In such cases, new justices have mostly rewritten the work of their predecessors. It’s far more rare for a single judge to acknowledge that he has changed his thinking, and even rarer for him to reverse his own opinion, rather than quietly joining someone else’s. The exceptions — judges who shift position and explain why — tend to be those who think pragmatically and empirically. They’re checking and rechecking their assumptions against the facts as they develop on the ground. We often think of appellate judges as being bound by the specific facts of a case, on one hand, and statutes, prior rulings or abstract principles on the other. But there can be other relevant evidence out in the world. That sort of evidence was pivotal in a Supreme Court shift in the 1940s. At the onset of World War II, the Supreme Court allowed public schools to demand that all students recite the Pledge of Allegiance and salute the flag. Emphasizing the value of “national cohesion,” the court rejected the religious freedom claims of Walter Gobitis, who said the schools were asking his children to violate their faith as Jehovah’s Witnesses by ascribing salvation to an earthly emblem. But after the decision, mobs attacked Jehovah’s Witnesses and burned their places of worship, and schools expelled children who refused to recite the pledge and salute the flag.

By 1943, when a similar case came to the court, three justices — Hugo Black, William O. Douglas and Frank Murphy — voted with a new majority to overturn the 1940 ruling. Writing to explain “the reasons for our change of view,” Black and Douglas said the nation’s war effort did not “depend on compelling little children to participate in a ceremony which ends in nothing for them but a fear of spiritual condemnation.” Seeing the concrete effects of the law, the justices treated the principles at stake not as absolute, but as pliable.

Judges sometimes weigh other kinds of evidence, too: academic research (in Brown, the court cited a study about the harmful effects of segregation on black children); or the mounting impact of public opinion (a likely factor in the forthcoming same-sex-marriage rulings, whether or not the court says so). In a sense, an empirical approach turns judging itself into a form of social science. “Scientists constantly test their hypotheses against an ever-­expanding body of knowledge,” Martha Minow, the dean of Harvard Law School, told me. “Progress depends on trial and error. Is that what judging is too?”

The question is especially relevant now because of the kinds of disputes the courts are being asked to resolve. Advances in fields like computer science, electrical engineering and biochemistry are introducing new complexity into litigation. “The way we think about intellectual property may not stay the same,” Minow says, citing one example. “Or free speech in the context of social media.” One question raised by a Supreme Court case this term is whether threats on Facebook are as dangerous as in-person threats.

At this moment in Washington, with the Democratic and Republican Parties increasingly polarized, and the president and Congress repeatedly deadlocked, President Obama has used executive orders to make policy on immigration, climate change and the rules of the road for the Internet. In response, his opponents have accused him of overstepping and have turned to judges to stop him.

As those disputes play out in the lower courts, the Supreme Court is about to determine the fate of the Affordable Care Act and a new method of lethal injection, as well as same-sex marriage. Next term, the meaning of “one person, one vote” is on the docket, and abortion and affirmative action may be as well. Advocates on the right and the left are asking the courts to referee the country’s biggest social battles and reverse old rulings. Can states require abortion providers to have admitting privileges at a local hospital if this practice is not correlated with better care for patients? If a college-admissions system disadvantages Asian-Americans as well as white students, is it unconstitutional? The pleas for judges to change the law, in the face of new evidence, are coming from all sides.

David L. Bazelon, my grandfather, was one of the rare judges who publicly reversed himself on one of the biggest decisions of his career. The case involved a man named Monte Durham, who, after a long history of psychiatric illness and hospitalization, was charged in 1951 with breaking into a house. During his trial, he said he was not guilty by reason of insanity. The standard test at the time, which dated from the 19th century, set a high bar: A court had to find that a defendant didn’t know right from wrong or had given way to an “irresistible impulse.” Durham was convicted.