Just like Don to argue then tell everyone he's out of the discussion as anyone's word besides his is "absolute rubbish". Anyone else notice the pattern?
----- Original Message ----- From: "Dr E D F Williams" <[EMAIL PROTECTED]> To: <[EMAIL PROTECTED]> Sent: Sunday, December 29, 2002 2:02 PM Subject: Re: Numbers and the Golden Section > abracadabra > abracadabr > abracadab > abracada > abracad > abraca > abrac > abra > abr > ab > a > > Right! > > Nature obeys no numbers. > > There are no recognised 'basic constants of the universe'. > > Numbers are no more special than we make them. > > DNA is not subject to ~mathematical~ constraints. > > Nothing in nature follows the 'Golden Section' - whatever that actually may > be. > > "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 in > turn the result of several of these universal constants." > > The above paragraph is meaningless rubbish. > > While it is true that the geometric arrangement of seeds on a sunflower > inflorescence are aesthetically attractive, sunflowers, or something very > like them, were growing aeons before numerical series were invented. > > -------------- > > I won't answer more of the ingenuous comments in this strange post - most of > which are absolute rubbish. Why? Because I begin, suddenly, to see imaginary > flecks of spittle in strange mathematical patterns between the lines. This > poster reads what I have written, or gives the impression of having read - > by adding a footnote - and then comes to utterly ridiculous conclusions. > > He might just as well have written "Blessed be Pi and his Holy name." It > would have made just as much sense. Now I suppose the cat will truly be > amongst the pigeons. Perhaps a magical doll will be constructed with > Fibonacci, or golden proportions, and pins methodically inserted into > various sensitive areas. > > Dr E D F Williams > > http://personal.inet.fi/cool/don.williams > Author's Web Site and Photo Gallery > Updated: March 30, 2002 > > > ----- Original Message ----- > From: "Bob Blakely" <[EMAIL PROTECTED]> > To: <[EMAIL PROTECTED]> > Sent: Sunday, December 29, 2002 6:38 PM > Subject: 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. > > > >
