Le 06-avr.-06, à 10:04, Dominic Tarr a écrit :

> Bruno wrote
>> ...
>> Karl Popper did make an attempt to explain
>> free-will in term of "self-diagonalization" indeed. The basic and
>> simple idea is that IF I can totally predict myself, then I have the
>> opportunity to refute such a prediction. This is why in a trial your
>> lawyer cannot invoke determinacy (like my client has made a murder, 
>> but
>> really he was just obeying to the physical laws), because if such a
>> determination can make sense then the "client" could have use in some
>> responsible way to escape its murderer fate still without violating 
>> the
>> physical laws. I don't pretend there is any rigor here.
>> "Free from what?": Free from what you can determine. The one who can
>> determine that heavy bodies fall, will soon or later be able to fly.
>
> I was just about to make a post to this effect, and then when i read
> down to the end i found it.
>
> but so how could primes be said to have free will? primes are complex
> in the sense that they can not be predicted except by performing the
> calculation they literally represent faster than some algorithm which
> you are trying to beat.
>
> likewise, one could surely calculate the outcome of a coin flip with a
> sufficiently large and accurate number of measurements and fast
> calculations, or even a human being, if you could accurately model
> them and a sufficient amount of their local environment. there is no
> shortcut to computing these things, you just have do all the hard work
> quickly to make a prediction, so they are all complex, if not free.
>
> however, as a person's local environment might plausibly contain a
> computer which modeled their local environment and predicted their
> behaviour. so the model would actually have to model itself, now
> having to recalculate what the subject will do after every calculation
> would take so long the subject would have already done something and
> the model wouldn't be making a prediction any more!
>
> this looks like a different order of magnitude of unpredictability to
> what primes and coins have, because of the potential self-referential
> step.
>
> perhaps the key is that primes and coins do not have a will, thus
> remain indifferent to being predicted. so you might say they are
> "free", but you could not say they had "freewill".


I did not intent to be so precise, and my "attribution" of free will to 
primes was, well, admittedly a little bit poetical. My point is this 
common point between the primes and human (as conceived by 
determinist):   they are simultaneously determinate and free (cf 
Zagier's quote). Of course primes does not have "will", at least as we 
conceive them today.

Bruno

http://iridia.ulb.ac.be/~marchal/


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