Why the Golden Ratio matters

In defense of using visual harmonies in Design

“Those who believe the golden ratio is the hidden math behind beauty are falling for a 150-year-old scam.”

I came across this quote last week, during my post-lunch ritual of catching up with Internet goings-on. It comes from a piece on FastCo Design titled “The Golden Ratio: Design’s Biggest Myth,” authored by John Brownlee, and it’s been nagging at me ever since.

It is a bit of writing that is at best unnecessary and sensationalist; At worst, coming from a content platform that has rapidly risen to the forefront of design discourse, it is dangerous. That may sound like a severe over-reaction, but here’s my concern: As the design field expands, many design education programs have replaced fundamental tenets of visual communication — things like semiotics, gestalt theory of composition, typesetting — in favor of teaching software and topical survey-like classes. I worry that many inexperienced or aspiring designers are ill-equipped to parse intelligent design discourse from under-informed nonsense.

So while it’s certainly not necessary to defend the use of mathematical constants in design, and at the risk of giving an inane piece of writing more exposure than it deserves, I am compelled to put out a point of view on the piece on behalf of designers the article claims don’t exist — those who apply visual harmonies, especially the Golden Ratio, on a near-daily basis — in hopes that other designers can learn something about the importance of mathematics in visual design.

Why take this on? I’m a daily reader of Fast Company and FastCo Design. Full disclosure, I have been quoted in their publication as an authority on design-related topics and been named to their Most Creative People in Business list. Their hugely influential role in informing the broader public’s understanding of Design is no small part in my compulsion to pen this rant. As a designer and frequent reader I have expectations for design discourse that are loftier than click-baiting hot takes. Apparently so do others in the readership, based on activity in the article’s comment feed.

A flawed thesis

The point of the Mr. Brownlee’s article — that the Golden Ratio is “bullshit” — is tested immediately by his own lede paragraph. Acknowledging noted contributors to visual culture such as Le Corbusier and Salvador Dalí frequently incorporated the Golden Ratio into their work, then claiming those endorsements as irrelevant because “many designers don’t use it” is no small red flag to credibility. Subsequent quotes from subject matter experts smell of being selected to confirm bias, one of many errors in a garbage fire of sensationalist rhetoric.

You’ll have to forgive me, but on this topic I think I’ll side with Le Corbusier, a master who spent a large amount of his career exploring visual harmony through mathematics.

A more defensible thesis — the Golden Ratio has achieved mythical status among mostly-amateur designers due to the sharing of misleading images across the Internet — is alluded to but quickly abandoned. The golden ratio is not a silver bullet is trumped by the racier argument the golden ratio is bullshit and no real designer uses it behind evidence from the wispiest of straw men. A popularly re-blogged image of the Fibonacci sequence found in the design of the Apple logo (an image which has been widely debunked), as well as an exceptionally misleading editorial illustration of the Parthenon, are held up as evidence in support* — never mind the many real and overt examples that permeate our visual culture. One of the biggest yuks here is the abysmal fact-checking serving to perpetuate the very thing the article claims to refute.

*Having worked within journalism in my early career, I acknowledge that image selection may not have been the author’s choice. Still.

What exactly is the Golden Ratio?

A quick introduction: The Golden Ratio is a simple, symmetrical mathematical relationship built from consistently asymmetrical parts. For the algebra-inclined (sorry), that relationship is a : b = b : (a + b).

Extrapolated radially, this creates a never-ending logarithmic spiral, getting closer and closer (but never actually achieving) the Golden Ratio, also referred to as ϕ (Phi). For most practical purposes related to human perception, ϕ can be expressed numerically 1 : 1.618. It is intrinsically related to the Fibonacci sequence (egregiously not mentioned in Mr. Brownlee’s post) in which the next number in a given sequence is the sum of the previous two.

