8 ms·

The Free Will Theorem

33 points by sajid 16y ago

mbateman 16y 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 http://www.ams.org/notices/200902/rtx090200226p.pdf
- kd0amg 16y 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.
  - mbateman 16y 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).
    - Qz 16y ago
      But what determines what the actor determines? 'agent-determinacy' just seems like a synonym for the idea of free will rather than anything that can justify it.
      - mbateman 16y ago
        According to agent-causal views, at a certain level nothing else determines what the actor determines. I don't here want to argue which view of human action is the right one, I just want to point out (or argue, since even this is contentious) that there's a three-fold alternative: determined, random, and free. The "free will" in this paper is actually the second and not the third alternative. In the paper they actually protest against this move, arguing that the kind of randomness involved in entanglement is importantly different than stochastic randomness. I only dimly understand the the Kochen-Specker theorem so I can't follow all the details of the argument in this paper, but the resulting view still seems to fall under indeterminism. So alternative title (and subtitle) for the paper: "The Indeterminism Theorem: If Humans Act Indeterministically, Then So Do Fundamental Particles."
        Qz 16y ago
        I just want to point out (or argue, since even this is contentious) that there's a three-fold alternative: determined, random, and free. The "free will" in this paper is actually the second and not the third alternative. My issue is that I understand determined, and random, but I don't understand 'free'. If you read the article you just linked to, they point out that in the case of this experiment, 'random' is equivalent to 'free', as the free-will human experimenters can be replaced by a computer program with a truly random number generator, but that the non-determinacy necessary for the random number generator to work is the same exact freedom necessary for a human experiment to have 'free' choice over the experiment. Furthermore, that the entangled nature of the particles precludes the type of 'randomness involved in entanglement' that you suggest. Entanglement is specifically non-random in exactly the quality at issue in this experiment. Basically the result of the theorem (as relevant to this conversation) is that 'random' and 'free' are equivalent. There is simply determinate or non-determinate.
        ugh 16y ago
        Determined and random I can understand, free I can’t. How can any actions be free (as in not determined and not random)? That, to me, seems impossible, at least in a great many situations where humans would claim to have free will. How can any action a agent makes be meaningful without causal links to the outside? Determinism to me seems to be a requirement for agents to make useful decisions.
        Qz 16y ago
        How can any action a agent makes be meaningful without causal links to the outside? One of the responses that has been raised to that issue goes like this: At any point we have a number of meaningful choices from which to choose. For example, if someone calls you up and asks you to go out to dinner with them, it would be meaningful to say, "sure that's great!" or "no thanks maybe later". In any situation like that, we are 'free' to choose from a set of meaningful choices. Each is meaningful in that it is related to the past, but regardless of eventually choosing one choice, we could have chosen another of those choices, and still had it be meaningful. I don't particularly buy that argument, as the idea of 'could have chosen something else' is just a further escaping of the question of free will. But it is a way of looking at it that seems to avoid the randomness/lack of meaningfulness associated with the idea of free will.
    - kd0amg 16y ago
      Ok, I was not aware of this difference in terminology. Thanks.
  - _delirium 16y 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/ http://plato.stanford.edu/entries/compatibilism/
    - danbmil99 16y ago
      this. Read "Freedom Evolves" or the shorter precursor "Elbow Room". This confusion of free will with indeterminacy, and the specious connection with Quantum Mechanics (taken to the absurd extreme by Penrose) really muddies the water wrt AI/cogsci and the understanding of consciousness, qualia etc.
    - Qz 16y ago
      That's fine, except that quantum mechanics messes with the idea of determinate physical causation, and the Free Will Theorem (as well as the KS Paradox that it extends) is based on a particular proof that certain things (in this case, the measurement of the spin of a particle under certain circumstances) do not follow physical causation. What the FW Theorem shows is that if you take a situation in which we assume humans have free will, then the result is that subatomic particles also have that exact same kind of free will.
amichail 16y ago
Has anyone tried to use this as a defense in court?
- stcredzero 16y ago
  I bet whoever tries it will have as much luck as Epimenides.
- Ardit20 16y 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 16y 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 16y 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?
- Qz 16y 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.
  - mbateman 16y 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.
    - Qz 16y ago
      Well basically the KS paradox says that for certain types of measurements (which not-coincidentally happens to be the exact type of measurement in the free will theorem), the result of the measurement is based on the direction of the measurement, not on anything prior to that measurement. Specifically, if you measure the 'spin' in 3 orthogonal directions, then the resulting values will always be the same (1,0,1 in some order), but that there is no function which can determine those values prior to the actual measurement, hence there is no possible hidden variable that can explain the quantum mechanical result. The free will theorem extends that result because the fundamental issue of the KS paradox hinges on the direction in which the spin is measured relative to the universe. The direction of the particular measurement is 'decided' upon by the person or thing doing the measuring, in this case the experimenter. But is that direction pre-determined, or does the person have free will in choosing the direction? The situation is tricky because we now have two experimenters who are measuring a pair of entangled particles, which we thus know will give the same result, if measured in the same direction. Because of the KS paradox, we know that the result of the measurement hinges on the direction chosen by the experimenter, not on anything prior to the experiment. If we take that the experimenters have 'free will' then the entangled nature of the particles means that the result of the spin measurement can't be 'random' but it is also 'non-determinate' because of KS, and thus the result of the measurement must have the same quality of 'freedom' as the 'freedom' experienced by the experimenters in choosing the direction of measurement.
stcredzero 16y 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 16y ago
This reminds me of Dust from His Dark Materials.
koanarc 16y 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 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 16y ago
  Conway comes up with the best names for things... Doomsday algorithm, monstrous moonshine, Game of Life, surreal numbers, cosmological theorem, etc.
siglesias 16y ago
Video lecture series here: http://deimos.apple.com/WebObjects/Core.woa/Browse/princeton.edu.2783684550 http://deimos.apple.com/WebObjects/Core.woa/Browse/princeton...
extension 16y ago
"Free will" is meaningless in the context of quantum scale physics.
fizx 16y 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 16y ago
  I assume that "free-willed" in this case is being used ironically?
- jberryman 16y 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)
  - fizx 16y 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.
- Qz 16y ago
  Except that the whole point of this theorem is that a free-willed human implies a non fully deterministic world.
shasta 16y ago
It has been argued (http://arxiv.org/PS_cache/arxiv/pdf/0905/0905.4641v1.pdf 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.

