enigm4tic’s thought experiment is describing a paradox. The apparent presence of a paradox usually (perhaps always) means our thought experiment has not correctly comprehended or described the system in which the paradox appears to exist. The grandfather paradox borne of the false assumption that time travel is possible; Zeno’s paradox is borne of the false assumption that space and time are infinitely divisible. And so on.
I therefore suggest that enigm4tic’s paradox is borne of the false assumption that the universe, in particular, as it pertains to human activity, is deterministic. (Which I think is the point enigm4tic is making).
how so, the third computer still has to solve an infinitely recurring problem, I don’t see how it can do so any better than the computer that’s directly attempting to solve the problem. I fail to see how using a third computer to solve an infinite problem makes it less infinite
indirect proofs, especially by contraposition, often assume that the conclusion in order to show that IF it is true, then you have created a paradox (see above). And since you have demonstrated that the conclusion, if true, creates a paradox, it must be false.
Computer B can look at Computer A together with Joe-Bob, and predict, “Computer A will go into a recursive loop and will be unable to make a prediciton. Joe-Bob, having seen no prediction either way, will do the following: X”
Do you want to let Joe-Bob see Computer B’s reports? No problem. Computer B will now no longer to make reports, but some computer D could look at all of this and come up with a report.
Your argument doesn’t show that the will is non-deterministic. Rather, it shows that a given computer can not predict the actions of a person if that person is allowed to see that computer’s reports.
Think of the following situation. You have a marble rolling, you have a person, and you have a weight. You have a table, and on the table are two squares. The person is instructed, “If you believe the marble will continue rolling to the edge of the table, put the weight on square A. If you believe otherwise, put it on square B.” The catch is, square A is directly in the path of the marble: putting a weight on it will block the marble, preventing it from rolling to the edge of the table.
You see where that’s going, I’m sure. We don’t want to attribute magical non-deterministic powers to the marble on the basis of the fact that the person with the weight can not successfully express his prediction given the constraints he has been saddled with, do we? Of course not. What we say, as third person observers, is that the person in the scenario has been rendered unable to successfully deliver any prediction. We also know the ball will continue on its determined way and roll to the edge of the table.
Of course, the person can say “I refuse to place a weight, since by doing so I would falsify whatever prediction I would thereby make.” But that is for the person to refuse to enter causally into the marble’s trajectory. The machine in your thought experiment is stipulated to be such that if it does make a prediction, then it does enter into the person’s causal trajectory.
I believe there is probably a connection to be made here between the kind of situation we’re looking at on the one hand, and incompleteness in mathematics and logic. But I am not sure, and maybe I shouldn’t have begin to crack open that can of worms. But the parallel would be: Just because a system can’t prove such and such theorem about itself, doesn’t mean the theorem isn’t true and proveable by some other system. Similarly, just because a person’s actions can’t be predicted by one particular system, doesn’t mean it couldn’t be predicted by some other system.
I disagree. I think the paradox is borne of the false assumption that the computer/demon is practicable in our universe. It is not. That point has been ceded several times above, and I fear that the discussion may be getting overly preoccupied with the impossibility of this machine.
I want to again reemphasize my argument without the demon/computer:
(I’m not presuming to steer the discussion. I just want to make sure my view is felt here.)
I think the solution to our problem may lie in the concept several people are arguing about quantum mechanics. If quantum physics has an element of true randomness (not simply aspects we cannot yet explain) then perhaps the universe is not deterministic, and that would brighten my day.
On a side note, IANA mathmatician, but I think we should discourage the use of the terms “chaos theory” and “chaos” to mean “random systems”. From my understanding, chaos theory essentially states that apparently chaotic systems ***are * ** deterministic. (chaos theory wiki)
how so? My position had the machine as a given, just like yours did. I was extending, not refuting your thought experiment
ah, ok, I see your point on this matter but I think you might be oversimplifying. If you extend that analogy than whether or not the person puts the block down affects whether or not the marble gets to the edge of the table, that is, it’s future is indeterminate based on the outcome of external events.
To extend that argument to humanity if everything were determined, we could arguably introduce anything in to a person’s “causal trajectory” and the same outcome would occur, but if our future outcome relies on the resolution of external events, then we don’t have a determined future.
