She is the nation's top female judge, a former ACLU lawyer who embodies the women's liberation movement of the 1970s.
He is a die-hard conservative who helped found the Federalist Society and who personifies the Republican effort to remove judges from America's social debates.
From the bench, she speaks in a slow, measured voice. Her hypothetical questions about lawyers feature a generic "she," not the conventional "he."
He is brash, fast-talking and wise-cracking. He could never be accused of being politically correct.
Yet this New Year's Eve, as they have done for more than two decades, Justice Ruth Bader Ginsburg and Justice Antonin Scalia will join with their spouses and another couple or two at the Ginsburgs' large Watergate apartment. After the caviar and wine, they may dine, as they have in the past, on something Scalia has bagged on one of his hunting trips.
A few days after they have toasted 2008, Ginsburg and Scalia will be back on the bench hearing cases involving voter-identification rules and the death penalty.
They are likely to be — once again — miles apart in their views.
The friendship of Ginsburg and Scalia, unlike that of any other pair of justices in recent times, has intrigued — and mystified — observers for nearly three decades.
"They are totally different people," says Washington lawyer Theodore Olson, who has joined their dinner in recent years and will again this year. "But they have a very comfortable relationship. They respect each other's intellect. They both love music and opera."
During Ginsburg's confirmation hearings in 1993, senators asked about her bond with Scalia. Democrats seemed to fear that he might influence her.
Sen. Herb Kohl, D-Wis., prefaced his questions by repeating a well-known story of the day: As President Clinton was considering various liberals for the court, one of Scalia's law clerks asked him whether he would rather be stranded on a desert island with Harvard University law professor Lawrence Tribe or former New York governor Mario Cuomo.
Scalia responded, "Ruth Bader Ginsburg."
Kohl asked Ginsburg whether she similarly would like to be stranded with Scalia and, more important, whether she shared his views.
"I can say one thing about Justice Scalia," Ginsburg replied. "He is one of the few people in the world who can make me laugh, and I appreciate him for that."
As to whether liberal Ginsburg joined Scalia on the right: not at all. Neither did Scalia move left. They have stayed ideological opposites.
Abortion rights? She's for. He's against. School integration plans? She's for. He's against. Affirmative action on campus? She's for. He's against. Even on legal questions that do not make the front page of newspapers, they often are at odds.
Last term, she disagreed with Scalia 52% of the time in non-unanimous cases, according to SCOTUS blog, a website run by the Washington law firm Akin Gump that tracks such data. The only justice she disagreed with more was Clarence Thomas, 55% of the time. Ginsburg disagreed with fellow Clinton appointee Stephen Breyer 13% of the time in non-unanimous cases.
Beyond the law, Ginsburg and Scalia seek each other out.
"I have always enjoyed Nino," Ginsburg said in an interview, echoing her comment at the hearing: "No matter how overworked and tired I feel, he can always say things that make me laugh. He can also say things I find provocative, even irritating."