Comments on: The Strong Free Will Theorem http://antimeta.wordpress.com/2009/02/06/the-strong-free-will-theorem/ A general distrust of strong metaphysical claims in mathematics and philosophy. Tue, 14 Jul 2009 21:45:18 +0000 http://wordpress.com/ hourly 1 By: Stephen Harris http://antimeta.wordpress.com/2009/02/06/the-strong-free-will-theorem/#comment-2740 Stephen Harris Tue, 14 Jul 2009 21:45:18 +0000 http://antimeta.wordpress.com/?p=182#comment-2740 I'm very suspicious of using logical results such as Penrose using Goedel's Incompleteness Theorem (GIT) to limit the possibility of strong AI machines. I'm not even comfortable with going the other direction, using the Heisenberg Uncertainty Principle used as a physical basis supporting/establishing GIT. (Also causality does not exactly mean determinism.) http://ti.arc.nasa.gov/m/profile/dhw/papers/71.pdf by David Wolpert Abstract: "In this paper strong limits on the accuracy of real-world physical computation are established. To derive these results a non-Turing Machine (TM) formulation of physical computation is used. First it is proven that there cannot be a physical computer C to which one can pose any and all computational tasks concerning the physical universe. Next it is proven that no physical computer C can correctly carry out every computational task in the subset of such tasks that could potentially be posed to C. This means in particular that there cannot be a physical computer that can be assured of correctly "processing information faster than the universe does". ... Note that since the universe is microscopically deterministic, (be it classical or quantum-mechanical, if we adopt the many-worlds interpretation for the latter case)..." I’m very suspicious of using logical results such as Penrose using Goedel’s Incompleteness Theorem (GIT) to limit the possibility of strong AI machines. I’m not even comfortable with going the other direction, using the Heisenberg Uncertainty Principle used as a physical basis supporting/establishing GIT. (Also causality does not exactly mean determinism.)

http://ti.arc.nasa.gov/m/profile/dhw/papers/71.pdf by David Wolpert
Abstract: “In this paper strong limits on the accuracy of real-world physical
computation are established. To derive these results a non-Turing Machine (TM)
formulation of physical computation is used. First it is proven that there
cannot be a physical computer C to which one can pose any and all computational
tasks concerning the physical universe. Next it is proven that no physical
computer C can correctly carry out every computational task in the subset of
such tasks that could potentially be posed to C. This means in particular that
there cannot be a physical computer that can be assured of correctly “processing
information faster than the universe does”. … Note that since the universe is
microscopically deterministic, (be it classical or quantum-mechanical, if we
adopt the many-worlds interpretation for the latter case)…”

]]> By: Charlie Stromeyer http://antimeta.wordpress.com/2009/02/06/the-strong-free-will-theorem/#comment-2714 Charlie Stromeyer Sat, 02 May 2009 21:20:40 +0000 http://antimeta.wordpress.com/?p=182#comment-2714 Let us suppose that quantum mechanics (QM) is truly more fundamental than classical mechanics. Then, the "free will" in the above theorem only has three possible origins: it somehow evolved into existence, for example, with something like the Big Bang, or it is from a physical reality that is more fundamental than QM or it is from a metaphysical source. Well, we can eliminate the first possibility because this brief paper shows that the wavefunction of QM is both non-local and non-sequential, meaning that the wavefunction of QM transcends conventional notions of causality, space and time: http://arxiv.org/abs/quant-ph/0102109 Let us suppose that quantum mechanics (QM) is truly more fundamental than classical mechanics. Then, the “free will” in the above theorem only has three possible origins: it somehow evolved into existence, for example, with something like the Big Bang, or it is from a physical reality that is more fundamental than QM or it is from a metaphysical source.

