On Mon, Sep 17, 2012 at 12:27 AM, Rex Allen <rexallen31...@gmail.com> wrote:
> > On Sun, Sep 16, 2012 at 6:10 PM, Stephen P. King <stephe...@charter.net>wrote: >> >> HI Rex, >> >> Nice post! Could you riff a bit on what the number PHI tells us about >> this characteristic. How is it that it seems that our perceptions of the >> world find anything that is close to a PHI valued relationship to be >> "beautiful"? >> >> > > Thanks Stephen! > > Actually my initial example of "numeracy" isn't quite right, but it's not > important to the rest of the argument. > > My main point is that you can get to the concept of "prime numbers" just > using relative magnitudes that we have an innate sense of. > > I think an easier way to intuit prime numbers that can't be represented as rectangles, only a 1-wide "lines". While the concept of primes is straight forward, there is an unending set of not-so-obvious facts that we continue to discover about the Primes. For example: The average distance between primes of size N is approximately the natural log of N, yet we know of no way to predict where the next prime will exactly be. ( http://en.wikipedia.org/wiki/Prime_gap ) Between N and 2N, there will always be at least one prime. ( http://en.wikipedia.org/wiki/Bertrand's_postulate ) There is a one-to-one correspondence, and method to get one from the other, between perfect numbers and primes of the form ((2^p) - 1) ( http://en.wikipedia.org/wiki/Perfect_number#Even_perfect_numbers ) For any prime p, and any integer i where 0 < i < p, i^p divided by p has a remainder of i. This almost never works for composite numbers. ( http://en.wikipedia.org/wiki/Fermat's_little_theorem ) the exception for composite numbers where this does hold are known as Carmichael numbers ( http://en.wikipedia.org/wiki/Carmichael_number ) but they are rare. And there are an infinite number of other such patterns waiting to be discovered. Jason As for the significance of PHI - well - I guess there's probably some > plausible sounding evolutionary story that could be told about that. > > Though how satisfying or useful an explanation like that is just depends > on what you're after and what your interests are. > > An explanation that might be useful in one context might be useless in > some other context. > > Explanations are observer dependent. > > Probably. > > Rex > > > -- > 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 > everything-list+unsubscr...@googlegroups.com. > For more options, visit this group at > http://groups.google.com/group/everything-list?hl=en. > -- 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 everything-list+unsubscr...@googlegroups.com. For more options, visit this group at http://groups.google.com/group/everything-list?hl=en.
