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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.


“We must be free not because we claim freedom, but because we practice it”*…




There is a growing sense of unease around algorithmic modes of governance (‘algocracies’) and their impact on freedom. Contrary to the emancipatory utopianism of digital enthusiasts, many now fear that the rise of algocracies will undermine our freedom. Nevertheless, there has been some struggle to explain exactly how this will happen. This chapter tries to address the shortcomings in the existing discussion by arguing for a broader conception/understanding of freedom as well as a broader conception/understanding of algocracy. Broadening the focus in this way enables us to see how algorithmic governance can be both emancipatory and enslaving, and provides a framework for future development and activism around the creation of this technology…

From a pre-print of John Danaher‘s (@JohnDanaher) chapter in the forthcoming Oxford Handbook on the Philosophy of Technology, edited by Shannon Vallor: “Freedom in an Age of Algocracy “… a little dense, but very useful.

[image above: source]

* William Faulkner


As we meet the new boss, same as the old boss, we might recall that it was on this date in 1962 that telephone and television signals were first relayed in space via the communications satellite Echo 1– basically a big metallic balloon that simply bounced radio signals off its surface.  Simple, but effective.

Forty thousand pounds (18,144 kg) of air was required to inflate the sphere on the ground; so it was inflated in space.  While in orbit it only required several pounds of gas to keep it inflated.

Fun fact: the Echo 1 was built for NASA by Gilmore Schjeldahl, a Minnesota inventor probably better remembered as the creator of the plastic-lined airsickness bag.

200px-Echo-1 source


Written by LW

February 24, 2020 at 1:01 am

“I don’t feel like speculating about them. All I know is what appeared on the film which was developed after the flight.”*…



… The [British] Ministry of Defence ran a UFO desk from 1952 until 2009; it was as underfunded as its American cousins, but it collected as many sightings (12,000) and was a bit more tolerant. Many of the MoD reports were accompanied by illustrations – diagrams, photos, sketches, even paintings – that were duly filed away. When the Freedom of Information Act was passed in 2000, the UFO desk was inundated with requests. The MoD knew better than to put up a fight. They’d seen nothing definite in over fifty years, so from one point of view the files were too trivial to hide.

David Clarke, a lecturer in journalism at Sheffield Hallam University, was made a consultant at the National Archives, where he spent ten years overseeing the UFO files’ release. There may be no extraordinary revelations in them, in the sense a UFOlogist would like, but there are fruits of a different sort. Clarke recently curated a peculiar and beautiful book called UFO Drawings from the National Archives, a showcase of the best ‘imaginative artwork’ sent to the MoD, ranging from scribbled crayon disks to diagrams in tidy pencil.

The book takes an old question (what did these people see?), sidesteps the nutjob theories and gives us a form of social history…

Hop aboard at “The UFOs we want.”

* NASA pilot Joseph Walker (referring to objects seen while he was tracking and photographing X-15 tests)


As we scan the skies, we might recall that it was on this date in 1950 that the first rocket was launched from Cape Canaveral in Florida– the “Bumper 2,” a V-2 missile base topped with a WAC Corporal rocket.

cape canav source


Written by LW

July 24, 2018 at 1:01 am

“The dice of Zeus always fall luckily”*…


14th century medieval dice from the Netherlands

Whether at a casino playing craps or engaging with family in a simple board game at home, rolling the dice introduces a bit of chance or “luck” into every game. We expect dice to be fair, where every number has equal probability of being rolled.

But a new study shows this was not always the case. In Roman times, many dice were visibly lopsided, unlike today’s perfect cubes. And in early medieval times, dice were often “unbalanced” in the arrangement of numbers, where 1 appears opposite 2, 3 opposite 4, and 5 opposite 6. It did not matter what the objects were made of (metal, clay, bone, antler and ivory), or whether they were precisely symmetrical or consistent in size or shape, because, like the weather, rolls were predetermined by gods or other supernatural elements.

All that began to change around 1450, when dice makers and players seemingly figured out that form affected function, explained Jelmer Eerkens, University of California, Davis, professor of anthropology and the lead author of a recent study on dice.

“A new worldview was emerging — the Renaissance. People like Galileo and Blaise Pascal were developing ideas about chance and probability, and we know from written records in some cases they were actually consulting with gamblers,” he said. “We think users of dice also adopted new ideas about fairness, and chance or probability in games”…

From fate to fairness: how dice changed over 2,000 years to be more fair: “It’s not how you play the game, but how the dice were made.”

[via Tim Carmody‘s always-illuminating newsletter, Noticing]

* Sophocles


As we consider the odds, we might send frontier-challenging birthday greetings to a man who tempted chance– Charles Elwood “Chuck” Yeager; he was born on this date in 1923.  A flying ace, test pilot, and ultimately U.S. Air Force General, Yeager became the first human to officially break the sound barrier when, in 1947, he flew the experimental Bell X-1 at Mach 1 at an altitude of 45,000 ft. 

Perhaps as famously, Yeager was a mentor and role model for the first class of NASA astronauts, as memorialized in Tom Wolfe’s The Right Stuff, and Philip Kaufman’s film adaptation.  On finishing high school at the beginning of World War II, Yeager had enlisted in the Air Force as a private; he served a mechanic before being accepted into the enlisted flight program, from which he graduated as a “Flight Officer” (equivalent to a Chief Warrant Officer).  His extraordinary skill as a pilot fueled his continued rise through the ranks.  But NASA’s requirement that all astronauts have college degrees disqualified Yeager from membership in the space program.  So though he was by most accounts far the most qualified potential astronaut, he became instead their head teacher, the first commandant of the USAF Aerospace Research Pilot School, which produced astronauts for NASA and the USAF.

Yeager in front of the Bell X-1, which, as with all of the aircraft assigned to him, he named Glamorous Glennis (or some variation thereof), after his wife.



Written by LW

February 13, 2018 at 1:01 am

“You can’t trust water: Even a straight stick turns crooked in it”*…


New Yorkers like to say their tap water is the best in the world. Surely, then, it’s worth a $1.99-a-month subscription to drink it when you’re away from your sink—right?

That is the concept behind Reefill, a startup that aims to bring the subscription model to the simple, free act of filling up a water bottle at a café. The company wants to build 200 smartphone-activated water fountains inside Manhattan businesses, less to make money off the Nalgene crowd than to hit Dasani, Aquafina, and the wasteful consumption habits of bottled water–guzzling Gothamites…

Just as one field of startups is dedicated to doing what Mom won’t do for you anymore, another is reviving the infrastructure of the 19th century. Uber eventually found its way to the bus; Reefill, to the public drinking fountain…

Top up at “The Startup That Wants to Sell You a Subscription to New York City Tap Water Explains Itself.”

* W.C. Fields


As we pine for the days of bigger visions, we might recall that it was on this date in 1961 that President John F. Kennedy gave the historic speech before a joint session of Congress that set the United States on a course to the moon.

In his speech, Kennedy called for an ambitious space exploration program that included not just missions to put astronauts on the moon, but also a Rover nuclear rocket, weather satellites, and other space projects.

Read the transcript here.



Written by LW

May 25, 2017 at 1:01 am

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