All dogs have four legs. All cows have four legs,. Therefore for all dogs are cows. Or tables, or chairs, or giraffes. Is a dog with three legs a dog?
------------------------------------------- Mr Blakely, How can you connect (1) below, with (2)? By what logic? (1) All mathematics is counting - (2) things exist or they do not. These two statements are not related and neither one supports nor refutes the other. Despite being unrelated they are meant to form the foundation, such as it is, for the next gem of wisdom: You say (3) "Mathematics has therefore always existed." The above two disconnected statements have nothing to do with the third which is patently untrue. And then: "Because you may have no language to describe something does not mean it doesn't exist." This is true as it stands. But ~what~ doesn't exist? Mathematics? If that's what you mean, and it had not yet been invented, then it certainly did not exist. But if you mean the ordered nature of things, which can be described by the man-made language of mathematics, why not say so? Then you make a statement about Mathematics which demonstrates that the above is not a correct assumption. You imply that ~Mathematics~ has an existence independent of man and it is the 'symbology' (symbolism) of mathematics that is the language. Here you are inventing terminology of your own that makes it very difficult for anyone to understand you. Perhaps what you are trying to say, again, is that the nature of things is independent of numbers and that we apply numbers to describe them. So why not say so? Numbers and mathematics did not exist before man invented them, believe me, that's a fact. If you are determined to debate these matters you have to get things clear in your own head first. You also need to speak the same language as the rest of us. And why don't you leave Pi out of this, it will get you nowhere. It is my opinion that arrangements that please the viewer in a photograph, or other form of visual artistic expression, cannot be made so by following a 'Golden Rule'. That some people choose to arrange things in a geometrical way and come to conclusions about how composition can best be done using numbers is a well known fact. It is not scientific, but intuitive, and does not withstand careful scrutiny. The resultant work may be pleasing or not. But this will not depend on whether the artist adhered, or did not, to some magical arrangement arrived at with compass and ruler. In a nutshell: some people have an eye, others don't. Example: In a portrait where the subject is in profile it is good practice to have more space in the direction the subject is looking. Less behind his or her head. Every experienced photographer knows this - no geometry needed. D 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 10:10 PM Subject: Re: Numbers and the Golden Section > All mathematics is counting - things exist or they do not. Because you may have no language to describe > something does not mean it doesn't exist. The symbology of mathematics is > the tool, not mathematics itself. Valence? Valence is a counting of charge. > Pressure? How much? Temperature? How high? Abundance? How many? They obey > their own rules? Who or what are they that they should determine rules that > please them? Pi is the same count whether you express it in binary, octal, > decimal, hexadecimal or give the definition of the ratio. You refuse to > speak the language necessary to describe the world and therefore cannot > contribute to the discussion in any constructive way which may or may not > aid in understanding. All you can really do is make unsubstantiated claims > in a language foreign to that necessary for the discussion. > > The math was always there. The symbology we use to describe it is the > invention or tool. > > Now, If you do have a way to impart your special and wonderful knowledge > concerning composition, I, for one, would like to hear it. As I said it's > always best to sit at the feet of a master... providing he is capable of > communicating his mastery. Otherwise, why listen. > > What? No gems of wisdom for me to try? > > Thought not. > > Then for now, I will continue to frame or crop at roughly the golden > rectangle and perhaps use a square or elongated rectangle as it may seem > adventurous to me. Yes, I will continue to pose in thirds. As to head shots, > I may center the portrait if I wish to express symmetry, but I think I'll > still usually put one eye in the center as has also been suggested as a > starting point by several masters of the trade. > > When I become an expert like you, then I'll wave my camera wildly in the > wind and snap in some manner which I cannot communicate to others. > > 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]> > > > > There was no Mathematics, or Physics, when crystals first started to grow. > > Mathematics governs nothing - it is a language with a set of rules. > Crystals > > do not ~obey~ any outside 'rules' of mathematics or physics. The atoms > will > > arrange themselves in a lattice depending upon valency, pressure, > > temperature, the medium, the composition and their abundance. In this > > respect they do obey rules - their own rules. However, Mathematics and the > > 'Laws' of Physics ~can~ be and are used to describe these rules (see > above) > > with varying degrees of accuracy. One may even predict how crystals will > > [Yea, right] >