The mystique of the Golden Ratio is that this proportion and related numerical sequence is found frequently in nature, notably in growth patterns of plants and shells, bone structure of some mammals, and in reproduction patterns of insects. It’s everywhere. The visually-inclined — artists, architects and designers, historically keen observers and documentarians of both nature and the human condition and who we can thank for much of what we know about the world — have for ages incorporated this ratio into their work due to its intrinsically alluring balance between symmetry and asymmetry. Sometimes very intentionally, though often by compositional intuition developed from decades of mastering their craft.

It’s widespread use has been greatly under-appreciated in the FastCo Design article.

The limits of human perception

“When you do the math, the golden ratio doesn’t come out to 1.6180. It comes out to 1.6180339887… And the decimal points go on forever.”

This is one proposed take against using ϕ in design: it is an irrational number and can not be accurately recreated in the physical world with any degree of mathematical exactness. While technically true, this arguement callously discounts the limitations of human visual perception, for which the Golden Ratio need only be followed to a couple of decimals, depending on medium and scale of application. Arguing that the Golden Ratio and other naturally-occurring but irrational ratios — such as Pi — are irrelevant because of their endless string of decimals makes no sense, as the human eye couldn’t perceive the difference made by those decimals anyway. Even the article’s Stanford professor must admit that rounding for practicality is common and necessary in most human mathematical endeavors.

Other arguments proposed invoke studies held to determine if a preferred ratio exists. One referenced study from the Haas School of Business was repurposed to disprove preference for the Golden Ratio. A little digging reveals an extremely unreliable testing methodology, asking participants to rate rectangular cards of various ratios by which they were most likely to choose.

Preference testing a single stimulus is generally a futile exercise, as an individual is rarely aware of the myriad of factors affecting their decision making process. Asking someone to prefer one rectangle over another is a highly unnatural question and introduces all manner of response biases. Unfortunately, it’s a lazy, C-minus piece of research based on poor hypotheses and a too-small sample size to be quoted as authority in a piece of journalism. Reducing human emotional response to simple data points is a deeply flawed practice, but unfortunately still common behavior among MBAs attempting to justify financial investment in design.

But even within that bullshit study — and I feel justified using that word in this instance — actually comes evidence in favor of the Golden Ratio as a visual constant. The study notes that ratios of the preferred rectangles fall between in the range of 1.414 through 1.7342. This is mentioned as a fault in the article, and yet the mean of that range (considering the wisdom of the crowd) and you get 1.573 — damn-fucking-close to the Golden Ratio, especially given limitations of human perception. Expand the scope of that study from a mere 122 participants (yikes) to 10,000 and I bet you end up bang-on.

Firstness and the inherent value of design

A principle question from the Haas study was “Do customers prefer a single ratio?” The answer, most designers would tell you, is that customers don’t even consider such things. The issue here is conflating prolonged analysis with subconscious preference — few who aren’t involved in the creation of visual work give a logo, or a sculpture, or a building longer than a quarter-second glance. But, for many designers, their most important work happens in that quarter-second.

In semiotics, this is the moment of “firstness,” or the instant and subconscious reaction to a particular designed thing. Firstness is elemental, what is immediately felt and internalized before any sort of deeper analysis can set in — something akin to visual pheromones. It’s why we are attracted to people with symmetrical faces, even though we don’t actively notice the underlying geometry. To paraphrase Le Corbusier, humans find comfort in math, even if they don’t know it.

When you’re dealing with designed objects reproduced at scale, the intentional use of inherently pleasing visual harmonies like the Golden Ratio have massive impact on perception at the firstness level. This is one of the primary drivers behind the commercial benefit of “design.” It’s also why good design is tremendously effective but hard to quantify — the inherent value is created through methods that are notoriously difficult to measure.

Using visual harmonies in contemporary design

Among those quoted in the FastCo Design article is architect Richard Meier, who admits indifference to the Golden Ratio in his work (all due respect intended — I stare longingly at Mr. Meier’s West Village towers from my apartment window as I type this).

