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/ > > > > > > --~--~---------~--~----~------------~-------~--~----~ You received this message because you are subscribed to the Google Groups "Everything List" group. To post to this group, send email to everything-list@googlegroups.com To unsubscribe from this group, send email to [EMAIL PROTECTED] For more options, visit this group at http://groups.google.com/group/everything-list -~----------~----~----~----~------~----~------~--~---