The Supreme Court is at the start of its new term, and the scene inside the courtroom at 1 First Street is as different from the world outside the building as one could imagine.

Chief Justice John Roberts and the seven associate justices of the Supreme Court understand that this is no ordinary moment, with a vacant court seat and a bitter confirmation battle raging in the Senate and across the country.

And yet, for the past two days, the court’s justices have seemed unusually calm — even compromising. With the court’s liberal-conservative split at 4–4 and the battle still unresolved over whether Judge Brett Kavanaugh will take the ninth seat, for now at least they appear to understand the need to compromise if they are to achieve the five-vote majority required to decide a case.

“God save the United States, and this honorable court.”

With those words on Monday, spoken by the court’s marshal, Pamela Talkin, the new term was underway.

In a simple gesture that took on added meaning given the partisan passions of the moment, Chief Justice John Roberts took a moment before hearing the first case to give a nod to his liberal colleague, Justice Ruth Bader Ginsburg, on the 25th anniversary of her investiture to the Supreme Court, noting, “We look forward to sharing many more years with you in our common calling.”

The cases the justices have heard so far have not been headline-grabbing ones, but the justices’ approach nonetheless was telling. If the court is going to resolve a case to nationwide effect — and doing so is often why the court decides to hear a case — it will have to get beyond the ideological split that has Roberts joined by Justices Clarence Thomas, Samuel Alito, and Neil Gorsuch on the right and Ginsburg joined by Justices Stephen Breyer, Sonia Sotomayor, and Elena Kagan on the left. A 4–4 split, under the Supreme Court’s rules, means the lower court’s ruling stands, but it does not create a national precedent.

What all of that means, in practice, is that if the case involves an ideological split, the only way to resolve it is through a word almost unheard of in 2018: compromise.

The justices’ first case of the term is the type of case that regularly splits along ideological grounds: A private business is challenging environmental regulatory action. The dispute — over the Mississippi gopher frog — centers around the circumstances under which the federal government can designate land as “critical habitat” under the Endangered Species Act.

It was clear on Monday that the court likely was split on those ideological grounds, with Kagan characterizing the issue as a choice between “extinction of the species” and allowing for the “critical habitat” designation even where, as here, improvements would need to be made to the land to make it actually habitable for the frogs, and Alito challenging that assessment by highlighting “other options available to the federal government.”

Later in the arguments, though, Sotomayor challenged the government’s definition of “habitat” and Breyer asked how far the needed improvements would go before they would go too far. The government’s answer then prompted Roberts to weigh in, asking what standard the government would recommend to judge how far is too far.

Even moments of clear disagreement have lacked the sharpness that several of the justices have shown in the past in their dealings with one another — a reality that was all the more clear on Tuesday.

In its second argument on Tuesday, the court considered a case over Alabama’s fight to execute a man whose lawyers say he has severe dementia. The case is the sort that has led Alito and Sotomayor to spar aggressively in the past. In one case a few years back, Alito famously accused opponents of the death penalty of engaging in a “guerrilla war” in their efforts to halt drugs from being sold to states for use in executions, and Sotomayor told the lawyer defending the state that she wasn’t going to believe anything he said until she could read it herself.

In Tuesday’s case, though, Sotomayor engaged in extensive back and forth with the state’s lawyer, and even Alito’s most aggressive questioning was understated. “I am quite confused by the arguments that you’re making,” he at one point told the lawyer for the man on death row, Vernon Madison. Later in the exchange, Alito said, “I don’t think you’re accurately representing what [Madison’s expert witness] had testified, but I don’t want to argue about what the record shows and doesn’t show.”

Throughout Tuesday’s arguments, Roberts — with help from some of his colleagues — appeared to be focusing the discussion on figuring out where the parties actually disagreed and how the case could be resolved. The first issue, he detailed, was whether someone who can’t remember their crime can, on that basis alone, meet the court’s standards for finding a person incompetent to be executed, as established in earlier cases. The second is whether vascular dementia can be the basis for such a claim.

“[T]hat’s why this case strikes me as unusual,” he said. “There are two questions. You concede on one, and the state concedes on the other.” Madison’s lawyer answered no to the first question — saying that more needed to be shown — and the state’s lawyer said yes to the second question — but said that Madison himself did not meet that standard.

When the state’s lawyer, later in the argument, said that “no inmate would ever admit to committing the crime if that meant that he were incompetent,” Roberts stopped him. Noting that Madison’s lawyer already conceded that point, the chief justice said, “I would have thought we can stop arguing about it.”

The justices know their unique role in American life — the decades that they each sit as one of nine voices making final determinations of what the law means. This week — in part a function of their 4–4 split but also likely in recognition of the need for the court to project stability and even-handedness in the face of a contentious nomination battle — the message they have chosen to put forward is one of comity even in disagreement and, perhaps, compromise.