33 points by sajid 16y 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 http://www.ams.org/notices/200902/rtx090200226p.pdf

kd0amg 16y 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.
- mbateman 16y 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).
  - Qz 16y ago
    But what determines what the actor determines? 'agent-determinacy' just seems like a synonym for the idea of free will rather than anything that can justify it.
    - mbateman 16y ago
      According to agent-causal views, at a certain level nothing else determines what the actor determines. I don't here want to argue which view of human action is the right one, I just want to point out (or argue, since even this is contentious) that there's a three-fold alternative: determined, random, and free. The "free will" in this paper is actually the second and not the third alternative. In the paper they actually protest against this move, arguing that the kind of randomness involved in entanglement is importantly different than stochastic randomness. I only dimly understand the the Kochen-Specker theorem so I can't follow all the details of the argument in this paper, but the resulting view still seems to fall under indeterminism. So alternative title (and subtitle) for the paper: "The Indeterminism Theorem: If Humans Act Indeterministically, Then So Do Fundamental Particles."
      - Qz 16y ago
        I just want to point out (or argue, since even this is contentious) that there's a three-fold alternative: determined, random, and free. The "free will" in this paper is actually the second and not the third alternative. My issue is that I understand determined, and random, but I don't understand 'free'. If you read the article you just linked to, they point out that in the case of this experiment, 'random' is equivalent to 'free', as the free-will human experimenters can be replaced by a computer program with a truly random number generator, but that the non-determinacy necessary for the random number generator to work is the same exact freedom necessary for a human experiment to have 'free' choice over the experiment. Furthermore, that the entangled nature of the particles precludes the type of 'randomness involved in entanglement' that you suggest. Entanglement is specifically non-random in exactly the quality at issue in this experiment. Basically the result of the theorem (as relevant to this conversation) is that 'random' and 'free' are equivalent. There is simply determinate or non-determinate.
      - ugh 16y ago
        Determined and random I can understand, free I can’t. How can any actions be free (as in not determined and not random)? That, to me, seems impossible, at least in a great many situations where humans would claim to have free will. How can any action a agent makes be meaningful without causal links to the outside? Determinism to me seems to be a requirement for agents to make useful decisions.
        Qz 16y ago
        How can any action a agent makes be meaningful without causal links to the outside? One of the responses that has been raised to that issue goes like this: At any point we have a number of meaningful choices from which to choose. For example, if someone calls you up and asks you to go out to dinner with them, it would be meaningful to say, "sure that's great!" or "no thanks maybe later". In any situation like that, we are 'free' to choose from a set of meaningful choices. Each is meaningful in that it is related to the past, but regardless of eventually choosing one choice, we could have chosen another of those choices, and still had it be meaningful. I don't particularly buy that argument, as the idea of 'could have chosen something else' is just a further escaping of the question of free will. But it is a way of looking at it that seems to avoid the randomness/lack of meaningfulness associated with the idea of free will.
  - kd0amg 16y ago
    Ok, I was not aware of this difference in terminology. Thanks.
- _delirium 16y 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/ http://plato.stanford.edu/entries/compatibilism/
  - danbmil99 16y ago
    this. Read "Freedom Evolves" or the shorter precursor "Elbow Room". This confusion of free will with indeterminacy, and the specious connection with Quantum Mechanics (taken to the absurd extreme by Penrose) really muddies the water wrt AI/cogsci and the understanding of consciousness, qualia etc.
  - Qz 16y ago
    That's fine, except that quantum mechanics messes with the idea of determinate physical causation, and the Free Will Theorem (as well as the KS Paradox that it extends) is based on a particular proof that certain things (in this case, the measurement of the spin of a particle under certain circumstances) do not follow physical causation. What the FW Theorem shows is that if you take a situation in which we assume humans have free will, then the result is that subatomic particles also have that exact same kind of free will.

