William Rehnquist, the chief justice of the U.S. Supreme Court, announced in October that he had thyroid cancer. John Paul Stevens, the long-serving associate justice, just turned 85. From the outside, it's hard to tell whether they're still able to perform the jobs they hold. But we do have an idea of what the worst-case scenario would look like.

In his last years on the Court, Thurgood Marshall reportedly spent his days telling tales, watching TV, and letting his clerks do the bulk of his work. Slow, feeble, and increasingly deaf, he once embarrassed himself during oral arguments by revealing he didn't realize which side the lawyer he was interrogating represented.

He probably didn't realize it, but he was part of a long Supreme Court tradition. A decade and a half earlier, William O. Douglas closed out his time on the bench by dozing during arguments, addressing people by the wrong names, and speaking in non sequiturs; after his resignation, he continued to show up for work, apparently convinced that he was still on the Court. Joseph McKenna was so incompetent at the end of his term that, in the words of his colleague William Howard Taft, he once "wrote an opinion deciding the case one way when there had been a unanimous vote the other, including his own." Taft stayed on the job a little too long himself: In 1930 Louis Brandeis wrote to Felix Frankfurter that their colleague "had really lost his grip."

This wasn't merely a sad sideshow. In some important cases--notably Bowers v. Hardwick, the infamous 1986 decision that upheld Georgia's sodomy law--an incapacitated judge (in that case, Lewis Powell) actually cast the deciding vote.