If you missed last week’s post, I explained what the so-called golden ratio is and detailed the proven instances of its appearance in math and nature. In this week’s continuation, I’m going to explore the less clear-cut claims about the golden ratio’s appearance, and whether artists or designers should ever use it in their work.
It’s incredible how passionate people can become become about a number. For every compilation of examples of the golden ratio in art, there’s someone offering pages of evidence to the contrary. For every skeptic analyzing the golden ratio in the human face, there’s someone else employing ad hominem attacks in attempt to refute them. And for every historical anecdote about the ratio, there’s someone saying the anecdote was misattributed or mistaken.
The golden ratio, also known as Phi or Φ, is a proportion said by many to either have divine properties, be inherently beautiful to humans, or be the "most beautiful ratio". As I detailed in Part 1, the number, roughly equal to 1.618, does have some provable significance, including its many appearances in geometry and in the growth of some plants.
I believe it’s also safe to say that the golden ratio does have aesthetic merit. It wouldn’t be so famous for being "the most beautiful ratio" if it were ugly. But how beautiful is it, really? Is it somehow the cause of the widespread appeal of any famous artists? Do humans have an innate preference for it? And most importantly, should designers and artists be using it?
Like much of history, the golden ratio’s past involves a lot of “he-said she-said.” As a result, there are multiple cases where the golden ratio’s appearance in famous art is alleged secondhand, despite a lack of concrete evidence. There’s a remarkable number of “facts” about the golden ratio that, although widespread, are disputed purely because it’s difficult to access original writings about them.
One of these concerns the Parthenon, said by some to be constructed according to the golden ratio. Circulating around the internet are numerous images like the one below, claiming to “prove” the golden ratio’s existence in this famous structure. Another very common assertion is about Leonardo Da Vinci’s use of the golden ratio in his paintings. This is often backed up by the fact that he illustrated Pacioli’s book De Divinia Proporcione, which dealt with the golden ratio among other mathematical theories of aesthetics.
Unfortunately, we just don’t know. Ratios do exist in these famous artworks that resemble the golden ratio (to varying degrees of accuracy, clarity, or certainty), but the most scientific evidence offered is an image overlaid with a rectangle and a quote from someone else with a different image overlaid with a rectangle.
The ancient Egyptians, Greeks, and Romans all did take an arcane interest in Φ, although they referred to it as the “extreme and mean ratio.” Part of its appeal has been attributed to how easy it is to construct geometrically. But no one wrote down that the Parthenon was designed using the golden ratio. Da Vinci did not write down that he used the golden ratio in his artworks. Even if they did, I don’t doubt that the writings would be so lost in translation today that the debate would be no clearer for it.
The source arguably responsible for today's widespread fascination with the number (no, other than "the Da Vinci Code") is Adolf Zeising’s 1855 book by a name too long to write here. This work rekindled interest in the number that had died down around the rise of empiricism in the 17th century. Zeising's book, along with the aforementioned De Divinia Proporcione, are at the heart of readily-citable information about the golden ratio's historical significance because of how recent they are. The original texts, however, are difficult to find readily-accessible translations of. As a result, each is invoked in equal measure by both sides of the golden ratio debate.
In more recent times, however, along with several debunked golden ratio specters, some famous artists and designers have confirmed or advertised their use of the golden ratio. These include Salvador Dali and Le Corbusier.
The most famous golden ratio-centric work of surrealist painter Dali is “the Sacrament of the Last Supper.” It was deliberately created on a canvas of golden ratio proportions, and he arranged many of the compositional elements of the painting according to that same ratio. Using this particular mathematical constant fit in well with the artist’s passion for mysticism and also for science. He wrote of the piece,
“The first Holy Communion on Earth is conceived as a sacred rite of the greatest happiness for humanity. This rite is expressed with plastic means and not with literary ones. My ambition was to incorporate to Zurbarán’s mystical realism [to] the experimental creativeness of modern painting in my desire to make it classic.”
Le Corbusier, on the other hand, was a Swiss/French architect who in the mid-twentieth century developed The Modulor, intended to be a universal system of proportions. It’s basic “module” is called “the Modulor Man,” who is a six-foot-tall figure proportioned by the golden ratio at his navel. By employing the Modular in his work, Le Corbusier produced many buildings that contained the golden ratio. The system was never widely adopted, however, despite Le Corbusier’s desire to “reconcile maths, the human form, architecture and beauty into a single system.”
All of this creates an interesting dilemma. We know that some recent artists and designers have used the golden ratio (although often in pursuit of mysticism or order, rather than pure aesthetics). Why can't we assume that ancient or even renaissance-era artists did? The fact is, though, most of the golden ratio analysis we're capable of doing today is at best inconclusive, and at worst, entirely misleading.
Take Da Vinci's unfinished work of art, St. Jerome, for example. It's certainly been invoked as an example of his use of the golden ratio. The placement of the rectangle, though, is entirely subjective. Why does it slightly overlap the head and left cloth? Why are there gaps beside his right knee and below his foot? Why measure to include the draping of his clothing at all, rather than only his figure? What is the midline supposed to line up with—his finger? Even barring those complaints, why is his errant hand not included in the box? Paintings, by nature, have countless edges and corners and important points in them. For that reason, overlaying a rectangle is not proof that an artist used the golden ratio.
But to return to the question of using the golden ratio today... the most fascinating thing about the whole golden ratio phenomenon, in my opinion, is that many of the very sources that advocate the use of the golden ratio often deemphasize the need to accurately measure out the ratio. A common refrain in articles explaining “how to design using the golden ratio” is that the “rule of thirds” is a good way to approximate the golden ratio and achieve similar results. (The rule of thirds is a compositional trick that relies on a 1/3 ratio instead of a 1.618 ratio.).
The rule of thirds, although it’s a proportion not dissimilar to the golden ratio, is completely different from a theoretical perspective. While proponents of the golden ratio argue that its appeal is somehow inherent to the human psyche, the rule of thirds says something more like “arrangements look more natural when the focal point is at neither the center nor the edge of a space.” It’s a lot simpler and less mystical. And offering it as an alternative to the golden ratio calls in to question just how special the golden ratio is.
Although I've made a case against how "special" the golden ratio is often considered to be, I’m inclined to say that there is still a place for it in design—because it’s an attractive number, and because having a library of compositional tricks and rules is conducive to deliberate, intelligent design. What there’s no place for, though, is sensationalizing its importance. The cult of the golden ratio, although admirable for its idealism and its pursuit of harmony and order, ultimately relies in many cases on secondhand facts and unresearched claims.
Despite the interests and obsessions of certain artist, designers, and mathematicians throughout history, it’s unlikely that one number could be the magical solution to aesthetics or beauty. It's still one good-looking number, though, and an interesting one to boot. In the end, my biggest recommendation is, in the face of confusing and contradictory facts, to figure it out for yourself. Test out when the golden ratio helps your work and when it doesn't—and for the love of logarithmic spirals, could someone please do some more scientific studies on this?
I made a list, with summaries, of a whole bunch of science or psychology papers about the golden ratio. You can skim it here to see all the hard evidence—and don't worry, it's a short list.
If you’re looking to use the golden ratio in your designs but not looking to do any math yourself, try a golden ratio calculator here or here.
If you're feeling flush, try splurging on some golden mean calipers. The possibilities are truly endless.
For a laugh or two, see this Twitter parody account that overlays the golden spiral on pictures and memes from popular culture.
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