Determinism vs prediction

Question

What is the difference between determinism and predictable. I have heard classical mechanics is both predictable and deterministic , chaos theory is deterministic but unpredictable , quantum mechanics is indeterministic and unpredictable. And how determinism is related to free will ?

Answer 1

Determinism means that what happens in the future is unambiguously determined by what happened in the past. Predictability means that you can figure out what will happen next based on what happened previously.

For example, suppose you swing a simple pendulum. Its movement is determined by the fact that it is constrained at one end, that it is acted upon by the force of gravity and air resistance. Its movement is also predictable- you can work out where the pendulum will be after it has been swinging for a given time. If you then make the pendulum more complicated, by adding some other moveable parts to it, its movement is still determined by gravity, air resistance and the relative positions of its fixed points, but those influences will be too complicated for you to model mathematically, and you won't be able to predict exactly where the pendulum will be after a given time.

In quantum mechanics, as we know it today, the idea of determinism breaks down, because the outcome of interactions between particles appears not to be determined unambiguously by any factors (as far as we can tell). For example, if you have a particle with some unknown spin direction and you measure its spin direction, the result you get appears not be determined by anything- it seems genuinely to be a chance outcome. That is quite different to tossing a coin say- as there the motion of the coin is governed, like the movement of the pendulum, by well-understood forces- the problem is simply that the details of how the coin interacts with its environment during the toss are too complicated to model. In other words, there are lots of factors at play which we understand and could in theory calculate. With the quantum particle that is not true- our best theories suggest that there cannot be 'hidden variable' that determine the results of experiments- the results are genuinely probabilistic in a fundamental sense.

The idea of free will seems incompatible with determinism. If your brain worked like a complicated clockwork mechanism, then all of your future actions would be unambiguously determined by all of the things that had happened to you previously.

Free will seems to require indeterminacy. However, indeterminacy alone isn't enough to explain free will, as this simple example will show...

Your thoughts seem to be associated with electrical activity in your brain- ie the movement of charged particles, which are, as far as we know, either behaving in a classical deterministic way or they are behaving as quantum particles so some of their interactions may be genuinely random. If you are asked to decide consciously to raise your left or right arm, at some point the result of your thinking is that electrical impulses travel down your nerves and one of your arms moves. In terms of our current knowledge of physics, that is again either the result of deterministic classical motion of charged particles or random quantum interactions. Neither of those is consistent with the idea of 'free will', which we usually take to mean more than just acting at random. Free will requires your thoughts to be to some extent independent of the configuration states of the particles within your brain, but at the same time able to understand those states (since those states represent the sensory inputs we experience) and at the same time able to influence those states (since those states are responsible for determining which arm you raise, for example).

There is nothing in physics, currently, that can provide a slam-dunk explanation for consciousness, so it remains a challenging open question for science and fertile ground for speculation in philosophy.

Answer 2

Classical mechanics as a theory is deterministic. It is based on a simplified model of reality (=determinism). A model with no inaccuracies or uncertainties (or free will).

A deterministic system, whose each state is an unambiguous mathematical function of every other state, is theoretically predictable to an outside observer (Laplace's Demon). Within that system it is not possible to predict anything for the following reasons:

• There is no free will, therefore no concept of knowledge, no-one capable of possessing, processing or wanting more knowledge.
• The system is already "predicting" its future states as fast as physically possible. It is not possible to set up a complete model of the system within that system and calculate future states faster than they happen in reality.

In a deterministic system all actions are causal reactions to prior events. There is no way any mental function like knowledge, preference or desire could have any effect whatsoever on the flow of physical events.

Answer 3

Determinism is a belief that physical behavior is 100% predictable without any randomness.

A prediction is an action in which the outcome of an event is stated (based on available information) prior to the actual event. Predictions are not limited to deterministic systems and can be applied to stochastic systems like lotteries.

So for weather systems, the equations used to model weather are deterministic; meaning that if EXACTLY the same numbers are entered into the model, then the outcome is the same no matter how many times the model is run. However, these same equations are extremely sensitive to the data entered. The slightest difference can produce output drastically different for each run. Limitations on the precision of measured data, mean that these models will work for a limited time with accuracy decreasing over time.

This is how chaotic systems can be deterministic but still lack predictability.

Free will and brain function are similar. While brain function and development are deterministic, the sensitive dependence on the stimulus that the brain receives makes predictability nearly impossible so free will and determinism can coexist.

Answer 4

Karl Popper's¹ and Michael Scriven's² theorems are two notable examples that challenge the view that determinism implies predictability.

The theorems are roughly as follows:

1. They assume a limited form of prediction, in the sense that the prediction is identical to the outcome (P = O).
2. They assume that a prediction of the output of some system S is available at some point, as input to that system.
3. The system is an invertor (what is termed contra-predictive) in that its output is the inversion of its input.
4. Thus P = O is always false. QED.

