Big Thoughts for a Friday

On a mailing list I subscribe to, Tom Duff pointed me at Conway’s Proof of the Free Will Theorem.

From the background:

In mid-2004, John Conway and Simon Kochen of Princeton University proved the Free-will Theorem. This theorem states “If there exist experimenters with (some) free will, then elementary particles also have (some) free will.” In other words, if some experimenters are able to behave in a way that is not completely predetermined, then the behavior of elementary particles is also not a function of their prior history. This is a very strong “no hidden variable” theorem.

I’m not sure I can wrap my head around this, being a Friday, but it is very, very strange. The idea of free will is something which I had decided was more or less unassailable by the methods of science (it wasn’t even clear to me that the phenomena had any real meaning whatsoever) but apparently someone with the intellect of Conway thought that it was worthy of study, so perhaps I was mistaken.

One of my personal regrets is that I didn’t drop in on John Conway while I was working in the Applied Math department at Princeton. I have little doubt that if I had, I’d have met the smartest person I’ve ever encountered so far.

Need a fun book by Conway? Try ::amazon(“038797993X”, “The Book of Numbers“):: that he coauthored with Richard Guy. Very entertaining, and quite accessable.

Note: “entertaining” here is used in the usual brainwagon sense of the word.

Addendum: Here is Tom’s take on it:

The proof, of course, depends on the underlying physics. What is remarkable is that they only require three physical axioms, which, in typical Conway style, they call SPIN, FIN and TWIN.

SPIN:
spins have the 101 property, i.e. the measured (squared) spins of a spin-1 particle in 3 perpendicular directions will be two 1’s and a zero in some order.
FIN:
there is a finite upper bound on the speed at which information travels.
TWIN:
if a pair of particles has total angular momentum 0 then one has
angular momentum s and the other -s.

SPIN and TWIN are fairly well-confirmed experimentally, and while most physicists believe FIN, it’s not the sort of statement that experiments can confirm. (Conway says: “We do not know if some unknown method allows for instantaneous transfer of information, almost by definition.”)

It’s interesting to me that SPIN and TWIN are quantum-mechanical statements and FIN is true in General Relativity. It’s fairly widely held that QM and GR are inconsistent, which might lead you to believe that Conway and Kochen are skating on thin ice. But there may be other SPIN/FIN/TWIN models that aren’t as problematic.

My head hurts.

3 thoughts on “Big Thoughts for a Friday”

  1. Theo

    I think you were probably right in the first place about science and free will. Conway is brainy, but he’s a mathematician, not a philosopher, and he specialises in rather mechanistic models of the world. His discussion of the concept free will sounds philosophically naive — and I’m not really sure he cares; it sounds like it’s really just an excuse for some (possibly very important) recreational mathematics for him.

    The world could be completely deterministic, and yet we might still feel as if we had free will. There is a philosophical position called compatibilism (http://plato.stanford.edu/entries/compatibilism/) that argues this. It’s a good example of the kind of issue and conversation Conway totally ignores.

  2. Dan Lyke

    Doesn’t this just restate the basics of: Either our sense of self is the result of a repeatable physical process, in which case we have the perceptiion of free will, or we’re not, in which case free will comes from randomness?

  3. Theo

    I don’t think so. Conway isn’t saying free will comes from randomness. He doesn’t provide any justification for believing that it exists. As far as his argument is concerned, “free will” might look like randomness to an observer.

    He admits that his intention in using the term is to wind people up:
    “I deliberately and tendentiously and provocatively used the term free will for the particles, for the very good reason that the theorem itself shows it to be the same property that has always been called ‘free will’ for people.”
    http://www.workopolis.com/servlet/Content/qprinter/20050319/PARTICLES19

    Reading some more about the Kochen-Specker theorem, it really sounds like this has hardly anything to do with the properties of free will at all. The SEP has a partly comprehensible entry:
    http://plato.stanford.edu/entries/kochen-specker/

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