Why nations rely on geometry to create order

The story of geometry is bound up in the Renaissance, the rise of nation states, and the expression of absolute power. Geometric designs came to represent order in the universe. But order’s war with chaos continues — just compare the geometric plans for Washington, D.C., with the lived reality. Historian Amir Alexander traces the rise of geometry from Euclid to the United Nations.

Washington D.C. is a potent example of geometric nation-building, says author

Military engineer Major Pierre Charles L'Enfant designed the basic plan for Washington, D.C. in 1791 for the first President of the United States, George Washington. He envisioned a palace for the Whitehouse and when it was later built called it 'a country house that is unworthy of the nation.' (Drew Angerer/Getty Images)
Listen to the full episode53:59

** Originally published on May 26, 2020.

You might not guess it by looking at the daily news from Washington D.C., but the city is an example of perfectly harnessed order and balance.

Stand long enough on Capitol Hill, and you may sense a deep underlying logic.

"We are standing in the middle of an elaborate geometrical construction that was put there with great care, precision and intent," said Amir Alexander, speaking with IDEAS host Nahlah Ayed. (The two were imagining themselves in that spot, looking westward over Washington's Great Mall.)

An aerial view from 1936 of the U.S. Capitol with the Washington Monument and Federal Triangle in the background. Historian Amir Alexander says the centres of power are balanced on the two ends of Pennsylvania Avenue — the Washington monument being the third node of the triangle. (National Archives/Newsmakers/Getty Images)

Alexander argues that the careful geometric design of Washington D.C.'s physical space helps — a little, anyway — to keep order on a political and cultural level as well.

And the design symbolizes one of the most persistent desires of all societies: to respond to chaos and uncertainty by imposing what's thought to be the best source of order yet discovered.

"What does geometry represent more than anything else? Order! A deep, underlying, perfect, beautiful truth," explains Alexander.

Euclid's influence on cities

While the use of geometry goes back to prehistory, its power in modern culture comes in large part from the world's most famous geometer, Euclid.

He (or she—nobody knows much about Euclid's real identity) lived in Alexandria around 300 B.C., and compiled all the proofs about triangles, circles and lines into a single structure of what appeared to be absolute, undeniable knowledge.

Award-winning historian Amir Alexander traces the path of the geometrical vision of the world as it coursed its way from ancient Egypt to the present — shaping our societies, our politics, and our ideals in his book, Proof! How the World Became Geometrical. (Ronna Kovner/Macmillan )

The suggestion that the physical world obeys an ordered, hierarchical logic came as welcome news to world leaders at the time.

"What could be more appealing to Ptolemy the First, or Hiero of Syracuse?" Alexander asks. The power of that idea — of a fixed order, beyond question — explains many of the designs of palaces and capital cities.

"Poor old Euclid seems to be responsible for everything!" says Ulrike Al-Khamis, director of collections at the Aga Khan Museum in Toronto. She points out that geometry has symbolized different things in different times and places.

While Middle Eastern leaders used simple geometrical design to project power with big, imposing buildings, artists also saw in geometry a humbler message.

The fountain of the Aga Khan Museum in Toronto is made of marble and sandstone. The centre of the fountain is created in the shape of an eight-lobed pattern. Its tri-coloured stones suggest that it follows a Mamluk tradition. One of the existing examples in Cairo is in the Bayt Zainab Khatun. (© The Aga Khan Museum, AKM960)

This humility can be seen in decorative geometrical works throughout the Islamic world.

"If you imagine any geometric design, it's a design that's perfectly in harmony, that is repeatable ad infinitum," Al-Khamis explains.

"Every single piece also relies on the harmony of the whole. So that, for some philosophers, really worked very well to contemplate God's perfection and harmony."

An ambitious promise

Euclid's geometry couldn't live up to the promise of complete perfection. But as Alexander points out, that's not really the point.

The point, Alexander adds, is akin to Plato's ambitious pure rational principle: it's not about achieving, but rather on the profound effect that striving for perfection has on us.

The historian anticipates that future leaders will always rely on geometry for its powerful resonance. 

"Geometry retains a hold on us," says Alexander.

"I think that's true in Paris, it's true in Washington D.C. There's something about it. When people attack this notion of fundamental truth, they're also implicitly attacking this notion of Euclidean geometry — somehow even its opponents cannot do without it."

Guests in this episode:

Amir Alexander is a writer in Los Angeles, where he teaches history at the University of California. His latest book is Proof! How the World Became Geometrical. His previous works are Infinitesimal, Geometrical Landscapes, and Duel at Dawn.

Ulrike Al-Khamis is director of collections and public programming at the Aga Khan Museum in Toronto. 


** This episode was produced by Tom Howell.


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