Tom, - ha ha,
I would have asked the same stupid question, because a
"poisitve" integer is just so the product of -1 and
the NEGATIVE of the integer plus the (positive)
integer itself and 1. You did not want that either. 
I think a better restriction is in order, but let me
stop here. I don't want to start math 101.
Sorry for having been facetious.

John



--- [EMAIL PROTECTED] wrote:

> 
> John,
> 
> As I was typing that post, I thought about the fact
> that I was leaving 
> out the word "positive" but I left it out anyway.  I
> should have typed 
> "a prime is a positive integer having no factors
> other than 1 and 
> itself."
> 
> While I'm at it, I wanted to correct something else
> in the same post.  
> Instead of
> 
> 1) The reductionist definition that something can be
> predicted by the
> sum of atomic parts and rules.
> 
> I think I should have said
> 
> 1) The reductionist definition that something is
> determined by the
> sum of atomic parts and rules.
> 
> Saying "is determined by" is theoretical and so
> covers the cases like 
> with a coin when limitations and uncertainties
> prohibit actual 
> prediction.  I guess this is a difference between
> the primes and 
> tossing a coin.  But perhaps it's only a difference
> of degree, because 
> when you add and multiply there is always the chance
> that you will make 
> an error.  But then you can repeat the computation,
> whereas you can't 
> repeat the *same* coin toss.  How does this relate
> to free will?  I 
> probably don't want to talk about that too much. 
> There's *probably* a 
> *deterministic* reason for that too.  ;)
> 
> Tom
> 
> -----Original Message-----
> From: John M <[EMAIL PROTECTED]>
> To: everything-list@googlegroups.com
> Sent: Tue, 4 Apr 2006 11:57:21 -0700 (PDT)
> Subject: Re: Do prime numbers have free will?
> 
> 
> 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. <
> (I heard that somewhere already)
> 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
> 
> 
> 
> --- [EMAIL PROTECTED] wrote:
> 
> >
> > 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 <[EMAIL PROTECTED]>
> > To: FoR <[EMAIL PROTECTED]>
> > Cc: everything-list@googlegroups.com
> > 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/
> 
=== message truncated ===


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