Well, we can eliminate the first possibility because this brief paper shows that the wavefunction of QM is both non-local and non-sequential, meaning that the wavefunction of QM transcends conventional notions of causality, space and time:

http://arxiv.org/abs/quant-ph/0102109

]]> By: Charlie Stromeyer http://antimeta.wordpress.com/2009/02/06/the-strong-free-will-theorem/#comment-2708 Charlie Stromeyer Mon, 20 Apr 2009 13:19:38 +0000 http://antimeta.wordpress.com/?p=182#comment-2708 I emailed Conway and Kochen because their Strong Free Will Theorem appears to me to be a computational skill within the context of G. Castagnoli's work on the fundamentally non-deterministic nature of quantum computation. For example, see this newly revised paper by Castagnoli et al. which argues that quantum entanglement is essential for quantum computation and that the latter transcends conventional physical notions of both causality and dynamics: http://xxx.lanl.gov/abs/quant-ph/0005069 I emailed Conway and Kochen because their Strong Free Will Theorem appears to me to be a computational skill within the context of G. Castagnoli’s work on the fundamentally non-deterministic nature of quantum computation. For example, see this newly revised paper by Castagnoli et al. which argues that quantum entanglement is essential for quantum computation and that the latter transcends conventional physical notions of both causality and dynamics:

http://xxx.lanl.gov/abs/quant-ph/0005069

]]> By: R. T. Mercuri http://antimeta.wordpress.com/2009/02/06/the-strong-free-will-theorem/#comment-2707 R. T. Mercuri Tue, 14 Apr 2009 23:34:30 +0000 http://antimeta.wordpress.com/?p=182#comment-2707 True. They do say that if the observer has free will "then the particle's response is not determined by the entire previous history of the universe" and they say that "there's no longer any evidence to support determinism," but they've also said that they haven't disproven the possibility of determinism either. I think the confusion occurs when we try to consider free will as the dual of determinism which I'm not sure they are saying it necessarily is or is not. I'll try to get a clarification on this during next Monday's Q&A if I have a chance to ask. True. They do say that if the observer has free will “then the particle’s response is not determined by the entire previous history of the universe” and they say that “there’s no longer any evidence to support determinism,” but they’ve also said that they haven’t disproven the possibility of determinism either.

I think the confusion occurs when we try to consider free will as the dual of determinism which I’m not sure they are saying it necessarily is or is not. I’ll try to get a clarification on this during next Monday’s Q&A if I have a chance to ask.

]]> By: Dave Baker http://antimeta.wordpress.com/2009/02/06/the-strong-free-will-theorem/#comment-2706 Dave Baker Tue, 14 Apr 2009 22:57:21 +0000 http://antimeta.wordpress.com/?p=182#comment-2706 Posting again to correct some misconceptions above: <i>Baker (above) is incorrect about their assumption of indeterminism of measurement decisions </i> In their argument against Bohm, which is what I was talking about, they do assume "free will" (via the MIN/FIN axioms) as a premise. <i> indeed they say that IF free will does NOT exist, then the measurement decisions are deterministic. </i> They definitely don't think that, since they believe that "free will" is incompatible with the GRW model, which is indeterministic. Posting again to correct some misconceptions above:

Baker (above) is incorrect about their assumption of indeterminism of measurement decisions

In their argument against Bohm, which is what I was talking about, they do assume “free will” (via the MIN/FIN axioms) as a premise.

indeed they say that IF free will does NOT exist, then the measurement decisions are deterministic.

They definitely don’t think that, since they believe that “free will” is incompatible with the GRW model, which is indeterministic.

]]> By: R. T. Mercuri http://antimeta.wordpress.com/2009/02/06/the-strong-free-will-theorem/#comment-2705 R. T. Mercuri Tue, 14 Apr 2009 22:33:23 +0000 http://antimeta.wordpress.com/?p=182#comment-2705 I think they've tried to be very clear about the terminology and seem to have put a lot of thought into the words they've selected to use. Personally, I wouldn't use the word "non-deterministic," because that term has a rather specific connotation, especially in computer science as related to finite automata (Turing machines, etc.), that I believe is not the same as what Conway and Kochen intend to convey by "free will." They've been careful to explain that other indeterministic aspects, such as "randomness" or "probabilities" are also excluded. So one might consider "free will" as a constrained type of non-determinism. Conway did say, though, in (I think) lecture 2, that if you're uncomfortable with the phrase "free will" it could be substituted with "free whim." As for the lack of natural intuitions or evidence, many said the same about quantum mechanics decades ago, but it's generally accepted nowadays. Conway points out that SPIN and TWIN are measurable (although perhaps not yet with sufficient accuracy), and results to date do seem to confirm the theory (as well as the paradoxes). I think they’ve tried to be very clear about the terminology and seem to have put a lot of thought into the words they’ve selected to use.

