasn't been determined yet. You really can affect your own future on purpose.

We can't even predict how Jello will bounce, but so many of us are so sure Jello-bounces are fated.

It's hopeless and helpless to think my answer and your response was determined at the Big Bang.

[Garrett]

Look at it this way. Think of a system within our universe that is, to a good approximation, determinate- say two masses so far away from any other masses that they can be treated as the ideal two-body problem. Can't we predict all states and events for this system, given knowledge of the system state at any one time? If we can't do that, then how are we to claim the system is determinate?

Maybe I'm not using the same definitions of 'determine' and 'predict' the rest of you are using. If so, I await any clarifications with interest.
At a given level, perhaps. But reality isn't confined to two-body physics problems.

[Yahzi]

So far people have mentioned quantum indeterminacy and chaos
You don't even need that.

Chess is perfectly deterministic. No quantum/chaos theory in it at all. But good luck predicting it.

The calculations required to perfectly predict a chess game (i.e. guarantee a win) are so involved that there aren't enough molecules in the galaxy to perform them.

Some problems are just too difficult to be predicted in anything close to real time. The universe is one of them.

[Preno]

Chess is perfectly deterministic. No quantum/chaos theory in it at all. But good luck predicting it.

The calculations required to perfectly predict a chess game (i.e. guarantee a win) are so involved that there aren't enough molecules in the galaxy to perform them.I'm not aware of any proof that White can guarantee a win in chess. Reference, pls?

Also, there is no reason to assume that if such a strategy exists, it is unique, so you seem to be using the word "predict" somewhat loosely.

[Febble]

That's the point - why do we need to predict stuff in order to assume predictability? It either is or isn't, whether we observe or not.

If predictability isn't anything to do with being able to predict stuff, then why use the word at all? Why not just use "determined"?

[Yahzi]

I'm not aware of any proof that White can guarantee a win in chess.
That's not necessary for chess to be deterministic; it is possible that a perfect game results in a draw, a victory for white, or a victory for black. And yes, there may be multiple equally perfect games.

However, the fact remains that chess is a non-random problem with an undeterminable solution. The universe could easily be the same.