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'Da Vinci's' Golden Flaw
Use of math ratio doesn't add up, experts say

Dan Brown's blockbuster book, ''The Da Vinci Code,'' already has upset the Catholic church and confounded medieval historians. Now, you can add mathematicians to the list.

As the movie version of the book settles into local theaters for what appears to be an extended stay, Brown's math scholarship is quietly drawing criticisms from math experts. At the center of the mathematicians' ire is Brown's use of an ancient mathematical principle, the ''Golden Ratio,'' also known as ''The Golden Number,'' ''The Divine Proportion.'' It additionally is known as phi, the 21st letter from the Greek alphabet.

By suggesting Da Vinci was influenced by the Golden Ratio, Brown establishes the idea that his paintings had some hidden meaning. But, according to mathematicians, there's no proof  DaVinci, nor any of the artists, musicians or architects whose works are often cited as examples of the Golden Ratio in action, were really influenced by the mathematical notion or used it as a basis for their work.

From a mathematical standpoint, the connections between the Golden Ratio and the Parthenon seem most ridiculous, says Ursinus College mathematics professor Gordon Williams. To prove their point, Golden Ratio proponents draw a Golden Rectangle — where the sides of a rectangle are in Golden Ratio to each other — around the temple. But the rectangle is drawn around the entire building, to include the Parthenon's now-crumbled crown, or apex, but not including all of the building's steps or pedestals. The empty space inside the rectangle, to the left and right of the crumbling remains of the Parthenon's sloping apex, bring into question the exact role the Golden Ratio might have played in the Parthenon's design, Williams says.
Morning Call (Allentown Pa.) - May 22, 2006


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A Fibonacci Fracas?
Category: FIBONACCI
By: Pete Kendall, June 13, 2006
The Fibonacci sequence provides the mathematical basis of the Wave Principle. ...Logos, a Greek word, was defined variously by Heraclitus and subsequent pagan, Jewish and Christian philosophers as meaning the rational order of the universe, the universal structural force governing and permeating the world. Consider when reading such grand yet vague descriptions that these people could not clearly see what they sensed. They did not have graphs and the Wave Principle to make nature’s growth pattern manifest and were doing the best they could to describe an organizational principle that they discerned as shaping the natural world.
Elliott Wave Principle

There are several interesting elements to this article. One big one is the agitation that suddenly surrounds discussions of the Fibonacci sequence and the Golden Mean, the ratio formed by dividing a Fibonacci number by the next highest number in the sequence.  Here at Elliott Wave International, we’ve been talking about Fibonacci and its place in the natural and classical worlds since the firm was founded in 1978. In all that time, this is the first we’ve heard anyone contest the notion that the presence of the Golden Mean, or phi, in the pyramids, the Parthenon and the Mona Lisa was due to anything other than the design of their creators. Back in December 1975, when a long bull market was just getting underway, Smithsonian Magazine ran an article stating that the “mathematical basis for the Parthenon” was the Golden Mean and added that “the continual occurrence of Fibonacci numbers and the golden spiral in nature explains precisely why the proportion of .618034 to 1 is so pleasing in art.” The quote has been included in the original and subsequent volumes of the Elliott Wave Principle (1978) but this is the first disputations we’ve heard. It just goes to show, in a big bear market, people will argue about anything and everythnig, even a classic mathematical representation of universal harmony.

da vinci's v-manThe idea that the architect of the Parthenon and Da Vinci were unaware of  the golden ratio is a little hard to fathom because the ratios are present in their works and those works have survived for hundreds of years, undoubtedly because of the presence of  the golden mean. In the Uffizi Gallary in Florence, you will now find an exhibit in which this famous drawing, Da Vinci’s Vitruvian Man, is projected and measured in various ways to show the significance of phi in the human form. 

But various sources on the web say Leonardo never explicitly demonstated a knowledge of Fibonacci. He was, however, clearly familiar with the ancient Roman architect Vitruvius and his ten-volume treatise De Architectura: The Planning of Temples, which was espoused the incorporation of the human form in the construction of religious buildings. If various sources on the web can be trusted, there are no direct references to Fibonacci in any of Vitruvius’ or Da Vinci’s works. “Nothing definitively suggests that Leonardo was aware of phi per se, but he certainly knew about divine proportion and the beautifully proportioned human figure.” But this is actually another compelling parallel because it means that Da Vinci, like Elliott, didn’t simply squeeze a mathematic formula into his work. He observed its presence in nature and applied it. Elliott didn’t know what Fibonacci and the golden ratio were either; at least not until after he had developed the key structural elements of the Wave Principle.

By alluding to DaVinci’s understanding of the “human” but not necessarily Fibonacci form in his work, the story at left hints at the other pioneering aspect of the Wave Principle, the idea of fractality. With his Vitruvian Man, Leonardo demonstrated the presence of phi in the individual human. Elliott discovered the presence of phi in collective human activities. This is covered by Prechter and Frost in Elliott Wave Principle in which they ask whether it is “possible, even reasonable, that [human] progress has the spiraling form of phi, and that this form is discernible in the movement of the valuation of [man’s] productive capacity, i.e., the stock market?” For the full quote, see Additional References below.

Another pleasant surprise is that the author of the article, Tim Blangger, demonstrates a real understanding of his subject matter. To read the whole article click here. In the past, the media’s Fibonacci coverage seemed more awkward, like it was being reported rather than understood. This may be one more sign that socionomics is starting to capture the imagination of writers and social observers.  Those not familiar with Fibonacci can learn all about it Chapter 8 of EWI’s home tutorial. It’s free to Club EWI members.

 

Additional References

Elliott Wave Principle
If these ancient philosophers were right that a universal structural force governs and permeates the world, should it not govern and permeate the world of man? If forms throughout the universe, including man’s body, brain and DNA, reflect the form of phi, might man’s activities reflect it as well? If phi is the growth-force in the universe, might it be the impulse behind the progress in man’s productive capacity? If phi is a symbol of the creative function, might it govern the creative activity of man? If man’s progress is based upon production and reproduction “in an endless series,” is it not possible, even reasonable, that such progress has the spiraling form of phi, and that this form is discernible in the movement of the valuation of his productive capacity, i.e., the stock market? Intelligent Egyptians apparently learned that there are hidden truths of order and growth in the universe behind the apparent randomness. Modern “chaos theory” has rediscovered this idea in the 1980s. Similarly, the stock market, in our opinion, can be understood properly only if it is taken for what it is rather than for what it crudely appears to be upon cursory consideration. The stock market is not a random, formless mess reacting to current news events but a remarkably precise recording of the formal structure of the progress of man.

 

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ARTICLE COMMENTS
In a nut-shell, it all speaks of "DESIGN" to me.
Posted by: Wayne Peckett
June 13, 2006 11:26 AM

Love your webpage. A good complement to EWI.
Posted by: ron porter
June 13, 2006 11:26 AM



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