Then we followed the history of how golden mean geometry became accepted into art training, often accompanied by broader claims that golden mean geometry "permeates all structures" in nature, especially the human form.
This is more than just idle philosophical speculation for us as artists, because in order to draw accurately, we must always be looking for hidden proportions in the figure.
Art teachers have developed diagrams showing what appear to be golden mean relationships in the proportions of the face and the bones of the hand, and in other measurements of the figure. Below, the ratio of successive phalangeal bones of the digits appears to match the golden mean.
Are these measurements somehow baked into the human form as a kind of universal geometry, or are they convenient coincidences that inevitably appear to those who are looking for them?
The advocate will point to the diagrams themselves as proof. Just look at the evidence. It's right in front of you.
The skeptic will argue that these measurements are a form of pareidolia, a phenomenon of perception where a random stimulus is given special meaning, such as seeing faces in clouds or hearing hidden messages in music. To convince the skeptic, one would need to demonstrate a physical mechanism, a logical cause, by which those relationships become manifest in humans. Such mechanisms have been proposed for golden mean properties of plants.
In the absence of such scientific evidence, this debate can never be settled rationally. Logically speaking, no skeptic can prove that golden mean geometry is not operating, and no believer can win over the skeptic with more and more examples, no matter how compelling.
Let's pivot to the second question for today, which is much more practical:
Are golden section diagrams of the figure the most useful kind of structural understanding for us to use as artists? Or are we better off relying on Vitruvian diagrams (that is, diagrams based on whole number divisions)?
Below is a classic Vitruvian diagram of the human head, broken down in halves and thirds, (from Drawing the Head and Hands, by Andrew Loomis).
My answer to the question, as it is with any argument about rival methods, is to learn them both and use what works for you. But don't overlook the Vitruvian system. These whole-number fraction systems have been used by artists for a long time—that's what Leonardo professed to be illustrating with his Vitruvian Man drawing, after all.
And Vitruvian systems were used in the 19th century Ecole des Beaux Arts, the Royal Academy, and the Art Students League. Why throw out those classic methods in favor of something Le Corbusier and the Bauhaus (second diagram) promoted?
The prime measurement in the "divine proportions" analysis is the navel. That may have cosmic significance, but it's not a very important structural point for figure drawing. Vitruvian measurements are easy to see, measure, replicate, and subdivide on the drawing. It's much easier to place a mark in the 2/3 position than in the .6180339 position. When you're filming a dynamic scene with a video camera, it's easier to place a figure on the 1/3 position than in the golden mean position.
No one is claiming that Vitruvian measurements have any mystical significance (except maybe Leonardo). They're just there as a convenient guide, to be replaced by another if it works better.
Regardless of what system one prefers, it's good to keep in mind that real humans don't fit any rule, thank goodness. We're not Barbie and Ken or Venus and Apollo, and any system of measurement is just a starting point for observation. Like many movements of anthropometry, claims of "divine proportions" in human figures are at best idealistic, and at worst unrealistic. Even if you average a lot of data, the measurement to the navel from the ground is higher than phi in men, and lower than phi in women.
Final note: I'm just trying to take a logical approach to this subject, to try and sort fact from misinformation. I'm not against mystical approaches--far from it. And I'm ultimately pragmatic. Whatever works to improve your art is good. What I'm going after are authoritative, scientific sounding assertions that students aren't allowed to question.
Tomorrow I would like to approach the last—and perhaps biggest—question: Is the golden mean rectangle somehow more attractive than other rectangles?
GurneyJourney series: Mythbusting the Golden Mean
Part 3: How the golden mean caught on with artists
Part 4: The golden mean and the human body
Part 5: Last question about the golden rectangle
Also: Pareidolia and Apophenia
Additional reading:Drawing the Head and Hands by Andrew Loomis
Book: The Golden Ratio: The Story of PHI, the World's Most Astonishing Numberby Mario Livio
YouTube video: "Nature by Numbers"
Finger measurement slide from here.