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In the 1890s, my Eastern European Jewish ancestors emigrated to an American Jewish farming community in Woodbine, N.J., where the millionaire philanthropist Baron de Hirsch provided land, tools, and training at one of the nation’s first agricultural colleges. But within a generation, the family had settled in Philadelphia where they became accountants, tailors, merchants, and eventually, lawyers and college professors.

De Hirsch had a vision of American Jews achieving economic liberation by working the land. If he’d had a better sense of history, he would have built not an agricultural college but a medical school, because for well over a millennium prior to the settlement of Woodbine, Jews had not been farmers—not in Palestine, not in the Muslim empire, not in Western Europe, not in Eastern Europe, not anywhere in the world.

You have to go back almost 2,000 years to find a time when Jews, like virtually every other identifiable group, were primarily an agricultural people. Around A.D. 200, Jews began to quit the land. By the seventh century, Jews had left their farms in large numbers to become craftsmen, artisans, merchants, and moneylenders—the only group to have given up on agriculture. Jewish participation in farming fell to about 10 percent through most of the world; even in Palestine it was only about 25 percent. Everyone else stayed on the farms.

(Even in the modern state of Israel, where agriculture has been an important component of the economy, it’s been a peculiarly capital-intensive form of agriculture, one that employed well under a quarter of the population at the height of the Kibbutz movement, and less than 3 percent of the population today.)

The obvious question is: Why? Why did Jews and only Jews take up urban occupations, and why did it happen so dramatically throughout the world? Two economic historians—Maristella Botticini (of Boston University and Universitá di Torino) and Zvi Eckstein (of Tel Aviv University and the University of Minnesota)—have recently been giving that question a lot of thought.

First, say Botticini and Eckstein, the exodus from farms to towns was probably not a response to discrimination. It’s true that in the Middle Ages, Jews were often prohibited from owning land. But the transition to urban occupations and urban living occurred long before anybody ever thought of those restrictions. In the Muslim world, Jews faced no limits on occupation, land ownership, or anything else that might have been relevant to the choice of whether to farm. Moreover, a prohibition on land ownership is not a prohibition on farming—other groups facing similar restrictions (such as Samaritans) went right on working other people’s land.

Nor, despite an influential thesis by the economic historian Simon Kuznets, can you explain the urbanization of the Jews as an internal attempt to forge and maintain a unique group identity. Samaritans and Christians maintained unique group identities without leaving the land. The Amish maintain a unique group identity to this day, and they’ve done it without giving up their farms.

So, what’s different about the Jews? First, Botticini and Eckstein explain why other groups didn’t leave the land. The temptation was certainly there: Skilled urban jobs have always paid better than farming, and that’s been true since the time of Christ. But those jobs require literacy, which requires education—and for hundreds of years, education was so expensive that it proved a poor investment despite those higher wages. (Botticini and Eckstein have data on ancient teachers’ salaries to back this up.) So, rational economic calculus dictated that pretty much everyone should have stayed on the farms.

But the Jews (like everyone else) were beholden not just to economic rationalism, but also to the dictates of their religion. And the Jewish religion, unique among religions of the early Middle Ages, imposed an obligation to be literate. To be a good Jew you had to read the Torah four times a week at services: twice on the Sabbath, and once every Monday and Thursday morning. And to be a good Jewish parent you had to educate your children so that they could do the same.

The literacy obligation had two effects. First, it meant that Jews were uniquely qualified to enter higher-paying urban occupations. Of course, anyone else who wanted to could have gone to school and become a moneylender, but school was so expensive that it made no sense. Jews, who had to go to school for religious reasons, naturally sought to earn at least some return on their investment. Only many centuries later did education start to make sense economically, and by then the Jews had become well established in banking, trade, and so forth.

