Re: Vs: Numbers and the Golden Section
Isn't zero simply one point in a series of values where values one side of it are arbitrarily ascribed 'minus' values, and those the other side 'plus' values? And is it not the case that until mathematicians were able to conceive of and use zero as a valid value, that most maths didn't work? Pi is an expression of the relationship between two properties of a geometric figure, no more, no less. We can use an approximation of it in our real-world calculations to design things, but we always have a degree of inaccuracy built-in to those calculations, which we can more or less ignore. It may be mind-blowing that we can never bring it's calculation to a conclusion, but it ain't magic and it ain't religion! To bring it back at least towards being on-topic, I try to compose my Pentax pictures with either a sense of 'stasis', or a sense of dynamism, and will use the so-called 'golden mean' or rule of thirds', unconsciously as these merely describe the theoretical analysis of what I see as the balance of the elements in the composition, achieving the effect I want. John Coyle Brisbane, Australia - Original Message - From: Brad Dobo [EMAIL PROTECTED] To: [EMAIL PROTECTED] Sent: Monday, December 30, 2002 2:58 PM Subject: Re: Vs: Numbers and the Golden Section I think the most universal and mathematical number is '0'. Why that is, I don't know, but why should a number that supposedly has quantitative value represent 'nothing'. You can't put a value on something that does not exist, yet we do. It means nothing and is nothing, but we make it something. Just a thought. Brad
Re: Vs: Numbers and the Golden Section
Obviously, you have never had to deal with imaginary numbers. Bob - Original Message - From: Brad Dobo [EMAIL PROTECTED] I think the most universal and mathematical number is '0'. Why that is, I don't know, but why should a number that supposedly has quantitative value represent 'nothing'. You can't put a value on something that does not exist, yet we do. It means nothing and is nothing, but we make it something. Just a thought. Brad
Re: Vs: Numbers and the Golden Section
Zero is not a number, it is a place holder. Funny thing is that without it mathematics is very difficult. Ciao, Graywolf http://pages.prodigy.net/graywolfphoto - Original Message - From: Brad Dobo [EMAIL PROTECTED] To: [EMAIL PROTECTED] Sent: Sunday, December 29, 2002 11:58 PM Subject: Re: Vs: Numbers and the Golden Section I think the most universal and mathematical number is '0'. Why that is, I don't know, but why should a number that supposedly has quantitative value represent 'nothing'. You can't put a value on something that does not exist, yet we do. It means nothing and is nothing, but we make it something. Just a thought. Brad - Original Message - From: Bob Rapp [EMAIL PROTECTED] To: [EMAIL PROTECTED] Sent: Sunday, December 29, 2002 11:44 PM Subject: Re: Vs: Numbers and the Golden Section Ok, That is it! From: http://www.cecm.sfu.ca/pi/pi.html an excerpt: Pi is one of the few concepts in mathematics whose mention evokes a response of recognition and interest in those not concerned professionally with the subject. It has been a part of human culture and the educated imagination for more than twenty five hundred years. Bob - Original Message - From: William Robb [EMAIL PROTECTED] To: [EMAIL PROTECTED] Sent: Monday, December 30, 2002 3:37 PM Subject: Re: Vs: Numbers and the Golden Section - Original Message - From: T Rittenhouse Subject: Re: Vs: Numbers and the Golden Section Another thing that is bothering me about all these threads: why is nobody complaining about all these religion posts? We're busted. WW
Re: Vs: Numbers and the Golden Section
On Mon, 30 Dec 2002 09:14:16 -0500, Mark Roberts wrote: David Hume to the white courtesy telephone, please! David Hume could out consume Schopenhauer and Hegel, but Wittgenstein was a beery swine who was just a sloshed as Schlegel. TTYL, DougF KG4LMZ
Re: Vs: Numbers and the Golden Section
