Babies Bamboozled by Numbers

What’s so hard about four?


Listen to a narrated version of this essay:

Most of the time, when I am blindsided by a seemingly perplexing psychological phenomenon—prephonological spelling, for instance, or the downside of social intelligence—it doesn’t take more than a day’s research to convince me that said phenomenon makes sense after all, at least on some level, at least well enough to write about. I often come away questioning whether it was really that surprising in the first place.

But it’s safe to say that babies and numbers—specifically one-year-olds and the number four—are an exception. What am I talking about? In studies published in 2003 and 2005, Lisa Feigenson of Johns Hopkins and Susan Carey of Harvard brought 12-to-14-month-old infants into a lab for a manual search task. The infants first watched as an experimenter placed one Ping-Pong ball at a time into a box. “Look at this!” the experimenter said. “What’s in my box?” The babies, who, thanks to the presence of a spiraling ball chute, were pretty motivated to retrieve the balls, subsequently reached into the box themselves to pull them out.

Except, this being an experiment, the box also had a hidden slit in the back. Thus, after depositing the balls, the experimenter could remove any number of them without the baby being any the wiser. The researchers were interested in whether an infant who had watched three balls enter the box, but could only retrieve two, would scour the box for a longer period of time than if he’d been able to retrieve all three. This would suggest he was able to mentally represent three individual objects.

Indeed, the babies did demonstrate increased scouring time (by about one to two seconds) in conditions where “balls entered” did not match “balls retrieved.” But this pattern of results only held when the experimenter deposited two or three Ping-Pong balls. When she deposited four, infants lost all expectations about how many balls would be in the box. Incredibly, they searched no longer after retrieving two balls than after pulling out four. They searched no longer after retrieving one ball than after four: yes, they showed no understanding that four is even plural.

What could possibly be going on? Psychologists believe that humans (and other animals) represent small and large numbers of objects in fundamentally distinct ways. In smaller numbers, objects are represented individually. But in larger numbers they cannot be; instead they’re lumped together and treated approximately (and can be differentiated from other lumps of objects only if they differ in magnitude by a certain age- and species-dependent ratio). One-year-old humans are able to individually track three, but not four, objects. For older children and adults, incidentally, this increases to about four. (Though most of us can also count, which lets us cheat at tasks like this.)

Still, I’ve never come across a satisfying explanation for why infants don’t simply cease to update their representation when the numbers get too big: Why don’t they just max at three? Why does “too many to track” mean “couldn’t say if it’s plural?” If anyone has a hypothesis, I’d be happy to hear it. If you happen to study numerical cognition, I’d be especially happy.

Permission required for reprinting, reproducing, or other uses.

Jessica Love holds a doctorate in cognitive psychology and edits Kellogg Insight at Northwestern University’s Kellogg School of Management.


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