Then we follow the story of how the average gold geometry has become accepted in the formation of art, often with broader claims than average gold geometry "permeates all structures "in nature, particularly the human form
This is more than just idle philosophical speculation for us as artists, because, to draw accurately, we must always look for hidden proportions in the figure.
Art teachers have developed diagrams showing what appears to be average gold relations in the proportions of the face and the bones of the hand, and other measures of the figure. below the ratio of successive phalangeal bone figures seems to be the average gold.
these measures are somehow cooked in the human form as a kind of universal geometry, or are they convenient coincidences that inevitably appear in those are looking for them?
Counsel will point to the diagrams themselves as proof. Just look at the evidence. It is right in front of you.
The skeptic will argue that these measures are a form of pareidolia, a perceptual phenomenon where a random stimulus is given a special meaning, such as seeing faces in the clouds or hear hidden messages in music. To convince skeptics, it would demonstrate a physical mechanism, a logical question, by which these relations are manifested in humans. Such mechanisms have been proposed for the average properties of gold plants.
In the absence of such scientific evidence, this debate may never be resolved rationally. Logically speaking, no skeptic can prove that golden mean geometry is not operation, and no believer can win on the skeptic with more and more examples, no matter how compelling.
Pivot Turning to the second question for today, which is much more convenient:
are golden section diagrams of the figure, the most useful kind of structural understanding for us to use as artists? Or are we better rely on diagrams of Vitruvius (that is, diagrams based on integer division)?
This is a diagram of Vitruvius classic of the human head, divided into two halves and thirds, (drawing of the head and hands 
, by Andrew Loomis).
, by Andrew Loomis). 
My answer to the question, as with any argument over rival methods, is to both learn and use what works for you. But do not neglect the Vitruvian system. These integer fraction of systems have been used by artists for a long time which is what Leonardo professed to illustrate with his Vitruvian Man drawing, after all.
Vitruvius and systems were used in the 19th century Ecole des Beaux Arts, the Royal Academy and the Art Students League . Why throw these conventional methods for something Le Corbusier and the Bauhaus (second chart) promoted?
The measure of choice in the "divine proportion" analysis is the navel. This can have a cosmic significance, but it is not a very important point for the structural design of the figure. Vitruvius measures are easy to see, measure, reproduce, and subdivide the drawing. It is much easier to place a mark in the 2/3 position in the .6180339 position. When shooting a dynamic scene with a video camera, it is easier to place a figure on the third position in the average gold position.
Nobody claims that Vitruvius measures have mystical significance (except perhaps Leonardo). They are just there as a practical guide, to be replaced by another if it works better.
Regardless of what one prefers the system, it is good to keep in mind that real humans do not match any rule, thank you God. We are not Barbie or Ken and Venus and Apollo, and any measurement system is just a starting point for observation. Like many movements of anthropometry, claims of "divine proportions" in the human figures are idealistic at best, and at worst unrealistic. Even if you average a lot of data, the measurement on the navel of the earth is higher than in men phi and phi lower than in women
final note :. I 'm just trying to adopt a logical approach to this subject, trying to sort fact from disinformation. I'm not against the mystical approaches - far from it. And I finally pragmatic. Whatever works to improve your art is good. What I'm after is authorized, scientific survey of assertions that students are not allowed to question.
Tomorrow I want to address the last and perhaps greatest question: Is the golden mean rectangle somehow more attractive than other rectangles ?
GurneyJourney series: Demystifying the Golden Mean
Part 1: Debunking the claims of the Parthenon
Part 2: the average gold and Leonardo Part 3: How the gold took on average with artists
Part 4: the golden mean and the human body
Part 5: last question on the golden rectangle
also: Pareidolia and Apophenia
additional reading:
New York Times: "Control Proportion"
book: Drawing head and hands by Andrew Loomis book: the Golden Ratio: the story of PHI, the most amazing number of the world
by Mario Livio YouTube video :. "Nature by Numbers"
Measuring Finger slide from here
