What happens when a conscious, intelligent being interprets a deterministic model?

Question

Sorry, I’m new here, and I’ve truly no experience with philosophy. However, I’ve had this problem that I’ve been thinking about for awhile concerning a deterministic model for the universe.

Consider a hypothetical, experimental world where the universe is deterministic, and all states have exactly one immutable outcome. Now let’s say you, the conscious experimenter, discovered what appears to be a model for the universe that could predict all of the future events based on fundamental rules and initial conditions. Then, using this model, you calculate what you will do ten seconds from now. Let’s say in ten seconds the model says you will take a seat. However, you decide to contradict it, and simply remain standing. Haven’t you broken the model? It doesn’t matter whether the model is able to predict that you will contradict it, since it must describe one definite outcome (I imagine this means it can't contain conditionals), which you will then contradict after the calculation. Perhaps that wasn’t the true deterministic model. But doesn’t that mean that the true deterministic model is one that can/will never be exposed to conscious, intelligent interpretation?

Does this mean that humans, even given an infinite wealth of technological resources and time to research, will never be able to find a deterministic model for the universe (if there is one)? Can’t a conscious and intelligent being contradict any deterministic model that it can interpret? Does this say anything about the nature of consciousness or intelligence? What’s the best way to understand this?

Thanks for helping. I’m rather young, so please go easy on me!

Sidenote: my short lived online research expenditure led me to Thomas Breuer’s self-reference problem. I don’t understand it entirely, but I think it has something to do with the inability for an observer to take accurate measurements from inside of a system, or something. Is it related?

Answer 1

I think you've essentially rediscovered the undecidability of the Halting Problem. This is the statement that it is impossible to write a program that can determine whether any program will terminate. The actual proof uses some rather involved logic, but the result can be summarized by the following counterexample: write a program that takes the output of a hypothetical Halting program when run on itself, and terminate if and only if the Halting program predicted that the program would not terminate. This contradicts the Halting program, therefore such a universal program cannot exist.

Within the context of a model for the universe, my hypothetical explanation deals with how such a model would have to work. Suppose that we know a deterministic model for the universe, and from this construct a function called Predict10. This function takes any complete state as input and returns newState, which is what state is predicted to evolve to in ten seconds.

Predict10(state) = newState

Note that each state consists of many many points spread out across whichever (closed) system you're running the model on. Predict10 will function by applying the rules of the model to each point in state, taking into account every other relevant point. Essentially each point in newState is determined by a (presumably very complicated) series of equations operating on state. Let the current state of this very universe be thisState, and let nextState = Predict10(thisState).

Suppose we look at the Andromeda galaxy in nextState. The state of every point in the Andromeda galaxy will be determined by the aforementioned equations derived from our model. Of particular note is that, since the Andromeda galaxy ten seconds into the future is not in our (the observers') light cone, the fact that we use Predict10 at thisState can have no bearing on nextState in Andromeda. That is, our use of Predict10 is not part of the equations used to determine Andromeda in nextState. Thus we cannot "interfere" with the deterministic model's results for Andromeda, and the equations should converge to some reasonable answer yielding Andromeda ten seconds in the future.

Now, instead suppose that we want to look at the state of my computer in nextState. Here is where we run into a problem. Take any point in my computer, and consider the equations that go into determining its nextState. Part of these equations will be the fact that I use Predict10, since the point is in that event's light cone. However, the point is also in the light cone of my response to the result of Predict10 - and there's the rub. We need to know how I will respond to Predict10 in order to finish computing Predict10 for any point in my light cone (beyond points that take place before I've had sufficient neurological time to respond), but we cannot know how I will respond unless we finish the computation. It's a sort of catch-22 that prevents our algorithm from working in this situation. There's nothing inherently wrong with our model; it just can't converge to a solution in certain regions of the universe because of the above problem.

So in summary, your thought experiment doesn't disprove the possibility of a deterministic model per se. Rather it demonstrates (roughly) that any such deterministic model will have limitations in its range of application, though there should still be places where it functions perfectly.

As a final disclaimer, note that all this is heavily related to much more concretized problems in the study of differential equations. That is the field of mathematics (and physics) which deals with precisely the question of how states evolve over time.

Answer 2

In philosophy: 'all states have exactly one immutable outcome' is known as Hard determinism. The decision to contradict the out come implies free will.

Hard determinism is not compatible with free will.

In a deterministic universe, an agent can not decide anything at all. He can only act in a determined manner and his thoughts and actions are already supposed to be factored in the model. In that sense in a deterministic world a human is no different from a stone, in terms of his/her ability to alter the course of action.