Hume is famous for a reason. (My own view, however, is probably more in line with Kant's reply to Hume.) But this also fits well with the modern scientific approach to human understanding. By this I mean that what we think is a product of the brain which is a physical object that works by some set of rules like a computer (but probably a completely different set of rules.) The rules may lead to incredibly complex behavior, but this no different from anything else in nature. All I'm saying is that we have had great success modeling nature with math, e.g., pi, e, etc. appear in our representations of the laws of nature. The actual philosophical status of numbers is interesting but irrelevant. We have used them very successfully to model the world, they exist in our thinking, and can affect our thinking. Whether or not they exist in nature is another question. You know, I swore I would not get involved in this discussion. I even avoided several threads with different names. It kept appearing in a different guise, however, and finally caught me. I do have this great picture of me with the statue of Hume in Edinburgh. Maybe I'll change me PDML portrait . . .;-) Steven Desjardins Department of Chemistry Washington and Lee University Lexington, VA 24450 (540) 458-8873 FAX: (540) 458-8878 [EMAIL PROTECTED]
Re: Vs: Numbers and the Golden Section
Raimo Korhonen [EMAIL PROTECTED] wrote: Here we go again - another Pythagorean. Hmm, I would have said Platonist. -Alkuperäinen viesti- Lähettäjä: John Whicker [EMAIL PROTECTED] Vastaanottaja: [EMAIL PROTECTED] [EMAIL PROTECTED] Päivä: 30. joulukuuta 2002 20:22 Aihe: Re: Numbers and the Golden Section - Original Message - From: Dr E D F Williams [EMAIL PROTECTED] To: [EMAIL PROTECTED] Sent: Monday, December 30, 2002 6:16 PM Subject: Re: Numbers and the Golden Section Nope. Its absolutely clear what I mean. There is nothing philosophical about it. I hold that Mathematics is an invention of man. Hi Don, Mathematics was not *invented* by Man. It was *discovered*. Best regards, John -- Mark Roberts Photography and writing www.robertstech.com
Re: Vs: Numbers and the Golden Section
I'm glad you said that. It needed to be said. At 06:07 AM 12/30/2002 -0500, you wrote: Zero is not a number, it is a place holder. Funny thing is that without it mathematics is very difficult. Ciao, Graywolf http://pages.prodigy.net/graywolfphoto - Original Message - From: Brad Dobo [EMAIL PROTECTED] To: [EMAIL PROTECTED] Sent: Sunday, December 29, 2002 11:58 PM Subject: Re: Vs: Numbers and the Golden Section I think the most universal and mathematical number is '0'. Why that is, I don't know, but why should a number that supposedly has quantitative value represent 'nothing'. You can't put a value on something that does not exist, yet we do. It means nothing and is nothing, but we make it something. Just a thought. Brad - Original Message - From: Bob Rapp [EMAIL PROTECTED] To: [EMAIL PROTECTED] Sent: Sunday, December 29, 2002 11:44 PM Subject: Re: Vs: Numbers and the Golden Section Ok, That is it! From: http://www.cecm.sfu.ca/pi/pi.html an excerpt: Pi is one of the few concepts in mathematics whose mention evokes a response of recognition and interest in those not concerned professionally with the subject. It has been a part of human culture and the educated imagination for more than twenty five hundred years. Bob - Original Message - From: William Robb [EMAIL PROTECTED] To: [EMAIL PROTECTED] Sent: Monday, December 30, 2002 3:37 PM Subject: Re: Vs: Numbers and the Golden Section - Original Message - From: T Rittenhouse Subject: Re: Vs: Numbers and the Golden Section Another thing that is bothering me about all these threads: why is nobody complaining about all these religion posts? We're busted. WW Outside of a dog, a book is man's best friend. Inside of a dog, it's too dark to read. --Groucho Marx
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 -Alkuperäinen viesti- Lähettäjä: Bob Blakely [EMAIL PROTECTED] Vastaanottaja: [EMAIL PROTECTED] [EMAIL PROTECTED] Päivä: 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
Re: Vs: Numbers and the Golden Section
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 -Alkuperäinen viesti- Lähettäjä: Bob Blakely [EMAIL PROTECTED] Vastaanottaja: [EMAIL PROTECTED] [EMAIL PROTECTED] Päivä: 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
