WE all can relate to the saying “One death is a tragedy; a million deaths is a statistic.” Our sympathy for suffering and loss declines precipitously when we are presented with increasing numbers of victims. In the 1950s, the psychiatrist Robert Jay Lifton studied survivors of the atomic bombs dropped on Hiroshima and Nagasaki and discovered that a condition he labeled “psychic numbing” enabled them to withstand the psychological trauma of this experience.

Psychologists have since extended Dr. Lifton’s work to show how the concept of psychic numbing has implications in many other situations, such as our response to information about refugee crises, mass extinctions and climate change. This information can be deadening in its abstractness. We struggle to care when the numbers get big. The poet Zbigniew Herbert called this “the arithmetic of compassion.”

How big do the numbers have to be for insensitivity to begin? Not very, it turns out.

Consider the recent death of the Syrian child Aylan Kurdi when his family braved the choppy seas off the coast of Turkey. The image of Aylan lying face down on the beach captivated the world’s attention and even, in short order, resulted in refugee policy changes in countries as far away as the United States. But 14 Syrian children drowned in the Aegean Sea the next day. Did you notice? Did you care?

And even 14 is much higher than necessary to desensitize us. In studies published last year in the journal PLOS One, one of us, Paul Slovic, and colleagues demonstrated that “compassion fade” can occur when an incident involving a single person expands to as few as two people. Participants were asked, in both hypothetical and real situations, to make donations, and to report how they felt about donating, to either a single needy child or two needy children, each of whom was identified with a photograph, name and age. We found that people’s positive feelings about donating declined substantially when the group size was two, and that this decrease was related to lower levels of donations.