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“The golden ratio is the key”*…

… in any case, to good design. So, how did it come into currency? Western tradition tends to credit the Greeks and Euclid (via Fibonacci), while acknowledging that they may have been inspired by the Egyptians. But recent research has surfaced a a more tantalizing prospect:

Design remains a largely white profession, with Black people still vastly underrepresented – making up just 3% of the design industry, according to a 2019 survey

Part of the lack of representation might have had to do with the fact that prevailing tenets of design seemed to hew closely to Western traditions, with purported origins in Ancient Greece and the schools out of Germany, Russia and the Netherlands deemed paragons of the field. A “Black aesthetic” has seemed to be altogether absent.

But what if a uniquely African aesthetic has been deeply embedded in Western design all along? 

Through my research collaboration with design scholar Ron Eglash, author of “African Fractals,” I discovered that the design style that undergirds much of the graphic design profession today – the Swiss design tradition that uses the golden ratio – may have roots in African culture

The golden ratio refers to the mathematical expression of “1: phi,” where phi is an irrational number, roughly 1.618. 

Visually, this ratio can be represented as the “golden rectangle,” with the ratio of side “a” to side “b” the same as the ratio of the sides “a”-plus-“b” to “a.” 

The golden rectangle. If you divide ‘a’ by ‘b’ and ‘a’-plus-‘b’ by ‘a,’ you get phi, which is roughly 1.618

Create a square on one side of the golden rectangle, and the remaining space will form another golden rectangle. Repeat that process in each new golden rectangle, subdividing in the same direction, and you’ll get a golden spiral [the image at the top of this post], arguably the more popular and recognizable representation of the golden ratio.

This ratio is called “golden” or “divine” because it’s visually pleasing, and some scholars argue that the human eye can more readily interpret images that incorporate it.

For these reasons, you’ll see the golden ratio, rectangle and spiral incorporated into the design of public spaces and emulated in the artwork in museum halls and hanging on gallery walls. It’s also reflected in naturearchitecture, and design – and it forms a key component of modern Swiss design.

The Swiss design style emerged in the 20th century from an amalgamation of Russian, Dutch and German aesthetics. It’s been called one of the most important movements in the history of graphic design and provided the foundation for the rise of modernist graphic design in North America.

The Helvetica font, which originated in Switzerland, and Swiss graphic compositions – from ads to book covers, web pages and posters – are often organized according to the golden rectangle. Swiss architect Le Corbusier famously centered his design philosophy on the golden ratio, which he described as “[resounding] in man by an organic inevitability.”

An ad for Swiss Air by graphic designer Josef Müller-Brockmann incorporates the golden ratio. Grafic Notes

Graphic design scholars – represented particularly by Greek architecture scholar Marcus Vitruvius Pollo – have tended to credit early Greek culture for incorporating the golden rectangle into design. They’ll point to the Parthenon as a notable example of a building that implemented the ratio in its construction.

But empirical measurements don’t support the Parthenon’s purported golden proportions, since its actual ratio is 4:9 – two whole numbers. As I’ve pointed out, the Greeks, notably the mathematician Euclid, were aware of the golden ratio, but it was mentioned only in the context of the relationship between two lines or figures. No Greek sources use the phrase “golden rectangle” or suggest its use in design.

In fact, ancient Greek writings on architecture almost always stress the importance of whole number ratios, not the golden ratio. To the Greeks, whole number ratios represented Platonic concepts of perfection, so it’s far more likely that the Parthenon would have been built in accordance with these ideals.

If not from the ancient Greeks, where, then, did the golden rectangle originate? 

In Africa, design practices tend to focus on bottom-up growth and organic, fractal forms. They are created in a sort of feedback loop, what computer scientists call “recursion.” You start with a basic shape and then divide it into smaller versions of itself, so that the subdivisions are embedded in the original shape. What emerges is called a “self-similar” pattern, because the whole can be found in the parts… 

Robert Bringhurst, author of the canonical work “The Elements of Typographic Style,” subtly hints at the golden ratio’s African origins:

“If we look for a numerical approximation to this ratio, 1: phi, we will find it in something called the Fibonacci series, named for the thirteenth-century mathematician Leonardo Fibonacci. Though he died two centuries before Gutenberg, Fibonacci is important in the history of European typography as well as mathematics. He was born in Pisa but studied in North Africa.”