The second effect of the literacy obligation was to drive a lot of Jews away from their religion. Botticini and Eckstein admit that they have little direct evidence for this conclusion, but there’s a lot of indirect evidence. First, it makes sense: People do tend to run away from expensive obligations. Second, we can look at population trends: While the world population increased from 50 million in the sixth century to 285 million in the 18th, the population of Jews remained almost fixed at just a little over a million. Why were the Jews not expanding when everyone else was? We don’t know for sure, but a reasonable guess is that a lot of Jews were becoming Christians and Muslims.

So—which Jews stuck with Judaism? Presumably those with a particularly strong attachment to their religion and/or a particularly strong attachment to education for education’s sake. (The burden of acquiring an education is, after all, less of a burden for those who enjoy being educated.) The result: Over time, you’re left with a population of people who enjoy education, are required by their religion to be educated, and are particularly attached to their religion. Naturally, these people tend to become educated. And once they’re educated, they leave the farms.

Of course there are always exceptions. My great-grandfather raised chickens. But he did it in the basement of his row house in north Philadelphia.

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(If this were a less serious post, I might suggest that this famous letter was the first example of a Galois Correspondence.)

Now, two centuries later, every first year graduate student in mathematics spends a semester studying Galois Theory, and many devote their subsequent careers to its extensions and applications. Many of the greatest achievements of modern mathematics (for example, the solution to Fermat’s Last Theorem) are, at their core, elucidations of Galois’s 200-year-old insight.

As every high school student knows (or should know), a quadratic equation (like, say, x² – 4x – 1 = 0) can be solved by applying the quadratic formula (which, in this case, gives x = 2 ± √5). The quadratic formula uses only addition, subtraction, multiplication, division, and the extraction of square roots.

What about a cubic equation, like, say, x³ + 2 x² – 5 x – 3 = 0 ? The less well-known cubic formula finds the solutions, using only addition, subtraction, multiplication, division, and the extraction of square and cube roots.

And, yes, there’s a quartic formula, for equations of degree 4. But it stops there. Galois’s contemporary Niels Abel (who, unlike Galois, survived to the ripe old age of 26) showed that no formula can consistently solve equations of degree 5 using only addition, subtraction, multiplication, division, and the extraction of roots.

On the other hand, some equations of degree 5 and higher can be solved by such formulas. Call those equations solvable. Galois figured out how to identify the solvable equations. It all comes down to understanding symmetry. Galois was the first to see clearly that the solutions to any equation satisfy certain symmetries. (For example, the solutions 2-√5 and 2+√5 are symmetric under the interchange of the plus and minus signs on the square root.) The nature of those symmetries differs from equation to equation, and dictates whether the equation is solvable. This in turn leads to a much deeper appreciation of the importance of symmetries throughout the theory of equations and throughout algebra more generally.

Today, algebraists take it for granted that understanding an equation, or a system of equations, entails understanding its symmetries. The development of that instinct was a key advance in the history of thought. After almost two centuries, we still use it to discover new insights and to solve old problems every single day.

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Well, I was pretty young in 1963, probably too young to think about such matters. I remember having little interest in the Beatles, but being being very aware that they were something very big. Everyone was aware of that. But unless I am mistaken, pretty much nobody realized that we were witnessing something really big and lasting. More generally, I doubt that anyone at the time had any inkling of the long-term significance of rock ‘n’ roll. We knew it was popular, but we had no idea it would change the world. I’m not sure that in 1963 anyone knew that it was possible for music to change the world.

This led to the more general question: How quickly are great cultural watersheds recognized for what they are? In the few areas I know something about, I think the answer is “usually pretty quickly”. I remember 1910 even less vividly than I remember 1963, but I am pretty sure that it wasn’t long between the appearance of The Love Song of J. Alfred Prufrock and the realization (at least among people who care about this sort of thing) that poetry had changed forever. In mathematics, at least in the past century (and I’m pretty sure for several centuries, or even millenia, before that), major paradigm shifts have generally been recognized very quickly. When a Serre or a Grothendieck upends the mathematical world, the mathematical world quickly knows it’s been upended.

