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America’s Age, Empires, and Mathematics

I had a piece in the Ideas section of the Boston Globe this weekend about understanding the nature of empires and civilizations, seen through the lens of mathematics, entitled How Long Will America Last? An impossible question, answered with math:

With all the chatter about the rise of China, our possible economic collapse, and climate change, it is little wonder that Americans might be growing preoccupied with our nation’s staying power. Is the rise of the United States a fleeting moment in world history, or simply the beginning of many centuries of American ascendancy?

It might seem like a question for pundits to argue over, pessimists against optimists. But there is another way to answer the question as well: with some data.

History is filled with examples of powers much like America?—?nations whose wealth and influence allowed them outsized effects on the world. In the past, they were empires; America doesn’t usually see itself that way, but its wealth and influence put it in this peer group. And once we place it there, we can look at the lifetimes of lots of empires, see how long they’ve lasted, and use this to gain a bit of insight into our American situation.

This kind of approach, using a quantitative approach to understand history, is part of what has recently begun to be called cliodynamics. The field of cliodynamics?—?a term coined by the mathematician, biologist, and social scientist Peter Turchin from the name Clio, the muse of history?—?uses mathematics to understand the shape of history, and has been around for centuries. With a pedigree dating back to such approaches as that of Francis Galton, a relative of Darwin, who used math to understand the extinction of Victorian aristocratic surnames, a cliodynamic approach can be used to understand the ebb and flow of entire civilizations on a grand scale. Now, with the advent of the digitization of vast amounts of data, we can apply a certain precision to history that wasn’t possible before.

So that’s what I set out to do.

It’s based on my journal article The Life-Spans of Empires. The rest of the essay can be found here.

The Life-Spans of Empires

I recently published my first history article. Titled The Life-Spans of Empires, it’s published in the delightfully-named journal Historical Methods: A Journal of Quantitative and Interdisciplinary History. Using a fun dataset I unearthed from some articles in the Nineteen Seventies, I explore the lifespans of empires, and their similarities to other complex systems:

The collapse of empires is exceedingly difficult to understand. The author examined the distribution of imperial lifetimes using a data set that spans more than three millennia and found that it conforms to a memoryless exponential distribution in which the rate of collapse of an empire is independent of its age. Comparing this distribution to similar lifetime distributions of other complex systems—specifically, biological species and corporate firms—the author explores the reasons behind their lifetime distributions and how this approach can yield insights into empires.

This mathematical approach is part of a growing field of cliodynamics, a term coined by scientist Peter Turchin to describe the use of quantitative rigor in understanding history (there’s a new journal too of the same name). I look forward to more analyses that explore the long sweep of time using math.

Samuel Arbesman (2011). The Life-Spans of Empires Historical Methods, 44 (3), 127-129 : 10.1080/01615440.2011.577733

The Origins of Gotham

I was perusing through a list of the 98 nicknames of New York City, when I realized that I didn’t know the origin of the nickname ‘Gotham’ for New York. Apparently, it was nicknamed by Washington Irving after the city of Gotham in England. The British Gotham (which is actually pronounced Goatum), is noted for its Wise Men, who are actually fools. Unlike similar towns of fools in other traditions (Chelm and Abdera, for example), the Wise Men of Gotham were apparently only feigning foolishness (no one ever fakes foolishness, they only feign it). This was because at one time, madness was thought to be infectious, and in order to prevent a road being built through their town, they pretended to be crazy. Washington Irving, thinking that being crazy like a fox a characteristic of New Yorkers, nicknamed the city Gotham. And then Bob Kane came along and made a fictional version of Gotham City and let Batman live in it.