These scaling patterns can be seen in ancient Egyptian design, and archaeological evidence shows that African cultural influences traveled down the Nile river. For instance, Egyptologist Alexander Badaway found the Fibonacci Series’ use in the layout of the Temple of Karnak. It is arranged in the same way African villages grow: starting with a sacred altar or “seed shape” before accumulating larger spaces that spiral outward.

Given that Fibonacci specifically traveled to North Africa to learn about mathematics, it is not unreasonable to speculate that Fibonacci brought the sequence from North Africa. Its first appearance in Europe is not in ancient Greece, but in “Liber Abaci,” Fibonacci’s book of math published in Italy in 1202. 

Why does all of this matter?

Well, in many ways, it doesn’t. We care about “who was first” only because we live in a system obsessed with proclaiming some people winners – the intellectual property owners that history should remember. That same system declares some people losers, removed from history and, subsequently, their lands, undeserving of any due reparations. 

Yet as many strive to live in a just, equitable and peaceful world, it is important to restore a more multicultural sense of intellectual history, particularly within graphic design’s canon. And once Black graphic design students see the influences of their predecessors, perhaps they will be inspired and motivated anew to recover that history – and continue to build upon its legacy.

The longer-than-we’ve-acknowledged history of the Golden Ratio in design; Audrey Bennett (@audreygbennett) unpacks “The African roots of Swiss design.”

For more on Fibonacci‘s acquisitive habits, see this earlier post.

* Sir Edward Victor Appleton, Nobel Laureate in physics (1947)


As we ruminate on relationships, we might send careful-calculated birthday greetings to Mary Jackson; she was born on this date in 1921. A mathematician and aerospace engineer, she worked at Langley Research Center in Hampton, Virginia (part of the National Advisory Committee for Aeronautics [NACA], which in 1958 was succeeded by the National Aeronautics and Space Administration [NASA]) for most of her career. She began as a “computer” at the segregated West Area Computing division in 1951; in 1958, she became NASA’s first black female engineer.

Jackson’s story features in the 2016 non-fiction book Hidden Figures: The American Dream and the Untold Story of the Black Women Who Helped Win the Space Race. She is one of the three protagonists in Hidden Figures, the film adaptation released the same year. In 2019, she was posthumously awarded the Congressional Gold Medal; in 2020 the Washington, D.C. headquarters of NASA was renamed the Mary W. Jackson NASA Headquarters.


“What strip mining is to nature, the art market has become to culture”*…

Nyan Cat meme, sold for $590,000 as an NFT (non-fungible token)

Before Christmas, the only uncertain-times-era art world innovations I could think of were online art fairs and anonymous Instagram callout accounts. Now more innovation has arrived, and it’s come from outside, from the spheres of online culture and cryptocurrency speculation. Crypto has its origins in a mistrust of authority in various forms, from government-backed fiat, to the banking system, to the financial industry. Now it’s also challenging art world elites…

Cryptocurrency’s exploding again. NFTs (non-fungible tokens) in particular. The Nyan Cat meme goes for $590,000. The “ape in a fedora” CryptoPunk goes for $1.54 million. An animated gif of Trump’s bloated, naked corpse by someone called “Beeple” goes for $6.6 million, setting a new record for any Millennial artist, dead or alive. Christie’s launches a two-week sale of one of his works. It closes tomorrow and has already broken the record again. Current bid: $9,750,000…

The old gatekeepers have been losing their power for a while now. In his New York Times profile of KAWS (Brian Donnelly), who’s just opened a major retrospective at the Brooklyn Museum, Michael H. Miller writes, “One art reporter told me … that certain directors at Gagosian, the largest and most profitable gallery in the world, would automatically move anyone known to own a KAWS down on their waiting list to buy something.” Nevertheless KAWS is unstoppable. He has his career-defining homecoming museum show, his Peter Schjeldahl writeup, his many pages of coverage, his giant sculptures looming over Manhattan’s Park Avenue and Brooklyn’s Greenpoint waterfront, and, a couple years back, in 2019, he shocked the art establishment when his painting The Kaws Album (2005), a remake of The Simpsons’ remake of the Beatles’ Sgt. Pepper’s Lonely Hearts Club Band cover, sold at Sotheby’s Hong Kong for $14.8 million. Images and sculptures are accruing value in new ways: KAWS came up making street art and toy collectibles, and Beeple (Mike Winkelmann) made his name through Instagram and concert visuals. They symbolise the return of populism to the arts. I recently wrote for the Spectator about the trend of bad figurative painting that occupies the bardo between content and art: paintings that are easy to enjoy, and also to post. With NFTs, we’ve made another leap from art that’s easy to post, to art that simply is the post.

