# Re: Do prime numbers have free will?

From: John M <jamikes.domain.name.hidden>
Date: Tue, 4 Apr 2006 11:57:21 -0700 (PDT)

Tom,

I did not shoot my mouth about free will, because of
my esteem for Bruno. Now, however, your definition of
the primes tickled my mathematical ignorance and I ask
you:
IF - as you wrote,
">a prime is an integer having no factors other than
>1 and itself. <
My question: is a 'number' the same as its negative,
eg. is 2 = -2? because if not, then a prime number
"p" is both equal to p.1 and 1.p, (so far so good,)
but it is also p = -1.-p --
factors different from the prime itself and 1.
(And please spare me of the [..] absolut values)

What say you?

John

>
> Bruno,
>
> To help us understand this: How is this different
> from saying the toss
> of a coin is both unpredictable and yet determined
> by laws?
>
> Another thought is that there are the two extremes
> of the meaning of
> "law":
>
> 1) The reductionist definition that something can be
> predicted by the
> sum of atomic parts and rules.
> With the primes it is the integers and addition and
> multiplication.
> With a coin supposedly it is "atoms" and the laws of
> physics.
> 2) The statistical definition that something follows
> a certain
> distribution over many trials.
> With the primes it would be the prime number theorem
> or more precise
> bounds on the distribution of the primes. With a
> coin it would be the
> binomial distribution.
>
> This brought up another thought. The definition of
> the primes is a
> negative definition, an integer having no factors
> other than 1 and
> itself. Of course this is what makes it difficult
> to determine if a
> large number is prime. But is there something about
> a negative
> definition that sets us up for... what... not being
> able to understand
> something? This also reminds me of the
> diagonalization process,
> defining something by saying it is not something
> else, like Chaitin
> does with his Omega, and of course Cantor with the
> reals (resulting in
> the mystery of the continuum hypothesis). Another
> famous negative
> definition is that of infinity, which causes so many
> weirdnesses in
> divergent series, and talking about the multiverse,
> etc.
>
> Perhaps free will is such a mytery because it can be
> defined only
> negatively. Free from what?
>
> Tom
>
> -----Original Message-----
> From: Bruno Marchal <marchal.domain.name.hidden>
> To: FoR <Fabric-of-Reality.domain.name.hidden>
> Cc: everything-list.domain.name.hidden
> Sent: Tue, 4 Apr 2006 17:42:03 +0200
> Subject: Do prime numbers have free will?
>
> Hi,
>
> I love so much this citation (often quoted) of D.
> Zagier, which seems
> to me to describe so well what is peculiar with ...
> humans, which
> behaviors are simultaneously completely determinated
> by numbers/math or
> waves/physics and at the same time are so much rich
> and unpredictible.
> I find instructive to see that primes already
> behaves like that ....
>
>
> "There are two facts about the distribution of prime
> numbers of which I
> hope to convince you so overwhelmingly that they
> will be permanently
> engraved in your hearts. The first is that, despite
> their simple
> definition and role as the building blocks of the
> natural numbers, the
> prime numbers...grow like weeds among the natural
> numbers, seeming to
> obey no other law than that of chance, and nobody
> can predict where the
> next one will sprout. The second fact is even more
> astonishing, for it
> states just the opposite: that the prime numbers
> exhibit stunning
> regularity, that there are laws governing their
> behaviour, and that
> they obey these laws with almost military
> precision."
>
>
>
>
> Bruno
>
>
> http://iridia.ulb.ac.be/~marchal/
>
>
>
>
>
>

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Received on Tue Apr 04 2006 - 15:00:42 PDT

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