On the other hand, it took people remarakably long to catch on to the significance of the Internet. I remember trying to tell people in 1992 that this Internet thing was going to be very big someday, and meeting a lot of blank stares. And even I, who was a very early adopter of email, Usenet, FTP and IRC, initially dismissed the World Wide Web as a passing fad.

So here’s the (extremely vague) question of the day: How often are cultural watersheds widely and quickly recognized, and what characterizes those that are and those that aren not? I’m not talking about fads here (so LOLcats don’t count); I’m talking about real lasting world-shaking changes. Feel free to interpret the question in any way you please, and have at it.

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The Smithsonian Magazine asks its readers to vote on who had the best Civil War facial hair. Burnside wins, as well he should. But how is Longstreet not even among the candidates?

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Am I right about that? Over the course of human history, what is your estimate of the fraction of males who have reached adulthood without participating in a military conflict?

(Obviously, there’s some fuzziness about what counts as military conflict. I’m thinking here not about the occasional street fighter, but about the guy living in mud and getting shot at for weeks at a time — or things equally dangerous/traumatic/uncomfortable.)

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I led Nine Section for a time; leading or not, I was part of it. They were my mates, and to them I was bound by ties of duty, loyalty and honor… Could I say, yes, Grandarse or Nick or Forster were expendable, and should have died rather than the victims of Hiroshima? No, never. And the same goes for every Indian, American, Australian, African, Chinese and other soldier whose life was on the line in August, 1945. So [I'd have said]: drop the bomb.

…

And then I have another thought.

You see, I have a feeling that if—and I know it’s an impossible if—but if, on that sunny August morning, Nine Section had known all that we know now of Hiroshima and Nagasaki, and could have been shown the effect of that bombing, and if some voice from on high had said: “There — that can end the war for you, if you want. But it doesn’t have to happen, the alternative is that the war, as you’ve known it, goes on to a normal victorious conclusion, which may take some time, and if the past is anything to go by, some of you won’t reach the end of the road. Anyway, Malaya’s down that way … it’s up to you”, I think I know what would have happened. They would have cried “Aw, fook that!”, with one voice, and then they would have sat about, snarling, and lapsed into silence, and then someone would have said heavily, “Aye, weel” and got to his feet, and been asked “W’eer th’ ‘ell you gan, then?”, and given no reply, and at last, the rest would have got up, too, gathering their gear with moaning and foul language and ill-tempered harking back to the long dirty bloody miles from the Imphal boxes to the Sittang Bend and the iniquity of having to do it again, slinging their rifles and bickering about who was to go on point, and “Ah’s aboot ‘ed it, me!” and “You, ye bugger, ye’re knackered afower ye start, you!”, and “We’ll a’ git killed!”, and then they would have been moving south. Because that is the kind of men they were.

I’ll add no comments, though yours, of course, are welcome.

[A hat tip to my Mom and Dad, who told me to read this book. So should you.]

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To my mild surprise, the face that generated the most controvery—in both comments and email—was that of Abraham Lincoln, who was born 201 years ago on this day. Readers pulled no punches. ScottN wrote: “Lincoln is on a different list I have: People Who Caused the Most Unnecessary Deaths.” Peter wrote: “[Lincoln] was a tyrant and a racist to boot.” And the consistently provocative and thoughtful Bob Murphy wrote:

I would love to hear your reasons for including Lincoln. I have the same misgivings as the other commenter above, though I was going to introduce them with levity. (E.g. “I know you like math, Steve, so is that why you included the guy who maximized the wartime deaths of Americans?”)

I replied to Bob (and others) by email, with some sketchy thoughts and a promise to blog about Lincoln sometime on or before his birthday. With the deadline looming, I realize that I have little to add to those sketchy thoughts. So here, with only some minor editing, is the email I sent to Bob Murphy:

Dear Bob:

First, I do believe that a perfectly reasonable person could come to the judgment that Lincoln was a bloodthirsty madman.

Second, however, I am not one of those reasonable people. My reading of history is that Lincoln was motivated by a passion to end slavery, above all else. I agree that alternative readings are reasonable (see above). I also agree that there are a lot of other people who are more well-versed in this history than I am.