Now introduce the idea above from Spatial Rift
(authority resting on being a physics grad student)
and we reach the conclusion that our future events rest on external events that have no necessarily deterministic conclusions; just as the marble can’t "predict’ whether it will reach the edge of the table from it’s point of view, neither can we “predict” whether or not we will live to the end of the day with any certainity.
Nope; a seriously difficult computation task doesn’t create paradoxes, only hard work. Paradoxes arise from logical inconsistencies in premises, not practical difficulties.
I think that’s already been answered; the universe isn’t deterministic, to the best of our knowledge.
The paradox merely proves that something is not right with the premises. I recognize that you are an extremely intellignet person, but I don’t think that entitles you to label one premise “wrong” over another.
The paradox outlined above is proof that the machine is impractacable. Calling the paradox proof of a non-deterministic universe is a stretch, to say the least.
Again, I never said that the machine was impractical. I used your premises, then drew another conclusion from them. You used those premises to draw your “depressing” conclusion that the universe was deterministic, and I attempted to use those premises to show that it was not, indeed, deterministic. I think Frylock made a good point in refuting my specific claim, but again i responded to that claim by extending the same framework. Mangetout continued the argument in the paradox vein.
Either of the above arguments (helped out by Spatial Rift currently conclude at a non-deterministic universe
The state of the universe at the time the computer calculates does not include you having any knowledge of the computer or the answer to the computer. If you want a setup such that you are allowed to ask the computer and see the answer, then the computer will use a 2 pass process as follows:
Start from time 0, calculate the future based on you sitting there waiting for the answer
Start at time 0 again, calculate the future based on you knowing the answer from step 1
Provide the answer to you the questioner from step 1 (not the real answer from step 2)
Provide the real answer (from step 2) to everyone on the straightdope debating this topic
The bottom line is that you have created a different thought experiment that seems to create an interesting problem (knowledge of the future could be used to alter actions thus invalidating the future prediction), but I don’t think it indicates the original thought experiment is invalid.
Okay, first things first: the machine is certainly impractical, but more importantly, it is impracticable. (Perhaps it was my misspelling in post #87 that leads to this argument?) My original premises have nothing to do with a machine of any kind. I used the machine in the OP as a thought exercise, and now everyone is preoccupied with nit-picking that exercise.
No. I wish you had. You used my thought exercise and drew another conclusion from it.
I think **RaftPeople ** presents an interesting refutation of your point. But importantly, these discussions of problems-with-the-machine have very little bearing on the question of free will.
this is actually precisely what Frylock was arguing; and I’ve responded to it
@Randy: your thought experiment is used to demonstrate a point, that is, “think of this and you can see the following conclusion”. Ok, we realize that the machine is unable to be created, but we’re following the context from which you drew the conclusion, namely “this machine exists” and demonstrated how that same thought experiment can lead to a different conclusion.
if you want to abandon the thought experiment entirely, we’re relying on your physics explanation: every particle since the big bang can theoretically be traced, and subsequently, we can use that information to predict the future with 100% certainty, since there can be no other arrangement of particles (paraphrased)
Then look to Spatial Rift’s post above to conclude based on quantum uncertainty of particles that the universe is non-deterministic.
I was in a hurry and didn’t get a chance to read Frylock’s post before I posted mine.
Your response to Frylock:
“ah, ok, I see your point on this matter but I think you might be oversimplifying. If you extend that analogy than whether or not the person puts the block down affects whether or not the marble gets to the edge of the table, that is, it’s future is indeterminate based on the outcome of external events.”
The problem is your response doesn’t actually respond to the fact that you altered the thought experiment. The original thought experiment indicated that if we know the state of all particles at time N, then we can calculate the state of all particles at time N+1.
Your altered thought experiment is closer to this:
If we know the state of all particles at time N, and we introduce new information into the universe at time N+1 (the new information is the “prediction” presented to the actor’s input senses), thus altering the state of the universe and the original course of the universe, then the state of the universe at time N+2 is dependent on the new information presented at time N+1.
