Laplace's Demon
Posted on: June 14, 2008 - 4:36pm
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Laplace's Demon
With all the discussion of Indetermancy in another thread reminded me of this thought experiment.
Imagine a demon that has full knowledge of the present. The location/energy of every molecule everywhere in existance.
Now, as the scenario plays out, this demon can now succesfully predict the future using Newton's laws to calculate the future position/energy of all the molecules, and hence now knows the full future of the universe, from when/where the next hurricane will show up, to when stars will super-nova.
So I guess the question is, is this logical valid? If a demon did know everything about the present, could they could fully predict the future?
Discuss 
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I don't think that Newton's laws would be sufficient, but if an entity really did know everything about the universe, and was intelligent enough to make use of that knowledge, then I would fully expect that entity to be able to predict the future accurately. I would wonder, though, if an entity were that intelligent and that knowledgeable, would it still fit inside the universe? And, if it did exist inside the universe, wouldn't that mean that it would have to be predicting its own predictions? Also, would the entity be able to process all of the information faster than the universe itself? That is to say, it would be a race between this entity's ability to process the information and the universe's natural rate of progressing forward through time. From a mathematical perspective, would a thought construct inside the entity's calculations have the properties of being self-aware? And, if so, wouldn't it be impossible to distinguish between living in the universe and living as a thought construct inside the entity's mind?
I'm with QuasarX. The Demon character kind of blows up and gets confusing.
The neat thing about this thought experiment is that robustness of the mathematical framework would determine how accurate the future prediction would be, since there's always a gap between a model and reality. So what would the difference be in accuracy between the math from Newton's time and from Einstein's?
Of course, there's no answer, but it's a fun thought.
Saint Will: no gyration without funkstification.
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You guys aren't thinking, you're merely being logical.
Location and energy is not enough. You also need direction and velocity.
Ever hear of Hiesenberg and his uncertainly principle?
Remember how you figured out there is no Santa? Well, their god is just like Santa. They just haven’t figured out he’s not real yet.
You mean something along the lines of Kinetic energy? Which of course would be known if the energy was known?
You mean:
OA2OB2>/((1/2i.)[A,B])2
Yeah, I heard of it.
Using logic is a type of thinking, and a rather useful one at that.
You still need the direction - actually it should have been expressed as Location and Momentum.
Anyway Heisenberg's Uncertainty principle would seem to make this prediction of the future course of the Universe impossible even in principle.
I'm with QuasarX and HisWilliness on this.
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This problem was first proposed in the 1800's before the Uncertainty principle or QM.
Which of course is why it isn't included in the problem.
It really is just a way of trying to dramatise the implications of Newtonian mechanics, of course. In practice, even without Quantum Uncertainty it wouldn't work in the sense that the Demon would have to be more complex than the Universe itself, in order to map within its 'mind' the entire state of the Universe and also have the capability to process it. If it was within the Universe, it could not ignore its own existence, so you just end up with in infinite recursive loop.
In addition, in a deterministic model, one would need to know the state with infinite precision, to allow for divergent effects, where very small differences in starting conditions lead to very different outcomes, so it still is ultimately impossible, for a finite entity, even for a finite universe without Quantum effects.
If it outside the Universe, you are into a Supernatural scenario, so it just needs the Demon to make a perfect model of the Universe and then get it to run faster than the actual universe to allow actual prediction.
Favorite oxymorons: Gospel Truth, Rational Supernaturalist, Business Ethics, Christian Morality
"Theology is now little more than a branch of human ignorance. Indeed, it is ignorance with wings." - Sam Harris
The path to Truth lies via careful study of reality, not the dreams of our fallible minds - me
From the sublime to the ridiculous: Science -> Philosophy -> Theology
in christianity is that demons cannot predict the future but they know us (mankind) so well that they can basically predict what we are going to do just by our actions...some believe they can read our minds. Some say they don't have to. They can impart ideas into the mind (via the soul/spirit) but cannot actually read minds. We think we're pretty mysterious but not so unpredictable to them. In other words, they dont need to know every particle to be able to predict a large percentage of whats going to happen with humanity. (But technically, the Heisenberg uncertainty principle makes it impossible to know the position and momentum of a particle to any specified degree of accuracy. If one is good, the other is poor.)
Well yeah:
If you wanted non-logical thinking, you could have asked for it.
Saint Will: no gyration without funkstification.
fabulae! nil satis firmi video quam ob rem accipere hunc mi expediat metum. - Terence
Only in a hypothetical scenario, not in reality. Even if the demon had full knowledge, it would need to perform the calculations/simulation to make an accurate prediction. Unfortunately, if these calculations are to be done in reality, then they are limited in speed. In essence, the only thing that can simulate the universe fast enough to predict the future is the universe itself. Only in the hypothetical situation that the demon has a supernatural ability to perform the simulation faster than the universe itself operates could the demon accurately predict the entire future. Without this hypothetical ability, the demon would be limited by reality. If you know something about Turing machines, then its a situation of a Turing machine simulating another Turing machine. It is possible, but the simulation will always run slower than the actual machine itself. No simulation of reality can be complete and fast at the same time. It must either be incomplete or slow. And the more complete, the slower it will be.
