Well, I saw a Seven running around in the woods the other day. Or maybe it was those mushrooms I et.
Then there is 7 of 9 on that TV series, I used to watch her quite often <g>. I still don't like irrational numbers though, I can't get my mind around them. And, I think this thread has become a bit irrational also. Me, I am merely not rational. That is different than irrational, isn't it? Golly, what was in that green bottle? Ciao, Graywolf http://pages.prodigy.net/graywolfphoto ----- Original Message ----- From: "Peter Alling" <[EMAIL PROTECTED]> To: <[EMAIL PROTECTED]> Sent: Monday, December 30, 2002 1:23 AM Subject: Re: Vs: Numbers and the Golden Section > You mean it doesn't??????? > > At 07:47 PM 12/29/2002 +0100, you wrote: > >It is the other way round. Tell me one instance when a number has been > >observed in the nature. Lots of numbers can be found in the observations > >of nature which describe it - but these numbers are just descriptions. The > >laws are calculated afterwards. > >Next you will be arguing that nature follows photographs? > >All the best! > >Raimo > >Personal photography homepage at http://www.uusikaupunki.fi/~raikorho > > > >-----Alkuper�inen viesti----- > >L�hett�j�: Bob Blakely <[EMAIL PROTECTED]> > >Vastaanottaja: [EMAIL PROTECTED] <[EMAIL PROTECTED]> > >P�iv�: 29. joulukuuta 2002 17:38 > >Aihe: Re: Numbers and the Golden Section > > > > > > >Below... > > > > > >Regards, > > >Bob.... > > >-------------------------------------------------------------------- > > >"Beer is proof that God loves us and wants us to be happy!" > > > - Benjamin Franklin > > > > > >From: "Dr E D F Williams" <[EMAIL PROTECTED]> > > > > > > > > >> It only leads to the 'Golden Section' because you want it to Herb. Nature > > >> does not obey numbers! > > >> There is nothing special about those numbers at all. > > > > > >This is simply not true. Nature obeys all sorts of numbers. All nature is > > >subject to the basic constants of the universe. The numbers may be > > >considered special in that any variation in them would result in a very > > >different universe. Everything, you me, nature are subject to and > > >constrained by these numbers. If any item in nature grows and increases in > > >complexity as it grows, (say a tree) and the mature looks like the juvinal, > > >the branching must on average follow the "Golden Section". The number of > > >seed spirals in a sunflower will always be a Fibonacci number. Living nature > > >picks or obeys certain mathematical formations because evolution has > > >discarded others through competition, lower effeciency of propagation or > > >lack of robustness regarding survival. All DNA is subject to mathematical > > >constraints resulting from geometries of the molecules making up the DNA > > >which are in turn dictated by the mathematics of the geometry governing > > >their individual atoms which is inturn the result of several of these > > >universal constants. This results in a spiral of a spiral that compacts an > > >amazing amount of information in an extremely small space and which can > > >still be unzipped like a zipper to replicate a gene or code a protein. This > > >paticular pattern exists in all living things because this geometry, > > >resulting from fundamental constants is the only one that nature here on > > >earth has found to work. All undamaged snowflakes are hexagonal for a > > >reason. There is a "magic" number in a water molecule, 2/3pi. > > > > > >This does not mean that the "Golden Ratio" is some most pleasing form to > > >humans and I've offered no opinion on this. It presumes connections we > > >cannot prove. Nevertheless, Fibonacci numbers do show up in nature and there > > >is a reason why they do. To say that there is nothing naturally or > > >especially "pleasing" about the "Golden Ratio" to at least some humans is > > >probably arrogant. Keep in mind that the "Golden ratio" is an unique > > >geometric construction like pi, not some number picked from thin air. > > > > > >> But there may well be something very special about a thing they may have > > >> been used to describe. > > >> > > >> There are many ways in which a picture may be presented in a pleasing way. > > >> The 'golden' way is only one example. We all know that numbers are among > > >the > > >> symbols of a special universal language called Mathematics. The numbers > > >> themselves have no special quality. > > > > > >Pi is an exceptionally special number, and without knowledge of it our > > >entire civilation would be back to flaking rocks, attaching them to sticks > > >and spearing animals for dinner. There are a whole host of "special numbers" > > >that lie behind who we are, and without knowledge and use of them you would > > >not be taking photos or typing on your keyboard. The discovery of each of > > >these numbers has been as much a