Personally, I wouldn’t use the word “non-deterministic,” because that term has a rather specific connotation, especially in computer science as related to finite automata (Turing machines, etc.), that I believe is not the same as what Conway and Kochen intend to convey by “free will.” They’ve been careful to explain that other indeterministic aspects, such as “randomness” or “probabilities” are also excluded.

So one might consider “free will” as a constrained type of non-determinism. Conway did say, though, in (I think) lecture 2, that if you’re uncomfortable with the phrase “free will” it could be substituted with “free whim.”

As for the lack of natural intuitions or evidence, many said the same about quantum mechanics decades ago, but it’s generally accepted nowadays. Conway points out that SPIN and TWIN are measurable (although perhaps not yet with sufficient accuracy), and results to date do seem to confirm the theory (as well as the paradoxes).

]]> By: Kenny http://antimeta.wordpress.com/2009/02/06/the-strong-free-will-theorem/#comment-2704 Kenny Tue, 14 Apr 2009 21:29:29 +0000 http://antimeta.wordpress.com/?p=182#comment-2704 That's useful to hear the clarification about their views. However, I still think that they seem to be conflating free will with a certain type of indeterminism. It seems to me that a better statement of the content of their result is that "If humans are non-deterministic, then elementary particles are too". They have a technical definition of free will on which your statement is correct, but this technical definition of free will certainly isn't one that we have any natural intuitions about, or any evidence that humans actually have. Anyway, I'll have to check out the lectures some time - I know that Conway tends to be a great lecturer, so it'll be really good to see. That’s useful to hear the clarification about their views. However, I still think that they seem to be conflating free will with a certain type of indeterminism. It seems to me that a better statement of the content of their result is that “If humans are non-deterministic, then elementary particles are too”. They have a technical definition of free will on which your statement is correct, but this technical definition of free will certainly isn’t one that we have any natural intuitions about, or any evidence that humans actually have.

Anyway, I’ll have to check out the lectures some time – I know that Conway tends to be a great lecturer, so it’ll be really good to see.

]]> By: R. T. Mercuri http://antimeta.wordpress.com/2009/02/06/the-strong-free-will-theorem/#comment-2703 R. T. Mercuri Tue, 14 Apr 2009 19:53:03 +0000 http://antimeta.wordpress.com/?p=182#comment-2703 I've been attending Conway & Kochen's lecture series in Princeton on this subject. There, they've asserted that the Free Will Theorem is "IF humans have free will, then elementary particles do too." What you have stated as the Free Will Theorem in your blog posting (above) is actually the Strong FWT, as implied from the paradoxes of SPIN, TWIN and MIN. Conway was pretty emphatic about not knowing whether free will or determinism is actually the case, although he admits to a personal bias toward the concept of free will (as defined within the constraints of their quantum mechanics discussion). Baker (above) is incorrect about their assumption of indeterminism of measurement decisions -- indeed they say that IF free will does NOT exist, then the measurement decisions are deterministic. So it seems that they are being consistent on these points. Incidentally, videos of the lectures (there will be 6 in total) are viewable at: http://www.princeton.edu/WebMedia/flash/lectures/20090323_conway_free_will.shtml I’ve been attending Conway & Kochen’s lecture series in Princeton on this subject. There, they’ve asserted that the Free Will Theorem is “IF humans have free will, then elementary particles do too.” What you have stated as the Free Will Theorem in your blog posting (above) is actually the Strong FWT, as implied from the paradoxes of SPIN, TWIN and MIN. Conway was pretty emphatic about not knowing whether free will or determinism is actually the case, although he admits to a personal bias toward the concept of free will (as defined within the constraints of their quantum mechanics discussion). Baker (above) is incorrect about their assumption of indeterminism of measurement decisions — indeed they say that IF free will does NOT exist, then the measurement decisions are deterministic. So it seems that they are being consistent on these points.