The old ways of valuing an object at auction (backdoor dealings, price fixing, and clandestine, corrupt practices) are coming up against the new ways (wild speculative mania and hyperstition) and falling short, for now. Beeple and KAWS, who have dominated the year’s artistic discourse, are outsiders that made it to the top. But it’s a very boring sort of outsider art, made by nerds for other nerds…

So much of today’s culture is a poor-quality remake of something better and more compelling. KAWS bootlegs pop-cultural staples like Mickey Mouse, the Simpsons, Peanuts, and SpongeBob in his own depressive comic style, while Beeple takes Mickey, again, Pokémon and Shrek, plus politicians like Joe Biden, Hillary Clinton and Kim Jong-un, and composites them into dystopian CGI montages. There are two paths for the golden-age American cartoon star: to be withdrawn, like the lascivious skunk Pepé le Pew, or, worse, to be reimagined as bad art, as childish and nostalgic art for those that don’t like ideas, or beauty…

There’s just too much of everything. There are too many different Oreos. 65 flavours in 8 years is too many. Too many Hot Chicken Wing Oreos, Waffle & Syrup Oreos, Jelly Donut Oreos, Supreme Oreos. There’s too much content that appears different but is the same. Too many identities are available to us. Too many manias. Too many hysterias. Examine nearly any aspect of society and you can see it’s gone too far. The reason so many flavours of Oreos are invented, according to the cookie’s brand director, is that this overabundance of choice reminds us of and drives us back to the original. It reminds us of how much we like the old Oreo, the Platonic ideal of the Oreos of childhood, the Proustian Oreo with the glass of cold milk. When there’s too much of everything however, at some point the original is lost, the memory is lost, and all that remains are faded, flat, hollowed-out derivatives…

The most popular series of NFT collectibles are algorithmically generated. And what they reveal, compared to the rest of culture, is a broader and more prevalent trend of art and entertainment that has the uncanny feeling of having been made by algorithm, even though it wasn’t. A painter and performance artist once told me, in the brutalist basement of the old Met Breuer, that Future had destroyed the future. Trap music has taken over the world, and it all sounds more or less the same now. It might be amazing, but it sounds the same. It’s supposed to sound the same. That’s the idea, what makes it so powerful. A talented producer can make a song in ten minutes on a live stream. A talented producer can make a song in less time than it takes to listen to. It’s never been quicker to write a song than now. Songs keep getting shorter and shorter. Records keep getting shorter and shorter. It’s a numbers game. I can write these columns pretty quickly now. This is an age of great speed and competition. We’re all looking for more popularity, new ways to find an edge; and yet, all this competition only seems to lead to blandness and mediocrity, rather than breakthroughs. Nor does it lead to collapse; even accelerationism doesn’t work. We want too much content, too fast, and it just leads to this endless algorithmic churning, this paint-by-numbers effect. You see it in art. In Netflix documentaries. Spotify playlists. Op-ed pages. The news. The latest manufactured outrage. Well-reviewed first-person novels about nothing. All so dreadfully banal and repetitive. This is what results when everything is forged in economies of dollars, of ether, of attention. Most culture now has the feeling of having been made by algorithm; and the reason for this, is that humans have begun to act like algorithms…

What non-fungible (which is to say, unique) tokens show us, is the absolute fungibility of culture today: its hazy, interchangeable meaninglessness. How it all belongs on a blockchain. How it all belongs on an infinite self-generating playlist ouroboros. It all belongs on a streaming service that slowly steals the hours and the heartbeats from inside you. When you look at the Discover Page Hotties, you look back into your own soul through a clouded mirror. “Online,” a mysterious anonymous cipher writes to you, “so much is dependent on an algorithmic matrix of mined data that the user’s identity is distilled so accurately that you can’t breach the identity that’s fed back to you via the screen. So no chance encounters, just a recurrent overlap of what you already are.” If life was once about chasing after a dream, it’s now about running away from the comfortable, hypnagogic lifestyles prescribed to you by the culture we create together, reflexively and imitatively. You’re living inside other people’s dreams; and these are not good dreams. So much of modern life is algorithmically scripted so as to exclude surprise or chance, and you must try to break free of this script every day. Rejecting all this post-death culture is a good place to begin…

The art world, disrupted by crypto: Dean Kissick (@deankissick) on why that’s a sad thing: “The Downward Spiral: Popular Things.”