milestone of civilation as the invention of > > >the wheel. > > > > > >> Games have been played with these > > >> symbols for a long time. Thousands of books have been written, and read > > >too, > > >> on how numbers affect our lives. I saw, recently, a book about the secret > > >> code of the bible - number nonsense taken to an extreme. The only valid > > >> statements that can be made about it is that it is a book, printed on > > >paper > > >> and seems to have made money for the author and publisher. But it is only > > >> one of a long string of them going back for decades. > > > > > >No one is trying to "divine" secrets here. Folks have been making > > >observances here and also discussing the observances of those that came > > >before them. Sounds like scientific endeavor to me. > > > > > >> When you say that these special numbers occur in nature what you're > > >actually > > >> saying is that they have some kind of magical or special aesthetic > > >quality. > > > > > >No, so far as I can tell, folks have made observations of their own and > > >referred to those who came before them who made observations. No one here is > > >referring to magic. > > > > > >> Yes? Its the other way around. The numbers derive from the way nature is > > >> arranged. Looking at an X-ray diffraction pattern, or the arrangement of > > >> atoms in an electron micrograph, or the number of electrons in the shells > > >> about an atom, virus particles, or the incredible DNA molecule. Or even > > >> counting the number of coils in a sea-snail shell, or measuring snow > > >> crystals, and finally dividing, multiplying, solving quadratics, > > >> differentiating, integrating, and ending with some numbers that you > > >conclude > > >> represent some kind of a 'golden rule of nature' is comparable to the > > >secret > > >> worship of numbers by the Pythagoreans. > > > > > >Nonsense! The numbers do NOT derive from looking at an X-ray diffraction > > >pattern, or from any other diffraction pattern for that matter. Diffraction > > >patterns are described by Maxwell's Equasions for propagation of > > >electromagetic waves. These are Law. The only special numbers used are pi, > > >e, and c (speed of light). None of these numbers were derived by observing > > >diffraction patterns. In other words, nature IS constrained by these special > > >numbers. In the first paragraph I described how your other examples > > >discussed here exist as they do because of "special numbers". > > > > > >The 'golden ratio' is a geometric definition in much the same way as pi is > > >defined as the ratio of the circumfrence of a circle to it's diameter. Phi, > > >the 'golden ratio' is defined as "the ratio obtained if a line is divided so > > >that the length of the shorter segment is in the same proportion to that of > > >the longer segment as the length of the longer segment is to the entire > > >line." This is why it pertains to growth in nature. > > > > > >or the arrangement of atoms in an electron micrograph > > > > > >> There is no example of a golden section in nature. > > > > > >The golden ratio exists all through nature selected by evolution for reasons > > >of efficiency and conservation energy. > > > > > >> For every one you can > > >> make fit the rule by manipulating it into the shape of a rectangle, > > > > > >The "Golden rectangle" is not the golden ratio. The golden rectangle is a > > >rectangle where the ratio of two adjacent sides is the golden ratio. > > > > > >> millions > > >> can be found that simply don't match. And I add, although this might be a > > >> little out of place here, during the last 45 years or so pictorial > > >> 'fractals' have been appended to the 'number magic' quiver. The 'Golden > > >> Section' has no more aesthetic validity than the universal magic word > > >> abracadabra. > > > > > >Perhaps, but the pronouncement is arrogant. > > > > > >The most telling evidence of a tendency for selection of pleasing > > >photographic format within our society would be to develop the probably > > >density function of height to width of acclaimed art, especially that which > > >involves cropping without regard to paper format. It would be interesting to > > >see if it has two peaks, one around 0.62 and the other around 1.62. One > > >might then still argue that this is due to some sort of conditioning in > > >society, but then that's irrelevant isn't? It's still what they prefer and > > >what they found pleasing. > > > > > >[further anecdotal evidence deleted] > > > > > >> But as I said, this is really quite a load and will lead nowhere. Some > > >> members will go so far as to post with ~other member's names~ in the > > >subject > > >> line. > > > > > >You are correct to complain about this. > > > > > Outside of a dog, a book is man's best friend. > Inside of a dog, it's too dark to read. --Groucho Marx >