For more details visit: http://en.wikipedia.org/wiki/Free_will

Answer 3

I suggest Thomas Breuer's The Impossibility of Accurate State Self-Measurements (pdf):

It is shown that it is impossible for an observer to distinguish all present states of a system in which he or she is contained, irrespective of whether this system is a classical or a quantum mechanical one and irrespective of whether the time evolution is deterministic or stochastic. As a corollary, this implies that it is impossible for an observer to measure the EPR-correlations between himself or herself and an outside system. Implications of the main result are discussed for how we have to conceive of universally valid theories.

This would mean that you can never [perfectly] know all the inputs for your model; it implies that Laplace's demon and Maxwell's demon are impossible in principle†. If you don't have all the relevant inputs, you cannot make perfect predictions.

† Unless perhaps you start in a state of perfect self-knowledge? I've been thinking through Fitch's Paradox of Knowability lately. This makes the white stone in Revelation 2:17 intriguing!

Answer 4

Think of an oracle telling you the prediction. Because the universe is deterministic, whether you will be standing or sitting in 10 secs is a function f(v1,v2) of only two variables: v1. the initial state of your brain (and maybe some ambient environment) and v2. the "Standing" or "Sitting" you heard from the oracle.

Saying the divulging oracle can always make a correct prediction is the same as requiring f(v1,v2="Standing")=standing & f(v1,v2="Sit")=sitting, which may or may not be realizable depending on the initial state v1 of your brain.

Now think of the oracle and you as in fact the same person. The implication is you may not be able to tell/convince/divulge to yourself what you will do in 10 secs, not because of ignorance, but because your brain is in such a counter-reactional initial state: f(v1,v2="Standing")=sitting & f(v1,v2="Sit")=standing.

I'd like to think that's why we often see oracles possessed by some other identities when making predictions, or write their prophecies in obscure and inscrutable words. That's the price they have to pay make their predictions consistent in a deterministic world :-P

Answer 5

I think it would give you the answer that you will stand (in 10s), but the moment you would decide to oppose and sit it it then would change its answer that you will sit, and if you would not want to sit any-more to oppose it again it would change to stand again and then to sit or however you would think of opposing it. For model to be correct the answer would be valid only for certain amount and your actions such as looking into prediction would have to be variable that is affecting the model so it would be changing it all the time no matter how much you would try to contradict it.
I am now facing different problem: Same apparatus in next room should be telling the correct prediction all the time (will you sit or remain standing) as you cannot see and oppose it. How these different outputs should be interpreted?

Answer 6

Yes, you correctly pointed to the research by Breuer.

In short, his result shows that it is mathematically impossible to predict own future, even if otherwise the universe is deterministic.

Whatever you do to predict the future of a system where you are contained, your calculations will give a wrong result.

Answer 7

Your question rests on an unexamined assumption that leads to a false dichotomy. You seem to be arguing that, assuming we could derive a complete deterministic model of the universe,* we should be able to use that model to predict and subsequently contradict our own actions, thereby proving the model false. The assumption in this case is that deriving the model is the difficult part, and using it is the easy part. What if the reverse is true? There doesn't seem to be any evidence to indicate that even a perfect deterministic model of the universe would be usable for any practical purposes, even if it were 100% complete and valid. For instance, it might be the case that the model could perfectly predict your own actions ten seconds from now, but that it would take a minimum of thirty seconds to make the calculation. Or it could be the case that the model works perfectly as long as the initial state is known, but it's impossible to fully know the initial state.** Either way, there's no longer a paradox. So, while your example does suggest that a deterministic model of the universe could never be used to predict someone's behavior, it does not necessarily follow that a deterministic model does not exist or cannot be described.

*As others here have pointed out, our current understanding of quantum mechanics suggests that this is not the case, though not necessarily for the reason you propose.

**In fact, this is the case.

Answer 8

By your definition, your hypothetical universe is deterministic and immutable, therefore there are only really one possibility in such a situation: the model conceived of is wrong if it claims it can accurately predict a single outcome.

In essence, this problem boils down to the liar paradox: "whatever the predicted future is, I will do the opposite" is very similar to "this statement is a lie". If we could model this as some kind of contrary circuit in the brain, it would not be able to sit in a static state, instead it would flip-flop between updating the model with the knowledge of acting contrary to the model, and revising your decision on how to act. At any given moment, the state of the system would not be able to satisfy the paradox. In other words, your brain, or any predictive/deciding system, is unable to hold a correct model and be contrary to it at the same time.

From a higher level, any predictive/deciding system cannot second guess or deliberately contradict itself if it is to be accurate. That means that, relative to your own actions and decisions, a model of that course of action is indistinguishable from a plan. Modelling and planning are two sides of the same coin and it is paradoxical for the two to differ.

This isn't to say that a deterministic model can be reasonably predicted to give a singular outcome, mainly due to chaos theory: uncertainty arises due to your inability to measure all affecting factors or calculate in sufficient time the results of their interactions. A correct deterministic model can have intractable problems that prevent accurate prediction of all futures.