What limits the scope of these theorems is the limited sense in which prediction is taken (ie identity of prediction and outcome). For prediction in the general sense of an arbitrary but fixed one-to-one mapping P=F(O), the reasoning does not apply.

For example, if a prediction of temperature uses Fahrenheit, while the system predicted uses Celsius, the fact that the two readings never coincide numerically (ie P =/= O), makes it no less of a prediction (since P = C2F(O) and C2F is a fixed one-to-one mapping that translates Celsius to Fahrenheit).

In fact Scriven mentions as such in the criticisms and clarifications section:

“But we can precisely predict C’s behavior; C will always do the opposite of what P predicts.”

The prediction task of the theorem is prediction of the precise alternative which C selects. Of course, for other prediction tasks, this result does not apply.

Popper mentions the limited sense of predictability he used as well.

Considering determinism and the general sense of predictability above, there is no reason that determinism does not imply predictability. One can even argue, that it is a priori impossible for determinism to not imply predictability, since the core of determinism is that things are fully determined. That is, changing one thing, necessarily changes all other things as well, because if otherwise, that thing would not be fully determined by other things being determined as well. In this sense it is easy to see that in determinism everything can be used as a predictor for everything else.

Someone may argue that even if determinism is true, does not mean we know the exact mechanism that relates one state to the other (eg lack of precision, unknown parameters, or even complete lack of knowledge), thus we have uncertainty and unpredictability even with determinism. This argument is not good enough for the simple reason that uncertainty is a result of having more than one possible outcome and not a result of not knowing how the only possible outcome comes about. For example, when there is only one possible outcome to expect we do not experience uncertainty even if we don't know the exact mechanism the outcome comes about from the current state, we are sure it will happen anyway. So since in determinism there is only one possible outcome in any given state, there can be no (experience of) uncertainty and no unpredictability.

Chaotic systems are not in principle unpredictable in a deterministic universe. The "unpredictability" of a chaotic system can either be attributed to factors outside of what is assumed to be deterministic (eg quantum chaos), else for any finite interval, finite precision is adequate for prediction in that finite interval. The latter is demonstrated, for example, in weather prediction. One can argue that we can never achieve infinite precision as an a priori thesis. But infinite precision is necessary only for prediction over roughly infinite time, for any finite time, finite precision is adequate.

It can be argued that some systems may only be predicted by actually running the system in real time, thus prediction is impossible in this sense, since a simulation cannot be run faster. This argument may hold for some systems that run at the fastest speed (although implausible). But even in this case, one may not be able to run a simulation faster but one can run a simulation earlier. So this is not as grave an objection either.

On Separating Predictability and Determinism, Robert Bishop

There has been a long-standing debate about the relationship of predictability and determinism. Some have maintained that determinism implies predictability while others have maintained that predictability implies determinism. Many have maintained that there are no implication relations between determinism and predictability. This summary is, of course, somewhat oversimplified and quick at least in the sense that there are various notions of determinism and predictability at work in the philosophical literature. In this essay I will focus on what I take to be the Laplacean vision for determinism and predictability. While many forms of predictability are inconsistent with this vision, I argue that a suitably restricted notion of predictability, consistent with the practice of physicists, is implied by the Laplacean notion of determinism.

To address the other questions as well:

If both determinism and free will are assumed true, then this thesis is called compatibilism (of determinism and free will).

Classical mechanics can be re-formulated as an indeterministic theory, similar to quantum mechanics. See for example:

Indeterminism, causality and information: Has physics ever been deterministic?

A tradition handed down among physicists maintains that classical physics is a perfectly deterministic theory capable of predicting the future with absolute certainty, independently of any interpretations. It also tells that it was quantum mechanics that introduced fundamental indeterminacy into physics. We show that there exist alternative stories to be told in which classical mechanics, too, can be interpreted as a fundamentally indeterministic theory. On the one hand, this leaves room for the many possibilities of an open future, yet, on the other, it brings into classical physics some of the conceptual issues typical of quantum mechanics, such as the measurement problem. We discuss here some of the issues of an alternative, indeterministic classical physics and their relation to the theory of information and the notion of causality.

References:

1. Karl Popper, INDETERMINISM IN QUANTUM PHYSICS AND IN CLASSICAL PHYSICS: PART II
2. Michael Scriven, AN ESSENTIAL UNPREDICTABILITY IN HUMAN BEHAVIOR

Answer 5

Determinism posits that all events follow an unambiguous cause and effect relation. Predictability describes our theoretical and/or practical ability to discover such a cause and effect relations and free will is the assertion that we are not just driven by cause and effect but do poses agency over our lives.

And while it might not be obvious the implications of some of these ideas are huge and their relation somewhat complicated. Like depending on what is or isn't true, you could look short or far into past and future or might erase the usefulness of these concepts.

