Nautilus shells are thought to demonstrate the golden rectangle at work in nature (Image via Wikimedia Commons)

Nautilus shells are thought to demonstrate the golden rectangle at work in nature (image via Wikimedia Commons)

Le Corbusier designed glimmering high-rises while Salvador Dali painted implausible landscapes, yet they had one thing in common: both embraced the golden ratio as gospel and used it in their work. But could it be possible that these two 20th century masters had fallen for nothing more than the art world equivalent of an old wive’s tale?

A recent article published in Fast Company claims that’s the case, presenting some convincing evidence from Stanford University mathematician Keith Devlin. But before we take a look, let’s back up to consider what the golden ratio is for those who might be new to the concept.

Merriam-Webster defines the golden ratio as “a proportion … in which the ratio of the whole to the larger part is the same as the ratio of the larger part to the smaller.” That means that if you unevenly split a line in two, the longer line divided by the shorter one equals the whole length divided by the longer one — mathematically expressed with the value of 1.6180. Translating that for the mathematically un-inclined, a rectangle that fits the golden ratio can be cut up into a square and a smaller rectangle with the exact same proportions as the bigger one.

Anyway, mathematicians and philosophers have long claimed this shape — known as the “golden rectangle” — occurs throughout nature in objects like sea shells and pine cones and appears the most harmonious to the human eye. It’s an appealing idea, one that makes beauty neatly definable.

But Devlin told Fast Company that in actuality, you can actually only find approximations of the golden ratio in the real world, because its unending decimal points (1.6180339887…) render it mathematically an irrational number. So there’s that.

The professor has also conducted numerous experiments in Stanford’s psychology department wherein he asks students to pick out which rectangle they like best out of a diverse group. He said the ones they select are always random and frequently change. If the golden rectangle were really the most pleasing, wouldn’t students choose it every time?

“We’re creatures who are genetically programmed to see patterns and to seek meaning,” Devlin told the magazine. “People think they see the golden ratio around them, in the natural world and the objects they love, but they can’t actually substantiate it.”

The article blames the propagation of the golden rectangle idea on an alleged 18th-century misreading of a 16th-century text. It claims that when Franciscan friar Luca Pacioil published his book De Divina Proportione (1509), he misleadingly named it after the Greek mathematician Euclid’s golden ratio even though the text instead embraced the Roman architect Vitruvius’s system of rational proportions. In 1799, mathematicians falsely associated Pacioli with the golden ratio, which helped propagate the rumor that Leonardo da Vinci — who illustrated the book — used the golden ratio to create his masterpieces.

Then came the German mathematician and psychologist Adolf Zeisig, who took things to a whole new level. He claimed to find evidence of the golden ratio everywhere from plant leaves to animal skeletons to the human body. He believed the ratio represented “beauty and completeness in the realms of both nature and art … which permeates, as a paramount spiritual ideal, all structures, forms and proportions, whether cosmic or individual, organic or inorganic, acoustic or optical.” Ever since then, the golden ratio as a principle of design has been cited everywhere from art history textbooks to advertisements for beauty masks.

Obviously, you can’t question such accepted wisdom without pushback. Angry Fast Company commenters have dubbed the article “silly” and “snarky,” and the website Golden Number — which claims its purpose is to “help you appreciate the incredible beauty and design in the world around you” —  has even published a full rebuttal. It points to how the Parthenon demonstrates the golden rectangle at work and cites other scientific studies that support the concept, including one published in 2009 that shows its usefulness in understanding facial attractiveness.

While the Fast Company piece might not be enough on its own to completely refute the time-honored design principle, it does poke some worrisome holes through it — not to mention expose its status as unquestionable dogma.

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Laura C. Mallonee

Laura C. Mallonee is a Brooklyn-based writer. She holds an M.A. in Cultural Reporting and Criticism from NYU and a B.F.A. in painting from Missouri State University. She enjoys exploring new cities and...

2 replies on “Does the Golden Ratio Not Measure Up?”

  1. “Hidden harmonies are more than obvious.”

    TED would demur on this FastCo polemic (and on WIRED et al’s recent articles too).

    But really, looking exclusively at only Spatial interpretations are so last century anyway.

    And does that also mean the entire repertoire of plant phyllotaxis is an illusion?
    Plants are telling us something, that we need to think harder about the Temporal, thermodynamics and morphogenesis, as Alan Turning did in his last research on the Fibonacci series, phyllotaxis and morphogenesis before he tragically died at an early age.

    We need to look at both the animate and inanimate, at the dynamical and space-time, not just the frozen and static. It seems the way nature works is to manifest the golden ratio not as a spatial fossil, rather an optimal temporal energy flow signature. An efficiency (& beauty) constant.

    All this current argument is only over the residue or sedimentary forms of these dynamical flows – so we are missing half the picture (as I’ve been saying since first publication in AD Magazine).

    What the sciences of complexity and dynamical systems have been sharing recently is that the golden ratio is one of several optimal, analogical geometric signatures of how nature evolves emergent complexity most easily – over time.

    It’s a dynamical behaviour, a verb not a noun.
    It’s not the phone number, but the action of dialing.

    Here’s how I Tweet it:

    #Asynsis #DaoOfDesign on #TED at #TEDxWanchai #HongKong.
    A New, Extremely Lean, Mean (#Design) #TheoryOfEverything;search%3ANigel%20Reading

    The very latest examples (including E8 & ER=EPR #Universality), are shared here (enjoy!):

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