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
