greetings, i found the review of this book to be fascinating-- it thougly debunks the notion of the golden ratio and fibonaci significance in nature, markets, art, etc. i always KNEW that there was something not quite right when people claimed that the golden ratio is found everywhere--finally there is some research indicating same. http://search.barnesandnoble.com/bo...05&ISBN=0767908155&bfdate=02-06-2004+20:11:36 best, surfer
Although I have read this extremely good book by a fine mathematician I don't think he goes far enough . He more or less debunks the common falsies but go deep enough and you will see some interesting things that can't be denied. I read where Rentec uses the golden angle, but wasn't told why. Asking more questions I came to the conclusion they had replaced the sigmoid function with the golden angle as their last input before output in their NN. I've used sqrt 2 and found some interesting patterns. You may want to also read up on this youself starting with this http://www.brooksdesign-cg.com/Code/Html/godna2.htm
fascinating, plumber. i am always seeking to expand my knowledge base . thank you for the link ! surfer
Here's one more, unrelated to the book. The market is an ocean of contrary indicators with sentiment being one on the list, but what about number cycles? Wouldn't the most common number cycles be the least important and least common be the most important? This is for all Square of 9 users http://mathworld.wolfram.com/BenfordsLaw.html
No because fib numbers is NOT the LAW it is only CONVERGENCE of a LAW I know it because I have such a law: I have never introduced Fib ratios in my equations, fib ratios appear SOMETIMES but NOT ALWAYS at output. Convergence means that it is a sort of average so yes market tends towards this ratio but it is not obligatory. For example 10415 calculated the other day by my model - see http://www.elitetrader.com/vb/showthread.php?s=&threadid=27783 (in real Market made 10417 at bottom) - corresponds to NO FIB RATIO. I fact I never look for practical trading if a number is a fib ratio or not since I have the true law so I don't care about having only a sort of average which is more unprecise. Remember that a mathematical law doesn't appear by magic, it is REALISED by some CONCRETE means. In the case of Fibo rabbits the golden ratio would be FALSE if the HYPOTHESIS of reproduction of rabbits was different. The same for Normal Law, Power Law etc. It is mysticism to think that a law is true by "magic". A mathematical Law is true only if the premisces can be true and reality is never obliged to conform to these premisces except if there are CAUSES for these. Yes as said in Sornette and Bouchaud's article Fib ratios is used by "Folklorists" in the market: http://www.elitetrader.com/vb/showthread.php?s=&threadid=27695&perpage=6&pagenumber=2 But is it reasonable to think that the MINORITY of these FOLKLORISTS OUTWEIGTH the MAJORITY of NON FOLKLORISTS ? I say no and so the existence of these fib ratios is due to a more fundamental reason than just Folklorism above all when it is only used by a minority.
Those who would think that it is found "everywhere" are mystics or ignorant or misinterpret the term Universal or Natural. As I have said above a mathematical law is not true by "MAGIC". For example I have already posted this to show that the convergence of Fibo rabbits would be 1.839 and not 1.618 if the HYPOTHESIS MADE WAS DIFFERENT. http://www.elitetrader.com/vb/showthread.php?s=&postid=250373&highlight=reproduction#post250373 "Fibonacci was studying the reproduction of rabbits and he made the hypothesis that each generation was producing 1 couple and only one couple at each generation. In that case the ratio of two consecutive terms will be the solution of the equation x = x^2 +1 which would give 1.618. But nature is not so simplist and if he had supposed 3 couples distributed on 3 generations the new magic number would be the solution of the equation x^3 = x^2 + x + 1 and would give a ratio of 1.839. So the golden mean has no acquired universality at least on macroscopic scale where the initial conditions can be broadly numerous and that what makes richness of life possible ! It could be that on atomic scale golden ratio play a role as other universal constants but on macroscopic scale it has to be demonstrated case by case !" In the case of plants it is true at 92%. But it is not because it is true in plants that it must also be true in Stock Market. That fib ratios has some Universal or Natural character (which is not yet showed in Science although fib ratio has begun to appear in some phenomenas like Black Holes, the cosmological alpha constant 1/137 is the inverse of the 137 Golden Angle but Cosmologists never made the link as far as I know) like for example Normal Law or other laws like Power Law doesn't mean that it has to be true everywhere: Universal or Natural, term used by mathematicians and physicians, doesn't mean always true and everywhere, it means that it is true within a large family of problems (for example for Normal Law it is convergence for family of many probability laws from binomial to poisson law, in fact Levy has demonstrated that it is true for every probability law that has finite mean and variance so that it is very large indeed) . So the problem is that people with weak knowledge take the term Universal and Natural litteraly whereas mathematically it doesn't have this extremist interpretation.
An interesting read http://www.amazon.com/exec/obidos/t...103-6802270-3462255?v=glance&s=books&n=507846 as well as the latest issue of SmartMoney has this story "Where Great Ideas Come From" with one of my co-workers from my Los Alamos days quoted. http://www.smartmoney.com/mag/
harry, according to this book on phi, the Golden Ratio was around WAY WAY BEFORE Fib. As far back as Euclid and the greeks and Egyptians knew about it. I think it's deeper than just the initial conditions for rabbits reproduction... ======================================== http://search.barnesandnoble.com/bo...05&ISBN=0767908155&bfdate=02-06-2004+20:11:36 "Throughout history, thinkers from mathematicians to theologians have pondered the mysterious relationship between numbers and the nature of reality. In this fascinating book, Mario Livio tells the tale of a number at the heart of that mystery: phi, or 1.6180339887. This curious mathematical relationship, widely known as the "Golden Ratio," was defined by Euclid more than two thousand years ago because of its crucial role in the construction of the pentagram, to which magical properties had been attributed. Since then it has shown a propensity to appear in the most astonishing variety of places - from mollusk shells, sunflower florets, and the crystals of some materials, to the shapes of galaxies containing billions of stars. Psychological studies have investigated whether the Golden Ratio is the most aesthetically pleasing proportion extant, and it has been asserted that the creators of the Pyramids and the Parthenon employed it. It is believed to feature in works of art from Leonardo da Vinci's Mona Lisa to Salvador Dali's The Sacrament of the Last Supper, and poets and composers have used it in their works. It has even been suggested that it is connected to the behavior of the stock market!" The Golden Ratio is a journey through art and architecture, botany and biology, physics and mathematics. It tells the human story of numerous phi-fixated individuals, including the followers of Pythagoras, who believed that this proportion revealed the hand of God; astronomer Johannes Kepler, who saw phi as one of the greatest treasures of geometry; such medieval thinkers as mathematician Leonardo Fibonacci of Pisa; and such masters of the modern world as Debussy, Le Corbusier, Bartok, and physicist Roger Penrose. Wherever his quest for the meaning of phi takes him, Mario Livio reveals the world as a place where order, beauty, and eternal mystery will always coexist."