The professor, who is writing a book on capital punishment, has learned that convicted murderers have their own moral calculus for determining the worst among them.

He also writes that "I think both the profession and subjects have paid a high price for our easy acceptance of Malcolm's moral calculus."

Perhaps most important, his moral calculus never lapses into Q.E.D.

In a meticulous moral calculus, Mr. Singer measures the president's deeds against his words.

The moral calculus involved was indeed extraordinarily complex.

"I needed to go through the moral calculus," he told me.

"Suddenly," he said, "It seemed important to talk about a moral calculus."

The moral and strategic calculus was incontrovertible: the preservation of a great man had to take precedence over the destruction of an evil one.

In any case, the moral calculus requires supplementation by another sort of tool - to wit, weaponry.

Aid workers, who are doing heroic work in Darfur, face another painful moral calculus.