Re: Vs: Numbers and the Golden Section
- Original Message - From: T Rittenhouse Subject: Re: Vs: Numbers and the Golden Section Well, I saw a Seven running around in the woods the other day. Or maybe it was those mushrooms I et. My wife is a 9.2. William Robb
Re: Vs: Numbers and the Golden Section
Raimo Korhonen wrote: OK - if pi can really be found in the nature, it would have been found a couple of thousands of years ago. Now we have only approximations. Silly, isn´t it? Excuse me? What _ever_ are you talking about? Pi is the mathematical expression for the ratio between a circle's diameter and it's circumference. It just IS. No more strange than a circle's radius is exactly 1/2 half the diameter. It can be found wherever a circle is found ~ whether in nature or not. Nature has nothing to do with it! What do you mean, we only have approximations? These comments make no sense at all. This discussion is way off track. keith whaley All the best! Raimo Personal photography homepage at http://www.uusikaupunki.fi/~raikorho -Alkuperäinen viesti- Lähettäjä: Bob Blakely [EMAIL PROTECTED] Vastaanottaja: [EMAIL PROTECTED] [EMAIL PROTECTED] Päivä: 29. joulukuuta 2002 22:35 Aihe: Re: Numbers and the Golden Section I don't know why folks are so caustic these days. I don't know I'm so caustic these days. Perhaps I'm just thick and don't get it, but to me constants such as pi, universal gravitational constant, charge of an electron numbers of things and their combined effects the laws of thermodynamics existed since the dawn of time. Four electrons aggregated together produced four times the charge of a single electron (not five or three) before there was an earth, let alone a man or a language to describe this mathematics. Saying that values or things or concepts or relationships don't exist merely because they can be conveniently described mathematically seems to me ... silly. Regards, Bob
Re: Vs: Numbers and the Golden Section
Another thing that is bothering me about all these threads: why is nobody complaining about all these religion posts? We're busted. WW Yes, a dis-information tactic that failed. Once we got surrounded (circled) we were defeated by Pi.
Re: Vs: Numbers and the Golden Section
Ok, That is it! From: http://www.cecm.sfu.ca/pi/pi.html an excerpt: Pi is one of the few concepts in mathematics whose mention evokes a response of recognition and interest in those not concerned professionally with the subject. It has been a part of human culture and the educated imagination for more than twenty five hundred years. Bob - Original Message - From: William Robb [EMAIL PROTECTED] To: [EMAIL PROTECTED] Sent: Monday, December 30, 2002 3:37 PM Subject: Re: Vs: Numbers and the Golden Section - Original Message - From: T Rittenhouse Subject: Re: Vs: Numbers and the Golden Section Another thing that is bothering me about all these threads: why is nobody complaining about all these religion posts? We're busted. WW
Re: Vs: Numbers and the Golden Section
I think the most universal and mathematical number is '0'. Why that is, I don't know, but why should a number that supposedly has quantitative value represent 'nothing'. You can't put a value on something that does not exist, yet we do. It means nothing and is nothing, but we make it something. Just a thought. Brad - Original Message - From: Bob Rapp [EMAIL PROTECTED] To: [EMAIL PROTECTED] Sent: Sunday, December 29, 2002 11:44 PM Subject: Re: Vs: Numbers and the Golden Section Ok, That is it! From: http://www.cecm.sfu.ca/pi/pi.html an excerpt: Pi is one of the few concepts in mathematics whose mention evokes a response of recognition and interest in those not concerned professionally with the subject. It has been a part of human culture and the educated imagination for more than twenty five hundred years. Bob - Original Message - From: William Robb [EMAIL PROTECTED] To: [EMAIL PROTECTED] Sent: Monday, December 30, 2002 3:37 PM Subject: Re: Vs: Numbers and the Golden Section - Original Message - From: T Rittenhouse Subject: Re: Vs: Numbers and the Golden Section Another thing that is bothering me about all these threads: why is nobody complaining about all these religion posts? We're busted. WW