amichail 16y ago

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

stcredzero 16y ago
I bet whoever tries it will have as much luck as Epimenides.
Ardit20 16y 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 16y 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 16y 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?

Qz 16y 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.
- mbateman 16y 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.
  - Qz 16y ago
    Well basically the KS paradox says that for certain types of measurements (which not-coincidentally happens to be the exact type of measurement in the free will theorem), the result of the measurement is based on the direction of the measurement, not on anything prior to that measurement. Specifically, if you measure the 'spin' in 3 orthogonal directions, then the resulting values will always be the same (1,0,1 in some order), but that there is no function which can determine those values prior to the actual measurement, hence there is no possible hidden variable that can explain the quantum mechanical result. The free will theorem extends that result because the fundamental issue of the KS paradox hinges on the direction in which the spin is measured relative to the universe. The direction of the particular measurement is 'decided' upon by the person or thing doing the measuring, in this case the experimenter. But is that direction pre-determined, or does the person have free will in choosing the direction? The situation is tricky because we now have two experimenters who are measuring a pair of entangled particles, which we thus know will give the same result, if measured in the same direction. Because of the KS paradox, we know that the result of the measurement hinges on the direction chosen by the experimenter, not on anything prior to the experiment. If we take that the experimenters have 'free will' then the entangled nature of the particles means that the result of the spin measurement can't be 'random' but it is also 'non-determinate' because of KS, and thus the result of the measurement must have the same quality of 'freedom' as the 'freedom' experienced by the experimenters in choosing the direction of measurement.

stcredzero 16y 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 16y ago

This reminds me of Dust from His Dark Materials.

koanarc 16y 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 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 16y ago
Conway comes up with the best names for things... Doomsday algorithm, monstrous moonshine, Game of Life, surreal numbers, cosmological theorem, etc.

siglesias 16y ago

Video lecture series here: http://deimos.apple.com/WebObjects/Core.woa/Browse/princeton.edu.2783684550 http://deimos.apple.com/WebObjects/Core.woa/Browse/princeton...

extension 16y ago

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

fizx 16y 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 16y ago
I assume that "free-willed" in this case is being used ironically?
jberryman 16y 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)
- fizx 16y 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.
Qz 16y ago
Except that the whole point of this theorem is that a free-willed human implies a non fully deterministic world.

shasta 16y ago

It has been argued (http://arxiv.org/PS_cache/arxiv/pdf/0905/0905.4641v1.pdf 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.