See also “NFTs Weren’t Supposed to End Like This,” by Anil Dash, the co-creator of the NFT; further to which, this thread from Jonathan Zittrain.

And finally (as a cap on what’s turned out to be a trio of posts about scarcity, post-scarcity, and what matters in our economy; earlier here and here), “Red Bull, Elon Musk, and Matt Gaetz“… “post-scarcity is just another way of saying decadence.”

* Robert Hughes, writing presciently in 1989


As we appraise art, we might spare a thought for an artist who, roughly a century ago, played an outsized role in revolutionizing the art world of his time, Pablo Picasso; he died on this date in 1973. Picasso is universally regarded as one of the most influential artists of the 20th century; he is known for co-founding the Cubist movement, for the invention of constructed sculpture, for the co-invention of collage, and for the wide variety of styles that he helped develop and explore.

Picasso in 1908


“Society gives legitimacy and society can take it away”*…

Yesterday’s post featured an argument that attention (which social, economic, and commercial discourse increasingly treat as a limited resource) is not in fact scarce at all, and indeed, that it is dehumanizing to think of it in that way.

Today’s offering nominates a different kind of scarcity as worthy of our thought…

Legitimacy is a pattern of higher-order acceptance. An outcome in some social context is legitimate if the people in that social context broadly accept and play their part in enacting that outcome, and each individual person does so because they expect everyone else to do the same.

Legitimacy is a phenomenon that arises naturally in coordination games. If you’re not in a coordination game, there’s no reason to act according to your expectation of how other people will act, and so legitimacy is not important. But as we have seen, coordination games are everywhere in society, and so legitimacy turns out to be quite important indeed. In almost any environment with coordination games that exists for long enough, there inevitably emerge some mechanisms that can choose which decision to take. These mechanisms are powered by an established culture that everyone pays attention to these mechanisms and (usually) does what they say. Each person reasons that because everyone else follows these mechanisms, if they do something different they will only create conflict and suffer, or at least be left in a lonely forked ecosystem all by themselves. If a mechanism successfully has the ability to make these choices, then that mechanism has legitimacy.

There are many different ways in which legitimacy can come about. In general, legitimacy arises because the thing that gains legitimacy is psychologically appealing to most people. But of course, people’s psychological intuitions can be quite complex. It is impossible to make a full listing of theories of legitimacy, but we can start with a few:

Legitimacy by brute force: someone convinces everyone that they are powerful enough to impose their will and resisting them will be very hard. This drives most people to submit because each person expects that everyone elsewill be too scared to resist as well.

Legitimacy by continuity: if something was legitimate at time T, it is by default legitimate at time T+1.

Legitimacy by fairness: something can become legitimate because it satisfies an intuitive notion of fairness. See also: my post on credible neutrality, though note that this is not the only kind of fairness.

Legitimacy by process: if a process is legitimate, the outputs of that process gain legitimacy (eg. laws passed by democracies are sometimes described in this way).

Legitimacy by performance: if the outputs of a process lead to results that satisfy people, then that process can gain legitimacy (eg. successful dictatorships are sometimes described in this way).

Legitimacy by participation: if people participate in choosing an outcome, they are more likely to consider it legitimate. This is similar to fairness, but not quite: it rests on a psychological desire to be consistent with your previous actions.

Note that legitimacy is a descriptive concept; something can be legitimate even if you personally think that it is horrible. That said, if enough people think that an outcome is horrible, there is a higher chance that some event will happen in the future that will cause that legitimacy to go away, often at first gradually, then suddenly…

The co-founder of Etherium, Vitalik Butarin (@VitalikButerin) on why “The Most Important Scarce Resource is Legitimacy.” Whatever one’s feeling about cryptocurrency, it’s eminently worthy of reading in full… and of submitting to the same sort of questioning that L.M. Sarcasas mustered yesterday,

* Willis Harman


As we channel John Locke, we might recall that it was on thus date in 1933 that the the Cullen–Harrison Act, legalizing the sale of beer (after 14 years of Prohibition), came into force. Americans celebrated by consuming 1.5 million barrels of beer that day.

The Cullen-Harrison Act was not the official end of prohibition in the U.S., but it did redefine an “intoxicating beverage” under the Volstead Act (which was created in 1919 to carry out the intent of the 18th Amendment– and was fully repealed later in 1933).

