The conservative confabs are what the corporate world calls “team-building exercises.” They are, by design, circles of self-reinforcement and mutual affirmation, where the same familiar gospels — of low taxation, deregulation and strict construction — are preached, and where the high priests of American law sometimes deliver homilies. “We are focused on defending liberty,” Justice Thomas said in a recent speech to conservative law students, aligning himself with his wife and “the people around me.” In an obvious reference to the health care law, Justice Thomas wondered aloud whether the “fundamental changes that are going on now” were “reversible in any way.” He conceded that he did not know, but added that “they’re so big” that he thought it was worth trying.

Comments like these raise an important, if somewhat metaphysical, question: if a justice delivers a speech to conservative law students and virtually nobody else listens, does he make a sound? Judge Richard A. Posner, of the United States Court of Appeals for the Seventh Circuit, in Chicago, is not so sure. “The justices’ antics do little harm — or good,” he wrote recently. He cited a paradox: “The justices have become more public,” he said, “... without being much noticed by the public.” A recent Pew Research Center study called “The Invisible Court” — a title that speaks for itself — confirms that view, revealing (if this counts as a revelation) that most Americans cannot name the man now serving as chief justice.

All the same, the justices live in an era of increased scrutiny. Outside the Spectator dinner, Justice Alito was accosted by a blogger with a camera phone shooting video. “It’s not important that I’m here,” the justice said. There will surely be more of this, coming soon to the screen in your hand. And appearances have consequences. It’s not for nothing that “the appearance of impropriety” is a core ethical standard in the code of conduct for United States judges — that is, all federal judges other than Supreme Court justices, who are ostensibly exempt from its strictures. The test in the code is not whether an activity is actually improper; it is whether “reasonable minds” might think that it is. And reasonable minds could well conclude it improper for a justice to bestow his imprimatur on a gathering that aims to drive a political party into oblivion.

We are not naïve. Americans no longer imagine, as a renowned lawyer insisted in 1932, that “the Supreme Court is above and beyond politics.” We do not ask our justices to retreat into a monastery or convent and take a vow of silence. All of us gain something meaningful from their willingness to engage with the public. Presumably the justices do, too, albeit less so when they step from their judicial chambers into echo chambers like the Koch or Spectator events, trading one kind of isolation for another — physical for intellectual.

The public’s faith in the rule of law depends, to no small degree, on the idea that judges try, as best they can, to maintain a judicial temperament — that they keep a certain distance from public and even private events that appear, in the truest sense of the word, partisan, and that they maintain an open mind. Not a blank mind, devoid of a judicial philosophy, but an open mind — a certain receptiveness to reason, argument and fact. It’s not that we need justices without political impulses; we need justices who can keep them in check. “We need to believe in Santa Claus a little bit,” said a former Supreme Court clerk, “and these guys aren’t making it easy.”

During this past term, editorial boards, law professors and others have come forward with proposals to curb the court in various ways — changing the guidelines for recusal, for example, or holding justices accountable to the code of conduct. Whatever their virtues, none of these ideas are likely to take root. For more than a century, every meaningful attempt at Supreme Court reform has collapsed, and not for lack of ingenuity. The founders gave us a court that makes its own rules. As Justice Harlan Fiske Stone wrote in the 1930s, sternly rebuking some of his brethren, “the only check upon our own exercise of power is our own sense of self-restraint.”

In the face of criticism, the court’s conservatives may be doubling down. Justice Thomas, in particular, has lashed back, refusing to disclose activities and relationships that have been called into question. Stone’s admonition, clearly, is as relevant as ever. Over its history, the Supreme Court has faced periodic threats to its legitimacy and has survived with its powers intact, thanks in large part to its public esteem. At some point, another challenge will come. And the court, next time, may find fewer Americans on its side if its members allow themselves to be perceived, in Justice Breyer’s words, as “junior-varsity politicians” who possess, but do not merit, the last word.