Richard A. Posner

After breakfast one morning in August, the mathematician Terence Tao opened an email from three physicists he didn’t know. The trio explained that they’d stumbled across a simple formula that, if true, established an unexpected relationship between some of the most basic and important objects in linear algebra.

The formula “looked too good to be true,” says Tao, who is a professor at UCLA, a Fields medalist, and one of the world’s leading mathematicians. “Something this short and simple—it should have been in textbooks already,” he said. “So my first thought was, no, this can’t be true.”

Then he thought about it some more.

The physicists—Stephen Parke of Fermi National Accelerator Laboratory, Xining Zhang of the University of Chicago, and Peter Denton of Brookhaven National Laboratory—had arrived at the mathematical identity about two months earlier while grappling with the strange behavior of particles called neutrinos.

Is a color-blind political system possible under our Constitution? If it is, the Supreme Court’s evisceration of the Voting Rights Act in 2013 did little to help matters. While black people in America today are not experiencing 1950s levels of voter suppression, efforts to keep them and other citizens from participating in elections began within 24 hours of the Shelby County v. Holder ruling and have only increased since then.

In Shelby County’s oral argument, Justice Antonin Scalia cautioned, “Whenever a society adopts racial entitlements, it is very difficult to get them out through the normal political processes.” Ironically enough, there is some truth to an otherwise frighteningly numb claim. American elections have an acute history of racial entitlements—only they don’t privilege black Americans.

Democracy depends on the consent of the losers. For most of the 20th century, parties and candidates in the United States have competed in elections with the understanding that electoral defeats are neither permanent nor intolerable. The losers could accept the result, adjust their ideas and coalitions, and move on to fight in the next election. Ideas and policies would be contested, sometimes viciously, but however heated the rhetoric got, defeat was not generally equated with political annihilation. The stakes could feel high, but rarely existential. In recent years, however, beginning before the election of Donald Trump and accelerating since, that has changed.

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Remember these numbers. You’ll be asked about them at the end of the test: 70, 73, 76, and 78.

These are the ages of the leading candidates in the 2020 presidential election: Elizabeth Warren, Donald Trump, Joe Biden, and Bernie Sanders, respectively. In most any other line of work, people in their eighth decade are usually retired. For most of human history—and still in most of the world today—people of this age were usually dead.

Last month, Jimmy Carter, the 95-year-old former U.S. president, said that the office requires a person “to be very flexible with [one’s] mind,” and that by age 80 he wouldn’t have felt able to do the job. He joined the growing ranks of those suggesting they would support an upper age limit for the office, either for purposes of breaking up the gerontocracy or to ensure a person has the physical and cognitive capacity. “You have to be able to go from one subject to another and concentrate on each one adequately and then put them together in a comprehensive way,” Carter said.

Yesterday, strong winds and rainstorms pushed water levels in Venice, Italy, to the second-highest levels ever recorded. The high-water mark hit 74 inches (187 centimeters), just short of the record set in 1966. This exceptional acqua alta has flooded businesses and historic structures, sank boats, and been blamed for one death so far.

HONG KONG—For months now, I’ve been told that Hong Kong’s protests would end soon. They’ll end when school starts, I heard during the summer. School did start, but the protests wore on, only now I saw high-school students in crisp school uniforms joining the protesters’ ranks. Next, the mask ban of early October was supposed to slow protesters down, but the very first day after that ban, I watched streams of protesters in masks and helmets make their way to their usual haunts on Hong Kong Island.

The government shut down many of the subway lines that day, a practice that has become a de facto curfew, because Hong Kong’s über-efficient subway system is the way most people get around. No matter; the protesters ended up walking, sometimes a lot, and I walked with them, asking some of the same questions I had asked for months: Do you think you will continue protesting? What would it take for you to stop?

On the second day of the impeachment proceedings, President Donald Trump couldn’t control himself on Twitter: He lashed out at Marie Yovanovitch, the former ambassador to Ukraine who was subjected to a smear campaign, and who testified to that effect before the House Intelligence Committee. Trump’s lack of control, in itself, was not unusual. But, for some reason, Trump showed more restraint 48 hours earlier, when William Taylor and George Kent went before the Committee. It was almost as if the president found himself triggered by Yovanovitch, the 61-year-old career diplomat. But why was the president’s response so different to witnesses who were roughly saying the same thing? What was the big difference between Kent and Taylor and Yovanovitch? All three are career diplomats, all three are Ivy League graduates, all three have worked in the State Department, all three are experts in Ukraine. But only one of them is a woman. Could that be why the president singled out Yovanovitch? It is almost as if the president is unable to control his rage against women. It is almost as if the president thinks he can bully women and silence them.

Suppose that the biblical story of Creation were true: God created the universe in six days, including all the laws of physics and all the physical constants that apply throughout the universe. Now imagine that one day, in the early 21st century, God became bored and, just for fun, doubled the gravitational constant. What would it be like to live through such a change? We’d all be pulled toward the floor; many buildings would collapse; birds would fall from the sky; the Earth would move closer to the sun, reestablishing orbit in a far hotter zone.

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Let’s rerun this thought experiment in the social and political world, rather than the physical one. The U.S. Constitution was an exercise in intelligent design. The Founding Fathers knew that most previous democracies had been unstable and short-lived. But they were excellent psychologists, and they strove to create institutions and procedures that would work with human nature to resist the forces that had torn apart so many other attempts at self-governance.

None of the services seems happy with President Donald Trump’s decision to pardon two service members accused of war crimes, and reverse the demotion of a third. The Navy’s reply, however, sets some kind of record of disdain. The Twitter account of the U.S. Navy’s Chief of Information Office wrote on November 15: “As the Commander in Chief, the President has the authority to restore Special Warfare Operator First Class Gallagher to the pay grade of E-7. We acknowledge his order and are implementing it.”

Those icy words breathe the mood of the admonition from Band of Brothers: “We salute the rank, not the man.”

To understand why the Navy—and the other services, too—reacted so negatively to the pardons, here’s a story I heard on a visit to Germany a couple of months ago. I had the chance to talk with a senior U.S. officer in that country.

Joe Biden has fond memories of negotiating with James Eastland, the senator from Mississippi who once declared, “I am of the opinion that we should have segregation in all the States of the United States by law. What the people of this country must realize is that the white race is a superior race, and the Negro race is an inferior race.”

Recalling in June his debates with segregationists like Eastland, Biden lamented, “At least there was some civility,” compared with today. “We got things done. We didn’t agree on much of anything. We got things done. We got it finished. But today, you look at the other side and you’re the enemy. Not the opposition; the enemy. We don’t talk to each other anymore.”