During Prohibition, while alcohol consumption fell initially, it pretty briskly returned to 60-70% of its pre-Volstead Act levels. Indeed, it was in 1923 that the invented word “scofflaw” was introduced to the American vocabulary. Created to mean “a lawless drinker of illegally made or illegally obtained liquor,” it gained wide usage through Prohibition, and survives to day, referring to those who ignore/break minor laws that are infrequently enforced… which is to say, laws that rely on legitimacy for their effectiveness.


“To pay attention, this is our endless and proper work”*…

The Attention Economy…

“Attention discourse” is how I usually refer to the proliferation of essays, articles, talks, and books around the problem of attention (or, alternatively, distraction) in the age of digital media. While there have been important precursors to digital age attention discourse dating back to the 19th century, I’d say the present iteration probably kicked off around 2008 with Nick Carr’s essay in the Atlantic, “Is Google Making Us Stupid?” And while disinformation discourse has supplanted its place in the public imagination over the past few years, attention discourse is alive and well…

Attention discourse proceeds under the sign of scarcity. It treats attention as a resource, and, by doing so, maybe it has given up the game. To speak about attention as a resource is to grant and even encourage its commodification. If attention is scarce, then a competitive attention economy flows inevitably from it. In other words, to think of attention as a resource is already to invite the possibility that it may be extracted. Perhaps this seems like the natural way of thinking about attention, but, of course, this is precisely the kind of certainty [Ivan Illich] invited us to question…  

His crusade against the colonization of experience by economic rationality led him not only to challenge the assumption of scarcity and defend the realm of the vernacular, he also studiously avoided the language of “values” in favor of talk about the “good.” He believed that the good could be established by observing the requirements of proportionality or complementarity in a given moment or situation. The good was characterized by its fittingness. Illich sometimes characterized it as a matter of answering a call as opposed to applying a rule. 

“The transformation of the good into values,” he answers, “of commitment into decision, of question into problem, reflects a perception that our thoughts, our ideas, and our time have become resources, scarce means which can be used for either of two or several alternative ends. The word value reflects this transition, and the person who uses it incorporates himself in a sphere of scarcity.”

A little further on in the conversation, Illich explains that value is “a generalization of economics. It says, this is a value, this is a nonvalue, make a decision between the two of them. These are three different values, put them in precise order.” “But,” he goes on to explain, “when we speak about the good, we show a totally different appreciation of what is before us. The good is convertible with being, convertible with the beautiful, convertible with the true.”…

Your Attention Is Not a Resource“: L.M. Sacasas (@LMSacasas) wields Illich to argue that “you and I have exactly as much attention as we need.”

(image above: source)

* Mary Oliver


As we go for the good, we might recall that it was on his date in 1965 that NASA launched Hughes Aircraft’s Early Bird (now known officially as Intelsat I) into orbit. It was the first communications satellite to be placed in synchronous earth orbit– and successfully demonstrated their (subsequently explosively growing) use for commercial communications.

“Early Bird” being prepared


“To be overly concerned with the original materials, which are merely sentimental souvenirs of the past, is to fail to see the living building itself”*…

The human body replaces its own cells regularly. Scientists at the Weizmann Institute of Science in Rehovot, Israel, have finally pinned down the speed and extent of this “turnover.” About a third of our body mass is fluid outside of our cells, such as plasma, plus solids, such as the calcium scaffolding of bones. The remaining two thirds is made up of roughly 30 trillion human cells. About 72 percent of those, by mass, are fat and muscle, which last an average of 12 to 50 years, respectively. But we have far more, tiny cells in our blood, which live only three to 120 days, and lining our gut, which typically live less than a week. Those two groups therefore make up the giant majority of the turnover. About 330 billion cells are replaced daily, equivalent to about 1 percent of all our cells. In 80 to 100 days, 30 trillion will have replenished—the equivalent of a new you…

Our Bodies Replace Billions of Cells Every Day: “A New You in 80 Days.”

* Douglas Adams, Last Chance to See


As we sail on the Ship of Theseus, we might spare a thought for Hans Ernst August Buchner; he died on this date in 1902. A bacteriologist, he was a pioneer in the field of immunology, the first to discover a substance in blood, gamma globulins, natural bactericides capable of destroying bacteria.  He also worked with his brother Eduard Buchner, a chemist who won the Nobel Prize in 1907 for his work on fermentation (which helped pave the way for our understanding of the work of enzymes); Ernst had died in 1902, and so did not share in the honor.


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