Third, even if we grant that freeing the slaves was a noble cause and Lincoln’s sole motivation, we might well take the position that the victory was not worth the bloodshed.

Fourth—on the other hand, 3/4 of a million people died to save 4 million slaves. That’s over five slaves freed per war death, which does not seem to me to be an unreasonable ratio. And that doesn’t even count all the future generations who would otherwise have been enslaved. (Of course it also does not account for the possibility that slavery could have been brought to a more peaceable end.)

Fifth—moreover, I think it’s clear that neither Lincoln nor any other reasonable person had any way of anticipating that there would be casualties on that order, so the war looks like a much better bet ex ante than ex post; and I think ex ante is the right standard for judgment.

Sixth—On the other hand, Lincoln had a lot of pretty ugly secondary motivations. (Protectionism, something like a national industrial policy, etc.) Well, so did Reagan—but you’ll never take Reagan’s portrait off my wall.

Seventh: Bottom line is that I think Lincoln was out, above all, to end slavery (though a reasonable person might disagree) and that the price he paid, while enormous, was a reasonable one (though a reasonable person might disagree), and that the clarity of his vision was a form of greatness and a force for good (though a reasonable person might disagree). I am also acutely aware that I might change my mind about these things if I were better educated.

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So ends the email. Those readers who care to contribute to my better education are invited to fire away.

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“For 400 years the most sophisticated persons in Europe decided difficult criminal cases by asking the defendant to thrust his arm into a cauldron of boiling water and fish out a ring. If his arm was unharmed, he was exonerated. If not, he was convicted.”

According to Leeson, this is less crazy than it sounds: As long as defendants believe (superstitiously) that ordeals yield accurate verdicts, guilty defendants always confess to avoid the ordeal. At the same time innocent defendants always opt for the ordeal—and are always acquitted, provided the priests cheat by (for example) substituting tepid for boiling water, or “sprinkling” a few gallons of cold holy water over the cauldron, or liberally redefining what counts as “unharmed”.

Not only does the system work, but it’s continually reinforced. Even the superstitious masses are smart enough to figure out that their equally superstitious neighbors opt for ordeals only when innocent; therefore they expect all ordeals to yield acquittals, and their expectations are always confirmed.

If not everyone is perfectly superstitious then the story is a little more complicated. Still, as long as there’s a healthy amount of superstition floating around, and as long as the priests are eager to convict the guilty and acquit the innocent, you’d expect most ordeals to yield acquittals, and you’d expect non-believers to be denied the ordeal option. (After all, the system works only as long as the participants believe it’s rigged not by the priests but by God.) And indeed, there’s some historical evidence for these and other prediction of the Leeson theory. See his paper for more.

(The image at the top is by the children’s book illustrator Jeffrey Brian Fisher.)

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If there is such a thing as a just war, Red Cloud’s War of 1866 was more just than most. Black Kettle’s village of peaceful Cheyenne had been recently and wantonly slaughtered by the Colorado militia under Colonel John Chivington at Sand Creek. (The survivors of this unhappy band would meet their deaths a few years later at Washita Creek, at the equally murderous hands of General George Armstrong Custer.) Against this background, the chiefs had been betrayed at Fort Laramie, where the government had summoned them to negotiate for the right to build roads through Indian territory. With the conference still in session and no agreement in sight, Colonel Henry Carrington and a force of 700 men arrived to build the Bozeman Trail.

It seems to have been Red Cloud who converted thousands of disgruntled but essentially powerless Indians into—well, not exactly an organized fighting force (military organization being pretty much a foreign concept to the Plains Indians), but a force sufficiently coherent and sufficiently aroused to defeat the United States government, first in battle (at Fort Phil Kearney) and then at war. There are conflicting accounts of his military leadership (or lack thereof); it’s more likely that High Back Bone (a/k/a Hump) was the general-in-chief (at least at the Fort Phil Kearney battles). But Red Cloud’s political leadership was paramount; it was about this time that he displaced the hereditary leader Man Afraid Of His Horse as the most influential of the Sioux chiefs.