Contemporary architecture is however a tenuous analog. His point of view makes sense—Mr. Meier alludes to the fact that urban architects deal with a massively more complex problem set than that of painters, sculptures, industrial or graphic designers, starting with how a building dialogues with its immediate surroundings, neighborhood history, and how inhabitants exist within. In dense cities, the limitations of human size and truncated sightlines mean precious few buildings can be seen, let alone appreciated, by the purity of their form. Buildings are experienced more as a series of vignettes, which greatly reduces the effectiveness of visual harmonies like ϕ.

When, then, is application of the Golden Ratio appropriate?

Phi, and other visual harmonies, are tools to inform many aspects of contemporary design — underlying grid, composition, hierarchy, rhythm of form to counter-form, etc. The common theme, of course, is that these are things a designer never expects any reasonable person to notice at all. The Golden Ratio is intended to be invisible, a compositional organizing principle that is felt rather than understood.

To use an analog: If one is appreciating a wine glass instead of the wine it contains, then the designer of the glass has essentially failed at her job. This does not mean the myriad interpretations of the wine glass as design object are without merit: It is the mandate of the designer to establish beauty and harmony where before there was only function, even when it goes mostly unnoticed.

In this vein, it is far more common for designers who create mass-produced objects of permanence — think furniture, books or identity design — to be more considerate of ratios in their work. A lot of this has to do with wanting quality and harmony to be an inherent part of an object’s firstness. But it also has to do with the magnification of error through scale — the bigger the reach of a designed object, the more its creators should be obsessing such minute details. In my own work, which frequently involves the creation of brand identities which can have millions or even billions of impressions over their lifetime, careful consideration of visual harmony is paramount.

One source quoted in the article who frequently works at this mass production scale — industrial designer Yves Behar — unsurprisingly has the simplest, and in my opinion the most correct, take: ϕ is a guide, not a hard-and-fast rule.

The Golden Ratio just is one of many harmonies used by makers of visual work, likely the second most referenced after the Rule of Thirds. But there are many others — notably the square root of 2 (roughly 1.412, another impossible ratio) which guides the proportions of ISO A series paper sizes (the Metric system of paper, for us Americans). Also common is the Chromatic scale, which has roots in musical time signatures but in visual art describes many rational mathematic proportions.

Among these the Golden Ratio is often common in design because of its relation to ergonomics. The ratio is found throughout the human body — approximately of course: finger and arm bones, head-to-led-to-torso length, etc. Le Corbusier’s iconic LC4 chaise lounge is designed on the Vitruvian ideal of body proportion, which relates directly to Phi. In graphic design, as much early printing and typesetting was for objects interacted with at human scale (e.g. books and posters), it was natural to construct objects, grids and compositions using the golden section. These principles are still widely in use today.

Design is an often misunderstood profession because it frequently is tasked with operating at a subconscious level. Design objects are generally not considered by those they are intended to effect. Designers consider innumerable amounts of stimuli — color, form, composition, tactility, sound, smell — each of them with their own quirks and rationales, and when designing a given solution the interplay between these various components is often where the most effective outcomes emerge. The problem is when a single aspect of a solution is singled out for discussion outside of the context of rest of the design.

The FastCo Design article is correct in that Phi is not a “silver bullet” which by itself makes any design immediately more desirable than another. A compositional ratio featuring one-point-six-one-eight is rarely a concept, nor does it take into account the myriad of other visual and empathetic inputs that go into the creation of an effective piece of design.

But it is also not a scam. Nor an “urban legend, a myth, a design unicorn.”

Rather, the Golden Ratio is a powerful mathematical constant woven into the very fabric of biology. It is the unique visual tension between comforting symmetry and compelling asymmetry, and its thoughtful application can bring beauty and harmony and intrigue to all manner of designed things.

The Golden Ratio is all around — even when not noticed at all.

Darrin Crescenzi is a designer based in New York City. He is Design Director of Innovation at Interbrand New York, previously a designer with branding consultancy Prophet and the Global Brand Design team at Nike. He is an ADC Young Gun, and one of Fast Company magazine’s 100 Most Creative People in Business.


Header image via my-pink-code.tumblr.com