The Free Will Theorem

http://en.wikipedia.org/wiki/Free_will_theorem

by sajid • 16 years ago

33 37 16 years ago

en.wikipedia.org

mbateman4• 16 years ago

Kind of clever. This looks to be based on the supposition that free will is indeterministic. The argument ties the indeterminacy of the choice to take some sort of measurement to the quantum indeterminacy of the results of the measurements.

But indeterminacy is not what most people have in mind when they think of free will. A random action is not a free action.

EDIT: Here's the paper: http://www.ams.org/notices/200902/rtx090200226p.pdf

kd0amg2• 16 years ago

But indeterminacy is not what most people have in mind when they think of free will. A random action is not a free action.

It's not a sufficient condition, but it does seem to be a necessary condition. A determined action is also not a free action.

mbateman4• 16 years ago

Well, non-determinacy is a necessary condition, but that doesn't mean indeterminacy is. Non-determinacy can be divided into at least two things, indeterminacy (i.e. determined stochastically) and agent-determinacy (i.e. determined by the actor).

_delirium2• 16 years ago

I'd say probably most modern philosophers don't think that's the case. Daniel Dennett is a particularly strong proponent of the notion that free will is perfectly compatible with physical causation, and doesn't require agents to somehow magically be able to create gaps in it (and his view doesn't care much whether the causation is deterministic or has randomness in it).

Overview of the position: http://plato.stanford.edu/entries/compatibilism/

amichail• 16 years ago

Has anyone tried to use this as a defense in court?

stcredzero2• 16 years ago

I bet whoever tries it will have as much luck as Epimenides.

Ardit20• 16 years ago

There is the defence of necessity. For example is someone threatens to kill you unless you do something, then you wont be punished for that something you did.

daveungerer• 16 years ago

That would be a really stupid thing to do. A judge who accepts such an argument will also have no problem with sending you to jail forever. Because, you see, if your actions are pre-determined then so are his.

noahlt• 16 years ago

I've seen this a handful of times, but I don't know enough about physics to understand the specifics of the theorem to make meaningful statements about it.

Can anyone explain the free will theorem to laymen?

Qz8• 16 years ago

Here is my layman's understanding of it:

Say we have two people performing similar experiments who are far enough apart from each other that the information from one experiment can't affect the result of the other person's experiment. The experiment they are performing is to measure the 'spin' of a particle that has been 'entangled' with the particle measured by the other experimenter. Since the particles are entangled, if the experimenters measure the spin in the same direction, they will both get the same result.

The theorem then states that if the experimenters are 'free' (as in will) to choose which direction to measure the spin of their particle, then the result of measuring the spin cannot be determined by anything previous to the experiments (and can't be determined by the other experimenter, as established above).

Put into everyday terms, its impossible for the universe to be fully determinate and still have actors capable of free will, and vice versa: if people have free will then the world can't be fully determinate.

mbateman4• 16 years ago

> The theorem then states that if the experimenters are 'free' (as in will) to choose which direction to measure the spin of their particle, then the result of measuring the spin cannot be determined by anything previous to the experiments (and can't be determined by the other experimenter, as established above).

Yes, and this is because if it could be determined by anything, it would imply something like a hidden variable theory of quantum mechanics, which violates the Kochen-Specker theorem. This is the part of the argument that I don't understand. If anyone could help I'd be grateful.

stcredzero2• 16 years ago

Re: causality.

Fin: There is a maximum speed for propagation of information (not necessarily the speed of light). This assumption rests upon causality.

There have been sci-fi space drives involving the separation of inertia and mass. I wonder about a space drive based on the separation of causality and time. Perhaps there is a "causal dimension" or axis which happens to be the same for everything in this universe, which is what we call time. What if we can rotate this causal axis in a small region, like something the size of a ship? We should be able to exceed the speed of light. Something like this is supposed to happen when one falls through an event horizon. Inside an event horizon, all of the timelike directions intersect the singularity. That would be an interesting conceit: The observations that would easily reveal the physics of FTL travel are only available to observers who have passed an event horizon.

arethuza• 16 years ago

This reminds me of Dust from His Dark Materials.

koanarc• 16 years ago

Cool. Slightly off-topic, re: John Conway -- Some tangential wiki-ing led me to (what I think is) the even more interesting Look-and-say sequence & Conway's cosmological theorem:

http://en.wikipedia.org/wiki/Look-and-say_sequence

I'm not sure how far the atomic element analogy can be extended, but on its face it seems a little mind-blowing.

defen• 16 years ago

Conway comes up with the best names for things... Doomsday algorithm, monstrous moonshine, Game of Life, surreal numbers, cosmological theorem, etc.

siglesias2• 16 years ago

Video lecture series here: http://deimos.apple.com/WebObjects/Core.woa/Browse/princeton...

extension• 16 years ago

"Free will" is meaningless in the context of quantum scale physics.

fizx2• 16 years ago

I've thought of free-will as related to computational complexity. A complex (e.g. NP-hard) problem is one that cannot be solved by an algorithm significantly simpler than brute force. Analogously, a "free-willed" human's actions cannot be modelled by anything significantly simpler than a full simulation of the human and its environment.

This definition hinges on predictability, not determinism. You can have a 'free-willed" human in a fully deterministic world, if no one has the computational power to predict his actions.

joshuacc• 16 years ago

I assume that "free-willed" in this case is being used ironically?

jberryman• 16 years ago

That's interesting. It seems to me that rather than talking about NP-hard computation, you could say that free will is analogous to the undecidability of the halting problem. That is we can say that we have free will because the hypothetical act of predicting someone's future actions is equivalent to simply having their brain decide (i.e. running the computation)

fizx2• 16 years ago

Yeah, I'm not sure what the exactly correct formulation is. Your formulation may retain the spirit, but be more technically correct.

I guess the important point is that I like to define free will as "the ability to make a decision faster than any available entity can predict the result of the decision." A computer running a some program doesn't have free will, because I can beat it to its own decision with more or faster computers. Also, I can force it to solve problems to which I already know the answer. Interestingly, I may have free will today, but "lose" it tomorrow, when a sufficiently advanced simulation of my mind is released.

Qz8• 16 years ago

Except that the whole point of this theorem is that a free-willed human implies a non fully deterministic world.

philwelch• 16 years ago

Which is itself a matter of severe philosophical contention.

shasta• 16 years ago

It has been argued (http://arxiv.org/PS_cache/arxiv/pdf/0905/0905.4641v1.pdf) that this theorem is flawed (the premises don't match reality).

After briefly studying the matter, I agree, and suspect the flaw is that Conway and Kochen assume that, because the two experiments are separated by a great distance, they may be treated as separate random trials. I believe you can see from the multiple universe interpretation of QM that this assumption is incorrect.

I'm not a physicist and have only spent a few hours on it, so take this comment with a big grain of salt. I'm curious to hear if there's a consensus among physicists on the resolution.

The Free Will Theorem

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