There is nothing contradictory in your altered thought experiment and there really is no paradox, it’s just a different thought experiment than the original, and actually it’s completely consistent with the original in that both require the state of the universe to be determined from the previous state (except when we allowed the universe to instantly change with new information).
The argument is not that “everything is determined even if we magically introduced new information and altered the universe”, the argument is “everything is determined based on the previous state”. If the universe gets magically altered from an external source, then the subsequent state must take that into account.
FYI: My post is intentionally ignoring QM randomness because I wanted to discuss just this idea you brought up.
Once again let us clear up the difference between being determinable and deterministic. A system can be indeterminable and still be deterministic. The former means that it is possible to tell in advance what an outcome will be. And to be sure random factors (such as quantum flux) and chaotic systems make many systems indeterminate. Still, the results are the natural consequence of that which preceded it. They had antecedent causes which followed natural laws. That makes it deterministic. Think of a famous chaotic system: the weather. Would you believe that weather is not the natural result of antecedent causes?
You also misrepresent Chaos Theory. Chaotic systems are not quite indeterminable. Chaos theory instead recognizes that massive nonlinear (chaotic) systems are so sensitive to minor variations in starting conditions that widely divergent results can occur such that predicting a particular outcome is often beyond human ability. Yet sets of highly likely outcomes can be predicted. These are what Chaos Theory refers to as “attractor basins.” Chaos Theory is not an attempt to throw up our hands at determining outcomes; it is an attempt to provide tools to determine outcomes.
The human mind is not just “capable of chaotic processes”; it is a chaotic process … subject to external pacing. Sets of likely outcomes are highly predictable. Shine light of a particular wavelength and the mind will percieve red. I can determine that in advance.
As to the issue of quantum effects in the brain: sure the brain works at the most basic level with quanum effects … just like a baseball does … just like everything does. And just like with the path of a hit baseball, the brain functions at a macroscopic enough level as to make such quantum effects functionally meaningless to the system as a whole.
Human brains are not inherently indeterminable. And indeterminability has nothing to do with being deterministic.
I was thinking this also, but then Frylock pointed out geiger counters react to radiation (random), implying there could be an influence within the brain from the micro to the macro.
If you’re saying that the machine cannot be built because the problem itself is impossible to completely solve, then I’d agree this could be the source of the paradox.
If the machine cannot be built simply because it’s too big to fit our universe, too complex to program, etc - but that the problem itself would be solvable, if we could only make and program the machine, then this can’t be the source of the paradox. The paradox must derive from some logical impossibility, not just a monumentally difficult, yet still logically possible task.
I think we may be on the same page re: the machine. I agree that it’s possible it may be unbuildable because this paradox. It may also be unbuildable because of any number of physical limitations.
In short, I really don’t care whether the machine is buildable or not. At this point, I’m kind of regretting bringing the concept up at all. **Enigm4tic ** (and, you, I suppose), is trying to disprove the whole “clockwork universe” concept by pointing out a paradox in a supplimentary thought exercise. Yes, there are problems with Laplace’s Demon. That doesn’t mean determinism is bunk.
Determinism ***may ** * be bunk, but I don’t think discrediting the Omnicient Computer idea proves that.
I’m certain that dismissing the OC as ‘too hard to build’ or ‘too big to fit in the universe’ or any such practical limitation proves nothing at all.
I’m not so sure about the whole thing with the paradox. I can’t quite work out at the moment whether it’s a genuine paradox or just appears to be one, because this is such a difficult thing to think about.
But in any case, I think determinism is found false on other grounds - that is, our understanding of physics.
I think this is a poor and possibly misleading analogy.
The path of the baseball could be thought of as the sum (or perhaps the average) of the swarm of effects that are occurring to its particles; because they’re all doing more or less the same thing, the macroscopic behaviour is simple. The path of the ball isn’t determined by the complexity of interaction of its particles with one another - It could be made of a hypothetical amorphous solid and it would still behave the same way. A single particle-scale event can’t change anything at the macro level.
The brain isn’t like that at all; the complexity of interactions of its particles is an essential aspect of its function - a single particle-scale event could set off a cascade of other effects that can effect change at the macro level.
You used my thought exercise and drew another conclusion from it.