## Posts Tagged ‘**Fibonacci**’

## “Nothing is more wonderful than the art of being free, but nothing is harder to learn how to use than freedom”*…

Lynn Hunt on Alexis de Tocqueville, who left France to study the American prison system and returned with the material that would become *Democracy in America*…

Alexis de Tocqueville was a study in contradictions: a French aristocrat of proud heritage who trumpeted the inevitable, salutary rise of democracy, using the United States as his exemplar; a cosmopolitan with an English wife and many friends in the Anglo-American world who brandished a fervent French nationalism; an antislavery advocate who felt no discomfort in supporting the French colonization of Algeria and hired as his main assistant Arthur de Gobineau, who later published one of the founding texts of white supremacy; and finally a man of delicate constitution who undertook an arduous trip on horseback into the wilderness of northern Michigan in order to see Native Americans and new settler communities for himself. Such inconsistencies make for a fascinating story, and in

The Man Who Understood Democracy, Olivier Zunz, a French-educated historian who has taught US history for decades at the University of Virginia, shows that he is ideally suited to tell it.Tocqueville’s

Democracy in America, published in two volumes in 1835 and 1840, became an instant classic and has remained one to this day. On its hundredth anniversary in 1935, the French government presented a bust of the author to Franklin D. Roosevelt, and an article at the time referred to the book as “perhaps the greatest, most lucid, and most impartial commentary that free institutions in general, and American self-government in particular, had ever received.”Democracy in Americaserved as a kind of textbook for US students for many generations, but it is now more often cited than read. That dutiful disregard may be the fate of all such masterworks, especially one that runs about eight hundred pages, but Zunz has succeeded in restoring its appeal, first by vividly retracing its origins and then by skillfully evoking the enduring excitement and relevance of its analysis…

Alexis de Tocqueville, the Frenchman who unpacked the tension between freedom and equality in the United States: “‘A Great Democratic Revolution’.”

* Alexis de Tocqueville– who went on to observe that “Americans are so enamored of equality, they would rather be equal in slavery than unequal in freedom.”

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**As we dedicate ourselves to democracy,** we might note that today is Fibonacci Day, as today’s date is often rendered 11/23, and the Fibonacci sequence (also here and here) begins 1, 1, 2, 3…

Five Ways to Celebrate Fibonacci Day.

## “If one tells the truth, one is sure, sooner or later, to be found out”*…

That most quotable (well, after Shakespeare) of wits…

More enduring epigrams in the entertaining infographic “And the Oscar goes to…” (full and larger) from @guardian.

See also “Oscar Wilde Will Not Be Automated, ” from @benjaminerrett.

* Oscar Wilde

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**As we chortle,** we might recall that it was on this date (which is, by the way, Fibonacci Day) in 1644 that John Milton published *Areopagitica; A speech of Mr. John Milton for the Liberty of Unlicenc’d Printing, to the Parlament of England*. A prose polemic opposing licensing and censorship, it is among history’s most influential and impassioned philosophical defenses of the principle of a right to freedom of speech and expression. The full text is here.

## “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.”

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 nature, architecture, 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.”

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)

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**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.

## “Nothing is more memorable than truth beautifully told”*…

If physicists and mathematicians can’t be rock stars, they can at least have rock star logos. Dr. Prateek Lala, a physician and amateur calligrapher from Toronto has obliged with 50 nifty “scientific typographics” of important cosmologists and scientists through the ages.

Inspired by the “type biographies” of Indian graphic designer Kapil Bhagat, Lala designed his logos to make the lives and discoveries of various scientists more engaging and more immediately relatable to students.

Dr. Lala’s work was for a poster that was published in the latest issue of *Inside The Perimeter*, the official magazine of Canada’s Perimeter Institute for Theoretical Physics. One can subscribe to the magazine by email for free here.

Meantime, one can read the backstory, and see many more of Dr. L’s lyrical logos at CoDesign.

* Rick Julian

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**As we ponder personal branding,** we might send dynamic birthday greetings to Daniel Bernoulli; he was born on this date in 1700. One of the several prominent mathematicians and physicists in the Swiss Bernoulli family, Daniel is best remembered for or his applications of mathematics to mechanics, especially fluid mechanics, and for his pioneering work in probability and statistics. His name is commemorated in the Bernoulli principle, a particular example of the conservation of energy, which describes the mathematics of the mechanism underlying the operation of two important technologies of the 20th century: the carburetor and the airplane wing.

A contemporary and close friend of Leonhard Euler (see above), Bernoulli was the son of Johann Bernoulli (one of the early developers of calculus), nephew of Jakob Bernoulli (who was the first to discover the theory of probability), and the brother of Johann II (an expert on magnetism and the propagation of light). Daniel is said to have had a bad relationship with his father: when they tied for first place in a scientific contest at the University of Paris, Johann, unable to bear the “shame” of being compared as Daniel’s equal, banned Daniel from his house. Johann Bernoulli then plagiarized some key ideas from Daniel’s book *Hydrodynamica* in his own book *Hydraulica*, which he backdated to before *Hydrodynamica*. Despite Daniel’s attempts at reconciliation, his father carried the grudge until his death.

## Spiraling into control…

The Fibonacci spiral (*source*)

**As we remark that math really is beautiful,** we might send elegantly parsimonious birthday greetings to one of Fibonacci’s spiritual descendants, a father of Pure Mathematics, Leonhard Euler; he was born on this date in 1707. While crafting “

**the most remarkable formula in mathematics**,” Euler made foundational contributions to number theory, graph theory, mathematical logic, and applied math; he originated many commonly-used figures of mathematical notation, and invented the concept of the “mathematical function.” And he was no slouch in physics either, making renowned contributions in work in mechanics, fluid dynamics, optics, and astronomy.

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