Incidentally, videos of the lectures (there will be 6 in total) are viewable at:
http://www.princeton.edu/WebMedia/flash/lectures/20090323_conway_free_will.shtml

]]> By: Kenny http://antimeta.wordpress.com/2009/02/06/the-strong-free-will-theorem/#comment-2702 Kenny Mon, 09 Mar 2009 03:32:52 +0000 http://antimeta.wordpress.com/?p=182#comment-2702 Hi Dave, Thanks for the comment! I haven't really seen what other philosophers have said about this, just some idle comments from mathematicians. There's actually a summer math program for high school students (the Canada/USA Mathcamp) where I've taught for several times, and Conway comes to visit every summer for a week. I don't think we've overlapped there at the same time since I heard about this theorem, but I've definitely learned some useful tricks from him, both mathematical and non (like the trick I use to know what day of the week various dates will be). So I'm a bit surprised at how much he's stuck with this. Hi Dave,

Thanks for the comment! I haven’t really seen what other philosophers have said about this, just some idle comments from mathematicians. There’s actually a summer math program for high school students (the Canada/USA Mathcamp) where I’ve taught for several times, and Conway comes to visit every summer for a week. I don’t think we’ve overlapped there at the same time since I heard about this theorem, but I’ve definitely learned some useful tricks from him, both mathematical and non (like the trick I use to know what day of the week various dates will be). So I’m a bit surprised at how much he’s stuck with this.

]]> By: Dave Baker http://antimeta.wordpress.com/2009/02/06/the-strong-free-will-theorem/#comment-2701 Dave Baker Mon, 09 Mar 2009 03:16:12 +0000 http://antimeta.wordpress.com/?p=182#comment-2701 Hi Kenny, Nice to see that you're looking into this stuff. I agree with you about the Bohmian response; K&C seem to be entirely off-base in their criticisms of that position. One of their starting assumptions is indeterminism about measurement decisions -- obviously if that's your premise, you're going to conclude determinism is false. In fact, they seem to presume that a relativistic version of Bohm's theory will have to be deterministic, like the non-relativistic version, which isn't true. Some of the newer forms of the theory are stochastic (chancy) rather than deterministic. There also has to be something fishy about their appendix replying to Tumulka. Tumulka has papers with existence proofs of the "flash function" they're trying to say can't exist, and while I haven't read these in detail I can't imagine they're wrong. It surprises me that Kochen and Conway are still pushing this "free will" line, given the amount of cogent criticism they've received from philosophers and fellow mathematicians. I imagine the physical upshot of their result is being misunderstood by them or their opponents or both, so I'd advise agnosticism about almost everything they say. Hope all's well! Dave Hi Kenny,

Nice to see that you’re looking into this stuff. I agree with you about the Bohmian response; K&C seem to be entirely off-base in their criticisms of that position. One of their starting assumptions is indeterminism about measurement decisions — obviously if that’s your premise, you’re going to conclude determinism is false.

In fact, they seem to presume that a relativistic version of Bohm’s theory will have to be deterministic, like the non-relativistic version, which isn’t true. Some of the newer forms of the theory are stochastic (chancy) rather than deterministic.

There also has to be something fishy about their appendix replying to Tumulka. Tumulka has papers with existence proofs of the “flash function” they’re trying to say can’t exist, and while I haven’t read these in detail I can’t imagine they’re wrong.

It surprises me that Kochen and Conway are still pushing this “free will” line, given the amount of cogent criticism they’ve received from philosophers and fellow mathematicians. I imagine the physical upshot of their result is being misunderstood by them or their opponents or both, so I’d advise agnosticism about almost everything they say.

Hope all’s well!

Dave

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