

The Free Will Theorem - sajid
http://en.wikipedia.org/wiki/Free_will_theorem

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mbateman
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>

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kd0amg
_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.

~~~
_delirium
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/>

~~~
danbmil99
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.

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fizx
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.

~~~
jberryman
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
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.

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shasta
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.

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noahlt
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
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
> 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
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.

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

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

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siglesias
Video lecture series here:
[http://deimos.apple.com/WebObjects/Core.woa/Browse/princeton...](http://deimos.apple.com/WebObjects/Core.woa/Browse/princeton.edu.2783684550)

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arethuza
This reminds me of Dust from His Dark Materials.

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

~~~
daveungerer
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.

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stcredzero
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.