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Well our friend Godel comes back into play. How could the demon know that he knows everything? This is an axiom of the system they the demon could neither prove or disprove. So how does one ignore Godel in this imaginary world?
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I meant the existance of the demon isn't the question, the question is whether it can predict the future.
Well, if something can't exist, it can't predict anything... but I'm guessing your real question is not if the future is predictable, but whether or not reality is completely deterministic? To put it another way, it sounds like you're asking whether or not there is a single, definite future that must necessarily follow from the current state of reality and the rules which reality obeys.
Let's say that this demon was able to find a parallel universe that is the same in everyway except that the parallel universe is 2 days ahead in time. In order to predict the future, the demon would simply have to observe the events in the parallel universe. This is where one of the consequences of Heisenberg's Uncertainty Principle kicks in.
The moment the demon makes an observation, he changes the system he observes. It is unavoidable. Over time, the more he obverses, the more change his presence causes. Initially his predictions will be extremely accurate, but his presence, his mass, his metabolism will set off a kind of "butterfly effect" that will make this parallel universe no longer exactly like the first universe that the demon wanted to predict the future of.
The demon might be able to avoid this if he could create an exact quantum duplicate of himself that performs the exact same observations in the first universe. At that point, he'd not only be predicting the future, but also changing its natural course.
After all this quantum duplicate is set up, the demon in the parallel universe would be relaying his observations to the demon in the first universe so that the demon in the first universe would have knowledge of the events 2 days in the future. This would make the demons different again leading to divergent universes once again. He could compensate by finding an infinite amount of parallel universes that are 2 days apart and setting up an infinite amount of demons that relay back the future predictions to a demon in a universe 2 days behind.
At this point, the demon would need an infinite amount of matter and energy and such things make my head hurt. There doesn't seem to be anyway to consistently predict the future forever with this method without eventually causing the 2 universes to go out of synchronisation, without the need for an infinite amount of energy and matter and a method of relaying information between parallel universes.
Remember how you figured out there is no Santa? Well, their god is just like Santa. They just haven’t figured out he’s not real yet.
NO. At least as far as we know in terms of physics. Or, lol, as far as I know.
There are too many random variables.
For example, electron movements around an atom. They can appear close, far, here, there, across the parking lot suddenly, then back.... In theory an eletron can jump across the universe and back to it's original atom in an instant, but doing so is almost as unlikely as God. The further away from the atom, the more likely it'll be the electron will jump there. And how unlikely it is exponentially increases the further from the heart of the atom you get. But still, it's quite random. As far as we (or I) know.
How much of an impact would this random variable have? I dunno, I'm sure humanity doesn't know and probably couldn't know the impact of such an extremely common and numerous, but tiny phenomina. But its something that the demon (in theory) couldn't predict. So I'm sure there is probably much more to the universe that is completely and truely random, and sooner or later the random possibilies will impact or snow ball or something to the way that the demon won't be able to guess what the heck'll happen.
Sorry if I'm lacking in my jargon. I know my physics very well, but I only have the memory for the general ideas and themes, less the hard facts of trivia.
I don't know about anyone else, but I wasn't making a question of the demon's existence. I just meant its nature (including the all-seeingness) was confusing. But I thought I answered your question anyway: given that there's always a gap between a physical model and reality, the demon would be mostly right about the future within a reasonable margin of error. If you assumed a finite number of atoms in the universe, you could probably determine a (tongue-in-cheek) margin of error depending on how you want to quantify time and how far in the future you want to predict.
Saint Will: no gyration without funkstification.
fabulae! nil satis firmi video quam ob rem accipere hunc mi expediat metum. - Terence
I don't consider random to mean that something is nondeterministic... I think it just means that we don't have the ability to predict the outcome. I'm no physics expert, but when I read about the random nature of electron motion, I don't think that it actually means that an electron can jump across the universe and back... I think it just means that within a mathematical model that attempts to predict where electrons will be, the position across the universe is highly unlikely. The issue, as I understand it, is that electron motion is influenced by so many factors that we can't accurately predict their motion, and so a mathematical model is developed to compare general likelihoods for the position of a given electron at a given point in time... but the fact that the mathematical model assigns a nonzero probability for the electron's position to be on the other side of the universe doesn't mean that it's actually possible for the electron to do so. In fact, I'm rather confident that no electron has ever been observed to travel even just to the other side of our galaxy and back.
That's why I said in theory, or, "as far as we know" it can do it. It's something I remember my professors and I discussing. I always pestered them and pressured them. Maybe yer right, maybe they aren't "truely" random. But maybe they are. Or maybe something else is. But then again maybe nothing is. And if nothing is, then yes, the Demon could predict the future granted it had all the knowledge and intellectual ability to process it all. And if there are completely and truely random elements to the universe, then no, the demon won't be able to. That's all we can say as the human race.