So for all that we know the past is unalterably gone and the present is just now and while we can act in the present, we can't change how we act in the present, as change is not "immediate" and thus takes us out of the present and into the future. So the only temporal domain where we could change our actions is in the future. So in order to exercise our agency we would like to know what happens next, because if we'd know that we could change it. The past is fixed, the future isn't.

Now how can we predict something that isn't fixed? Well predictability somewhat implies determinism, that is in order to know what happens next you have to be able to create rules about "how future result B follows from a set of past initial conditions A". And in order to create such a rule which produces reliable results, it actually somewhat has to work like that. Otherwise you're not predicting the future, but are just guessing and thus you don't change the future, but you'd just act.

However this produces a different kind of problem namely that if your predictions are true (and not just by coincidence but because they are correct thus deterministic) and if thus determinism is true and thus future events follow from past events, then... yeah... well... future events follow from past events. So the future is also fixed, i.e. determined by past events.

So in other words we could see ahead but we couldn't change what comes ahead. So rather than a game, it's more like a movie. You can fast forward and rewind but the action at a certain point in time remains the same and "the end" is determined right from the very "beginning". Which prompts unanswerable questions about a pre-deterministic era, gods, big bangs and whatnot. Likewise you could also imagine it to be a stage play, where the plot is scripted but a heckler throwing a banana peel at the stage might force the plot to change ever so slightly, because the actors either need to avoid it or slip because of it. Yet the banana would determine the outcome just like the script had previous, different determinism yet still determinism.

So classical mechanics was on a track to create such a finite set of rules so that if you knew the location and momentum of every atom in the universe you'd be able to see past, present and future as clear as if you'd be there. That being said, this is a theoretical assumption because even if that would have been true, any computer that realistically models/simulates our entire universe would likely be of a similar size and complexity. That is to predict the future before it becomes the past you'd need to have a computer that runs the entire universe at a "faster than time"-speed, meaning physical interactions just need to happen faster than they would (which is not trivial as the process would proof the physics wrong that it is itself simulating...) or you'd need to simplify the model in order to be able to take short cuts.

So classical mechanic would, if true, be deterministic, theoretically predictable but practically un- or only approximately predictable. Another such practically unpredictable edge case is chaos theory, that is again acting on deterministic rules, but the initial conditions are sooooo fragile that a teeny tiny disturbance evolves into a whole different outcome in a rather short amount of time.

So you don't just need to know the initial conditions you'd need to know the initial conditions with precision. And this is where quantum mechanics delivers a deadly blow to classical mechanics, because measurements of the teeny tiny stuff become ... complicated. Like the hopes of getting location and momentum at the same time with perfect precision are torn apart, as these two can't be measured at the same time the more accurate you measure the one the more inaccurate the other one gets. And that's not just a problem of technical limitations it's a fundamental problem.

So it's unpredictable, but not just that it's also possible to know the state of a particle and still don't know the result of a measurement (indeterministic). So the knowledge of the initial conditions don't suffice to predict the result, but just a probability distribution. And even the definition of what a measurement itself actually is becomes difficult because the measurement doesn't just observe but interacts with the measured particle.

So to summarize the problem in relation to free will. In order to not just go with the flow but act out your agency, you'd need to be able to predict and plan, but in order to do that you'd need to find deterministic patterns that enable you to plan. But the more reality shows itself to be deterministic and the better the prediction the less agency you'd have to interfere with that. Because at some point you'd yourself become a relevant factor in the question of "how the world works".

And if literally everything is deterministic so are you. Yet if you are not deterministic then you'd somewhat be "super natural" in interesting ways. And while yes this "super natural" is just a demarcation line between rules that describe nature and rules that describe you, it actually would be something "god-like", because it would mean that you could be the primary cause of a chain of events, not just one domino brick but a literally creator or desctrutor. And no matter how much you'd follow the path of Compatibilism (which believes that free will and determinism are compatible) and how much you allow for determinism to expand, you'd still would end up with yourself or at least a part of yourself ending up being undeterministic. And not just undeterministic as that would just mean random and unpredictable, but controllable. So it's not even to prove determinism wrong you'd need to proof agency right. So you could concede that you can't think about anything that is possible but only about things that are thinkable for you (that you've experienced or can form from mixing experiences). Or that your body might take control if it "thinks" your doing things wrong (hunger, sleep deprivation, fatigue, ... emotions in general). You can't even "decide" for yourself how you feel about things, you just do. So you can push back this "god-like" entity quite a bit or negate it's existence altogether, because it's powers can ever be more curtailed by descriptions of deterministic processes. And it certainly makes for a rather interesting problem how the interface between something natural and something supernatural would actually look like because "we" (whatever this is) are part of the environment, our sensory inputs are hooked to a world that can be modeled to be deterministic and we also can interact with them so we can send out signals that lead to actions in this world. So no matter how narrow you draw the blackbox that is "the brain", "the consciousness", "the mind", "the soul" or however you want to call it, you'd need to have that somewhere or you'd need to be able to describe it in deterministic ways.

