From Thomas Malthus to Paul and Anne Ehrlich, authors of “The Population Bomb” (1968), population doomsayers have endured ridicule and vilification, largely because their predictions of imminent doom fail to materialize on schedule. In our own time, there are a few mitigating indicators. Much of the current population growth comes in the developing world, where carbon consumption remains low, so the environmental effect is relatively muted. The next thousand Americans will do more than twice as much damage as the next hundred thousand Nigeriens, though that is hardly a cause for celebration.

Perhaps more significantly, the global fertility rate has declined every year since 1965, from nearly five births per woman to 2.4. The problem is that anything above 2.33 — the rate at which births equal deaths, when child mortality is ­factored in — will yield a population expansion. Even when fertility drops below the ­replacement rate, it will take decades for the population to begin to decline. At today’s rate, world population would stabilize at 10 billion by 2100. But that will most likely never happen, Weisman writes, because seven billion people “are already turning the atmosphere into something ­unlivable.”

The grim prophecies are illustrated with statistics. Each year the world adds the equivalent of another Germany or Egypt; by 2040, China will have more than 100 million 80-year-olds. We add another million people every four and a half days. But statistics fail to tell the entire story. Weisman’s problem — and the problem of all those who warn about overpopulation or, for that matter, the correlative dangers of ecological devastation — is a problem of imagination. Not Weisman’s imagination. Ours. As one scholar says in “Countdown,” “most people’s minds go blank after 100,000.” Large numbers are difficult to visualize. Numbers are even more difficult to feel.

Metaphors bring us closer. Over the course of the book, man is likened to a cancer; to “a voracious monoculture” that sucks “resources in at the cost of the rest of life on the planet”; and to the mule deer of Arizona’s Kaibab Plateau, an example of a species once “doomed to ­overpopulate.”

But the book’s most indelible image comes from Weisman’s visit to Japan, where the fertility rate is so low — 1.4 children per female — that the population has been declining since 2006. This might make Japan something of a best-case situation, but an aging population means there are too many senior citizens, and not enough young people to take care of them. Already Japan has a shortage of geriatric nurses. Weisman visits Nagoya Science Park, where Japan’s oldest scientific firm has built RIBA II, a robotic white bear designed to carry elderly people around the house. It has large, widely-spaced black eyes, cute little ears and a painted smile.

“I will do my best,” says the bear, as it approaches a man who is lying on a hospital bed. “I will carry you as though you were a princess.”

RIBA II slides one paw under the patient’s knees, the other beneath his back. The robot cradles the man in its arms. It carries the man across the room, and lowers him tenderly into a wheelchair.

“I’m finished,” announces RIBA II, and it’s hard not to wonder whether the robot speaks for us all.