Counting the dead is a paradoxical business. Suppose I told you that around 150 million people have died over the last century in wars, genocides, man-made famines and other atrocities. This number might evoke in you a certain horror. But it is, of course, only a wild guess. Its very vagueness lends it an air of unreality. Yet what purpose would be served by making it more precise? Where mass death is concerned, the moral significance of scale seems to be one of those things that our brains aren't equipped to handle. A single life may have infinite value, but the difference between a million deaths and a million and one strikes us as negligible.

The moral meaning of death counts is further obscured by their apparent lack of objectivity. Take the war in Iraq. How many Iraqi civilians have died as a consequence of the American invasion? Supporters of the war say 30,000, a number that even President Bush finally brought himself to utter late last year. Opponents of the war say more than 100,000. Surely there must be a fact of the matter. In practice, though, there are only competing methodologies and assumptions, all of which yield different numbers. Even if we could put politics aside and agree on one, it would be hard to say what it meant. Does it matter, for instance, that the higher estimate of 100,000 is the same order of magnitude as the number of Iraqi Kurds that Saddam Hussein is reckoned to have killed in 1987 and 1988, in a genocidal campaign that, it has been claimed, justified his forcible removal?

"It is painful to contemplate that despite our technologies of assurance and mathematics of certainty, such a fundamental index of reality as numbers of the dead is a nightmarish muddle," wrote Gil Elliot in his 1972 volume, "The Twentieth Century Book of the Dead." Figuring out the number of man-caused deaths is rarely as straightforward as counting skulls in a mass grave. You can kill people with bombs, guns and machetes, but there are also more indirect ways: causing them to die of starvation, say, or of exposure or disease. (The disease need not be indirect — witness the radiation victims of Hiroshima and Nagasaki.) Of the nearly two million Cambodians killed by the Khmer Rouge, for instance, perhaps half were executed outright. By contrast, in the ongoing civil war in the Congo — the deadliest conflict since World War II — 2 percent of the estimated 3.9 million victims have died of direct violence; the rest perished when their subsistence-level lives were disrupted by the war.

Quantifying man-made death thus means, at the very least, having an idea of the rate at which people die naturally. And that entails recordkeeping. In 17th-century Europe, registers kept by church parishes — dates of baptisms, marriages and burials — made it possible to gauge the devastation caused by the Thirty Years' War, which was deadlier for civilians than for soldiers. The last century, strange to say, has not always matched this level of demographic sophistication. Even in the case of Nazi Germany, supposedly a model of efficiency, the implementation of the Final Solution was so chaotic that the number of victims can be known only to the nearest million.

If our methodology of counting man-made deaths is crude, our moral calculus for weighing the resulting numbers is even cruder. Quantification, it is often thought, confers precision and objectivity. Yet it tells us very little about comparative evil. We feel that Hitler was every bit as evil as Stalin, even though Stalin was far more successful in murdering people (in part because he had a longer run). Mao may have been more successful still; in their recent book, "Mao: The Unknown Story," Jung Chang and Jon Halliday estimate that the Chinese leader was responsible for "well over 70 million deaths," which would come to nearly half of the total number of man-made deaths in the 20th century. In relative terms, however, Mao is easily eclipsed by Pol Pot, who directed the killing of more than a quarter of his fellow Cambodians.

Raw death numbers may not be a reliable index of evil, but they still have value as a guide to action. That, at least, is the common-sense view. It is also part of the ethical theory known as utilitarianism, which holds that sacrificing x lives to save y lives is always justified as long as y is greater than x. This utilitarian principle is often invoked, for example, in defense of President Truman's decision to drop atomic bombs on Hiroshima and Nagasaki, which killed between 120,000 and 250,000 Japanese civilians, on the assumption that the death toll would have been worse had the war been prolonged.

Yet some thinkers (like the British philosopher Elizabeth Anscombe) have questioned whether, morally speaking, numbers really count. In a choice between saving 5 lives and saving 10, they ask, why should we be dutybound to act in behalf of the greater number? Because, you say, it would be worse for 10 people to die than for 5 people. They reply: Worse for whom? Arithmetic misleads us into thinking that deaths aggregate the way numbers do. Yet in reality there are only individuals suffering. In a dilemma where the deaths of one group of people or another is unavoidable, why should someone have to die merely by reason of being in the smaller group?

This sort of skepticism about the significance of numbers has some perverse consequences. It implies that all atrocities have an equal command on our moral attention, regardless of scale.

Yet a refusal to aggregate deaths can also be ethically salubrious. It helps us realize that the evil of each additional death is in no way diluted by the number of deaths that may have preceded it. The ongoing bloodbath in Darfur has, all agree, claimed an enormous number of victims. Saying just how many is a methodological nightmare; a ballpark figure is a quarter of a million, but estimates range up to 400,000 and beyond. Quantitatively, the new deaths that each day brings are absorbed into this vast, indeterminate number. Morally, they ought to be as urgent as those on the first day of the slaughter.

Jim Holt is a frequent contributor to the magazine.