Yet at the same time "we" also do feel to have free will. Like life doesn't feel like a movie, you're not a passive observer you're part of the action, you plan ahead, you feel feelings, but you can also make deliberate decisions that you know will cause harm and will make you feel uncomfortable or even kill yourself. If all this is an illusion and part of deterministic machine, that's one hell of a machine in such a relatively "tiny" space.

TL;DR predictability somewhat depends on determinism and determinism is somewhat incompatible with free will yet free will would really benefit from predictability.

Answer 6

Determinism is the only scientifically accepted method of prediction. We have some basic laws and we know how they work on matter and energy. Once we know the initial state, we can calculate quite precisely what's gonna happen.

There's another method, it's been discredited, and it's clairvoyance or ESP (psychic abilities). Mechanism ?

In short there are two ways we can make predictions - one actually works (scientific determinism) and the other (ESP) is, as per scientists, poppycock.

The relation between determinism and free will is quite simple. If the former is true, our minds participate in the causal web and our thoughts are for that reason effects of causes that are external to us. We're on this view just another cog in a clockwork universe i.e. we lack free will. To cut the long story short, if determinism is true, free will is impossible.

Now for the woo-woo part. God has been described as omniscient i.e. he knows the future. If so he know exactly what I'll do tomorrow at 4:14 PM. Can I change my mind tomorrow at 4:14PM and do something other than what god had predicted? If I can, god ain't omniscient and if I can't, I have no free will.

Note, clairvoyance/ESP/divine predictions may be possible in an indeterministic world; we just don't know how it's done. Hence my comment on the one combination that the OP left out viz. indeterministic & predictable.

Answer 7

As other answers have already stated, determinism is encoded in the nature, whereas predictability refers to our ability to predict/determine the future behavior, which is conditional on our knowledge of the initial/past state, correctness of our knowledge of the laws governing the behavior, computational power, etc. (see also Is limited computational capacity a fundamental obstacle?)

I have heard classical mechanics is both predictable and deterministic , chaos theory is deterministic but unpredictable , quantum mechanics is indeterministic and unpredictable.

Behavior governed by Newton laws (aka classical mechanics) is deterministic, because there are differential equations governing the behavior, which in principle could be solved. Simple cases of a few particles are often solvable, and hence predictable. There are two important situations where the simple classical behavior becomes unpredictable:

• Dynamical chaos - the non-linearity in equations may lead to even systems behaving in very complex way - in the sense that outcome at the later time is extremely sensitive to the initial conditions. Since the initial state is always known to a finite precision (and, in addition, the numerical computations are necessarily done to a finite precision), the prediction becomes impossible.
• Statistical mechanics - in systems with many particles (like a cubic meter of air, containing $\sim 10^{23}$ molecules) we simply cannot know the initial state of all the particles and solve simultaneously the equations of motion for all of them. Hence, we cannot predict the exact behavior, although we can use the underlying determinism to make useful conclusions about macroscopic parameters, which are insensitive to the molecular-level details - such as pressure, temperature, etc. A matter of an open debate is then whether we could eventually make predictions by using greater computational power - one can always counter that we still wouldn't be able to make predictions for a bigger system, and eventually, to make predictions for the whole Universe, we would have to use this same Universe...

It is mistaken to claim that Quantum mechanics is undeterministic. It looks as such only when you try to judge its determinism from the point of view classical mechanics, but the point is precisely that the laws of nature are not classical. Once we describe a system by a wave function, it obeys a well-defined equation (e.g., the Schrödinger equation), which, in theory, can be solved to make predictions (or statistical predictions, if you wish.) The true unpredictability then arises from the same sources that have been already mentioned above in respect to the classical case.

Note that quantum mechanics is just a wave theory - similar to the Maxwell theory of light - which however does not strike anyone as exhibiting any particular unpredictability.

Determinism and free will
Determinism does not imply the absence of free will. Indeed, free will means that no external agent (another person or a superhuman being) can predict and/or influence the one's actions and decisions. Since such ability to predict is limited even in deterministic universe, humans appear to have free will for all practical purposes. As far as the human actions are concerned, there is no way of distinguishing whether there is any non-deterministic element in non-predictable behavior. The Occam's razor then recommends us to reject any assumption about undetectable non-determinism in nature, which is akin to the notorious Invisible pink unicorn.

By the same token, assuming that the Universe is inherently non-deterministic is a belief that cannot be verified, and hence superfluous to the discussion of free will. As far as human knowledge is concerned (and this includes human decisions), the Universe is functioning in agreement with the laws of nature known to humans, and therefore for all the practical purposes can be treated as deterministic.