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).
, 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:
Book: Drawing the Head and Hands by Andrew LoomisBook: The Golden Ratio: The Story of PHI, the World's Most Astonishing Number
by Mario LivioYouTube video: "Nature by Numbers"
Finger measurement slide from here.
12 comments:
I'm more of a skeptic and it's always bothered me how often golden ratio is taught uncritically by teachers who often don't really use it. Thanks for doing this series, you're certainly a good candidate for it.
I'm loving this series. You make a good point here: If the Vitruvian system has given us some of the greatest art ever, but the Golden Section system has mainly given us strange architecture and uncomfortable furniture, it's a no-brainer which system the contemporary realist artist ought to prefer. Thanks!
Hi James. A bit off topic, but I wanted to mention your exhibition at the Lyman Allyn Art Museum. I'm a student at Concept Design Academy in Pasadena and I visited New London to see the exhibit on Tuesday. I learnt so much from seeing your beautiful paintings in person and enjoyed the time I spent in the exhibit. It's so big! I hope you'll have many more exhibits in future so as many people as possible have a chance to have a similar experience.
Daniel, glad you enjoyed the Lyman Allyn show. It will be up through February 2. After that there will be another Dinotopia exhibition from February 20-March 13 in Manchester, New Hampshire. This exhibit has completely different paintings. http://www.nhia.edu/dinotopia-the-fantastical-art-of-james-gurney/
Thanks, Edward and Craig!
Funny you should mention the ASL, I was just watching Robert Hale's videotaped lectures and he mentioned the 'five eye' measurement and how that can be used to measure other parts of the body - for example the humerus is two five eye lengths, the scapula is one, etc.
I also think we lose something when we rely on numeric measurement -which has become a mainstay in the digital age, vs. proportional measurement, which, quincidently, is making something of a 'comeback' because of responsive web design.
I'm loving this series, James. Thanks so much. I just enrolled in a refresher drawing class and the first day the teacher demonstrated the Vitruvian meansurement for the head as a 'starting point' for portrait drawing. He emphasized that of course no one matches these measurement exactly, but that if you use them as a starting point and then, through observation, modify them to match your model it's hard to go very wrong.
He didn't use the term Vitruvian. He's a down home kind of guy who uses terms like black and white and gray instead of talking about values, but he gets his point across very well and he demonstrated these measurements in a way that everyone in the class, including beginners, was able to make a very credible drawing from.
Awesome stuff Tim! It's been a while.. a couple years since I've seen your stuff.
TIM! Found you! Your stuff is lookin' siiiiiiiiiiick
Paintings
There's a reason that the Golden Mean is also called the "Divine Proportion." The fact is that there actually is a very logical cause as to why this proportion is played out in nature so universally—it's because the Creator made it that way. It can easily be argued that the universe intrinsically possess a single, aesthetically pleasing proportion if it was created by an intelligent being who values aesthetics and order. However, if nature is simply the product of random, unguided, and ultimately chaotic forces, then of course one will never find an explanation that is "scientifically" satisfactory. The reason you will never win over the skeptic is because the skeptic refuses to entertain the notion of God.
Hi, Jonathan, I didn't bring up religious implications, but since you did, may I respectfully offer some thoughts for your consideration? I don't know if you're speaking of the Creator from a Jewish, Christian, or Muslim perspective, but to my knowledge, neither the Hebrew Bible, the New Testament, nor the Quran make reference to the Golden Mean—it was the Greeks who discovered it, and they didn't regard it as divine, either, just an interesting math principle. The main proponents of the golden mean as the creative force of the universe were atheists in the 19th and 20th century. The mainline religions don't hold phi as a tenet of faith, so whether you find it interesting and useful or whether you are skeptical of it doesn't have any bearing on your core religious beliefs. Worshipping phi as "Divine," however, could be seen by some religions as a form of idolatry.
Thanks, James. I'm writing from a Christian perspective, not that it makes a difference here—the three monotheistic religions hold essentially the same beliefs about creation. The golden mean isn't mentioned in the Bible, no. But it doesn't need to be. And I'm certainly not basing my belief in God on mathematical observations of the universe. I'm simply saying that these observations fit very logically with the assumption that the universe is created.
I think the term "divine proportion" does not mean that the proportion "is" god, but that it is "of" God. In other words, if a creator exists, phi is his signature. If there was no creator, then we have a very hard time explaining this "aesthetic" phenomenon.
Thanks for explaining your thoughts, Jonathan. There's definitely room for a lot of points of view on this one!
Hi James,
Sorry to revive a really old thread (not even sure if you'll pick this up);
I'm a skeptic myself, but to say the Greeks didn't think that the golden ratio was divine is incorrect: the Greeks believed that mathematics *were* divine. The laws and principles that ordered and structured nature were seen as divine. Philosophers like Plato and Aristotle may have criticized simplistic, non-philosophical religious belief in dieties, but ultimately theorised their own gods and metaphysical agents like the Demiurge and the 'Unmoved Mover'. This was unavoidable because the highest power in the universe and its organising principle was assumed to be the power of thought, intelligence, consciousness, etc. which imposed structure upon the chaos of matter.
Scientific/philosophical and religious/mystical views of nature were joined at the hip for centuries and divorced only very late with the development of the secular scientific world view.
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