I’ve been reading the fascinating work of Paul Slovic, a psychologist who runs the social-science think tank Decision Research. He studies a troubling paradox in human empathy: We’ll usually race to help a single stranger in dire straits, while ignoring huge numbers of people in precisely the same plight. We’ll donate thousands of dollars to bring a single African war orphan to the US for lifesaving surgery, but we don’t offer much money or political pressure to stop widespread genocides in Rwanda or Darfur.

You could argue that we’re simply callous, or hypocrites. But Slovic doesn’t think so. The problem isn’t a moral failing: It’s a cognitive one. We’re very good at processing the plight of tiny groups of people but horrible at conceptualizing the suffering of large ones.

In one recent experiment, Slovic presented subjects with a picture of “Rokia,” a starving child in Mali, and asked them how much they’d be willing to give to help feed her. Then he showed a different group photos of two Malinese children — “Rokia and Moussa.” The group presented with two kids gave 15 percent less than those shown just one child. In a related experiment, people were asked to donate money to help a dying child. When a second set of subjects was asked to donate to a group of eight children dying of the same cause, the average donation was 50 percent lower.

Slovic suspects this stuff is hardwired. Psychologists have long observed that our ability to discriminate among quantities is finely tuned when dealing with small amounts but quickly degrades as the numbers get larger. Our ears work that way, too. When a very quiet sound becomes slightly louder, we detect the difference right away. But once a noise is really loud, it has to increase dramatically for it to seem “louder.” The same holds true for our judgments of weight and, of course, less tangible quantities like money. We’ll break the bank to save Baby Jessica, but when half of Africa is dying, we’re buying iPhones.

Which brings me back to Gates. The guy is practically a social cripple, and at times he has seemed to lack human empathy. But he’s also a geek, and geeks are incredibly good at thinking concretely about giant numbers. Their imagination can scale up and down the powers of 10 — mega, giga, tera, peta — because their jobs demand it.

So maybe that’s why he is able to truly understand mass disease in Africa. We look at the huge numbers and go numb. Gates looks at them and runs the moral algorithm: Preventable death = bad; preventable death x 1 million people = 1 million times as bad.

We tend to think that the way to address disease and death is to have more empathy. But maybe that’s precisely wrong. Perhaps we should avoid leaders who “feel your pain,” because their feelings will crap out at, you know, eight people.

What we need are more Bill Gateses — people with Aspergian focus, with a direct sensual ability to understand what a million means. They’ve got to be able to envision every angel on the head of a pin. Because when it comes to stopping the mass tragedies of today’s world, we’re going to need every one of them.