Franciscan Friar Pacioli is generally recognized as the Father of Accounting and the one mainly responsible for making the Golden Ratio (which he later called "The Divine Proportion") known during the Renaissance. It is very likely that Pacioli himself learned about Phi from the 5th century B.C. Greek sculpture and mathematician, whose biography is worth mentioning because his life seems typical of some government officials in the Philippines.
Phidias received a commission from the Athenian statesman Pericles to carve the monuments to adorn Athens and to serve as a general superintendent of public works. He used the Golden Ratio, or phi=1.61 in his design of the famous Parthenon and the friezes on Parthenon. The enemies of Pericles, however, accused Phidias of misappropriating the gold intended for the statues. He was also charged of sacrilege in sculpting himself and Pericles on the shield of the goddess Athena. He was thrown into prison and presumably died there. Here the parallel between him and our present Cabinet members ends because no Cabinet member accused of graft has ever been incarcerated and died in jail.
In any case, today it is already well known that phi appears in the proportion of human bodies, animals, plants, DNA’s, the solar system, art and architecture, music, population growth, the Bible and the stock market. Having already glimpsed through the presence of phi in human body and animal populations in our last column, let’s now have a look at phi’s relevance to the stock market. According to the information available from http://goldennumber.net , we have the following facts.
Human expectations occur in a ratio that approaches phi=1.618 meaning that changes in the prices of stocks largely reflect human opinions, valuations and expectations. Mathematical psychologist Vladimir Lefebvre showed that humans exhibit positive and negative evaluations of the opinions they hold in a ratio that approaches phi at 61.8% positive and 38.2% negative. Scientist Stephen Wolfram, who designed the software Mathematica on which I personally depend so much for very complicated symbolic mathematical calculations in my researches, claims "This seashell [referring the sea shell that is governed by phi in its structure] may hold the secret of stock market behavior, computers that think and the future of science."
But how did the Greeks obtain the value of the Golden Ratio, or phi? As promised in our last column, we shall derive it using only the quadratic equation. Consider the figure above illustrating a stick of length L+S.
It is to be divided into two pieces, a long one of length L and a short one of length S to strike a "perfect balance between long and the short." This can be done by making the proportion that the total length is to the long piece as the long piece is to the short piece. As an equation this comes out to be (L+S)/L = L/S.
When this equation is simplified it comes out to be L/S = 1 + S/L. Letting x = L/S = phi, the equation turns out to be x = 1 +1/x. Multiplying this last equation by x, yields the quadratic equation x^2 - x - 1 = 0. Using the quadratic formula to get the meaningful positive root of this last equation gives x = (1 + square root of 5)/2 = phi. Incidentally, being irrational, phi is a non-terminating and non-repeating number whose value calculated to 10 places is phi = 1.618033989… So there you have it!
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Richard Moody Jr., author of the NEXUS Magazine article "Albert Einstein Plagiarist of the Century," e-mailed me from New York to point out that the quotation attributed to Einstein, to wit, "The secret to creativity is knowing how to hide your sources," although floating in the Internet for sometime now, has not yet been definitely established to have really come from Einstein himself. Moody has a Master’s degree in Geology, is an author of three books on chess theory and is a contributor to the MENS Bulletin. If plans do not miscarry, we will be collaborating on a conference paper on Spinning Einstein and his conclusions on relativity theory.
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