Whoever led, the attacks on Fort Phil Kearney were devastatingly effective. The Indians, through all their decades of fighting against white soldiers, had exactly one military tactic: To send out a small party of decoys and lead the soldiers into a trap. The Fort Phil Kearney attack was the one and only occasion on which this tactic actually worked. (On every other occasion, without fail, the Indians hiding in ambuscade became overeager and showed themselves while there was still time for the soldiers to escape.) A hundred soldiers under the command of Captain William Fetterman left the fort to relieve a party of wood gatherers; Crazy Horse led the decoys, and the phrase “Fetterman Disaster” entered the national lexicon.

Between the Fetterman fight, a second attack on Fort Phil Kearney, and a series of raids throughout the Powder River Country, Red Cloud’s people devastated the army’s morale and won, in effect, a full surrender from the United States government, which agreed to abandon the Bozeman Trail and the forts that had been built to protect it. All troops were evacuated from the Powder River country and the Indians celebrated by burning the forts. Red Cloud had won the war.

But there were other wars to come. When Red Cloud, who could not read, signed the peace treaty of 1868, he had no idea that the government had inserted a clause requiring the Indian population to move west of the Missouri. As far as Red Cloud was concerned, he had agreed to no such thing. War loomed again.

Now Red Cloud, the great politician, made the first of several visits to Washington, DC to meet with President Grant. Several sources report that Red Cloud requested this visit, but I believe the historian George Hyde, who says that the urgent request came from Washington, where officials were desperate to avert yet another war with the Sioux.

Negotiations broke down when officials flourished the treaty of 1868 and Red Cloud—backed by all the other chiefs in the delegation—insisted that the provision about moving had never been read to any of them. The government then made the great mistake of insisting that Red Cloud visit New York City, hoping to intimidate him with a show of wealth and power. There, Red Cloud gave an impassioned speech at the Cooper Institute (now Cooper Union) that turned the tide of public opinion dramatically in his favor. Once again, Red Cloud had defeated the United States government, which abandoned its relocation plans and asked the Indians to accept an agency on the White River, where they could camp and receive food and blankets.

The hard part was selling his own people on the idea of peace. Having seen their own leaders bamboozled by the white men, many rank and file Indians were prepared to resume hostilities. Red Cloud, the great leader in war, now became the great leader in peace, working tirelessly to damp down the war fever.

For this he was not well repaid by the government, which proceeded in 1875 to steal the Black Hills of South Dakota, which belonged in perpetuity to the Indians in accordance with the Treaty of 1868. Red Cloud offered to sell the Black Hills for $600 million plus food for his people for the next seven generations; the government offered $6 million and no food. As rumors of gold spread and the government did nothing to prevent an influx of white prospectors and miners, it became clear that the Sioux would be lucky to get even that.

(A decade later, in 1883, when the Interior Department tried to expropriate even more Indian lands, the U.S. Congress overruled the action as a clear treaty violation. A Dakota judge immediately ruled that because the Black Hills had already been stolen, and because the Congress had now branded such land thefts as treaty violations, there was now ample precedent to violate all other Indian treaties!!)

The loss of the Black Hills meant war again, though by now it was more Sitting Bull’s war than Red Cloud’s. Following Custer’s dramatic defeat in this war, the government came to the chiefs with an ultimatum: Give up your lands and move to the Missouri, or we will starve you. There seemed little doubt that public opinion was very different now than it had been after the Cooper Institute speech, and the threat was serious. To save his people, Red Cloud capitulated.

After Red Cloud’s folk had been removed to the Pine Ridge reservation, he continued to his death to resist the white man’s ways, and to dream of restoring his vanished way of life. At the neighboring Rosebud Reservation, his lifelong rival Spotted Tail took the opposite tack, encouraging his people to prepare for a new and very different future.

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