Animals Can Count and Use Zero. How Far Does Their Number Sense Go?

An understanding of numbers is often viewed as a distinctly human faculty — a hallmark of our intelligence that, along with language, sets us apart from all other animals.

But that couldn’t be further from the truth. Honeybees count landmarks when navigating toward sources of nectar. Lionesses tally the number of roars they hear from an intruding pride before deciding whether to attack or retreat. Some ants keep track of their steps; some spiders keep track of how many prey are caught in their web. One species of frog bases its entire mating ritual on number: If a male calls out — a whining pew followed by a brief pulsing note called a chuck — his rival responds by placing two chucks at the end of his own call. The first frog then responds with three, the other with four, and so on up to around six, when they run out of breath.

Practically every animal that scientists have studied — insects and cephalopods, amphibians and reptiles, birds and mammals — can distinguish between different numbers of objects in a set or sounds in a sequence. They don’t just have a sense of “greater than” or “less than,” but an approximate sense of quantity: that two is distinct from three, that 15 is distinct from 20. This mental representation of set size, called numerosity, seems to be “a general ability,” and an ancient one, said Giorgio Vallortigara, a neuroscientist at the University of Trento in Italy.

Now, researchers are uncovering increasingly more complex numerical abilities in their animal subjects. Many species have displayed a capacity for abstraction that extends to performing simple arithmetic, while a select few have even demonstrated a grasp of the quantitative concept of “zero” — an idea so paradoxical that very young children sometimes struggle with it. In fact, experiments have shown that both monkeys and honeybees know how to treat zero as a numerosity, placing it on a mental number line much as they would numerosity one or two. And in a paper published in the Journal of Neuroscience in June, researchers reported that crows can do it, too.

The fact that those three species are from diverse taxonomic groups — primates, insects and birds — suggests that certain numerical abilities have evolved over and over again throughout the animal kingdom. Scientists are puzzling over why nature has gifted so many animals with at least a rudimentary knack for numbers, and what if anything that might tell us about the deep origins of human mathematics. There are still more questions than answers, but neuroscientists and other experts have learned enough to amend and broaden perspectives on animal cognition. Even in “tiny brains like those in bees or even ants,” said Brian Butterworth, a cognitive neuroscientist at University College London and author of the forthcoming book Can Fish Count?, “there is a mechanism that enables the creature to read the language of the universe.”

A Competence for “Number”
Nearly 120 years ago in Berlin, a horse named Clever Hans attained celebrity status: He could seemingly do arithmetic, tapping out the solutions to addition, subtraction, multiplication and division problems with his hoof. But a psychology graduate student soon realized that the animal was really just paying very close attention to subtle behavioral cues from his trainer or audience members who knew the answers.

The incident entrenched a skepticism about animals’ numerical capabilities that persists today. Some researchers, for example, propose that while humans have a “true” understanding of numerical concepts, animals only appear to be discriminating between groups of objects based on quantity when they’re instead relying on less abstract characteristics, like size or color.

But rigorous experiments during the past two decades have shown that even animals with very small brains can perform incredible feats of numerical cognition. One mechanism common to all of them seems to be a system for approximating numerosity that’s correct most of the time but is sometimes imprecise in specific ways. Animals are most effective, for instance, at distinguishing numerosities far apart in magnitude — so comparing a group of six dots to three dots is easier than comparing six to five. When the difference between two numerosities is the same, it’s easier to deal with smaller quantities than larger ones: Discriminating 34 items from 38 is much more difficult than discriminating four from eight.

Those strengths and weaknesses were reflected in animals’ neural activity. In the prefrontal cortex of monkeys, researchers found neurons that were selectively tuned to different numerosities. Neurons that responded to three dots on a screen also responded weakly to two and four, but not at all to more distant values, such as one or five. (Humans demonstrate this approximate sense of quantity, too. But they also associate numerosities with specific number symbols, and a different population of neurons represents those exact quantities.)

That observation seems to imply that a “sense” of number is innate and deeply rooted in the brains of animals, including humans. “Underlying the sense of number, there is a very ancient, fundamental psychophysical law,” Vallortigara said.

Once “you realize that almost every animal, or maybe even every animal, has some ability to do a numerical task, then you start wanting to know … what’s the threshold? What’s the limit?” said Scarlett Howard, a postdoctoral research fellow at Deakin University in Australia who studies numerical cognition in honeybees. If animals had this natural, hard-wired ability for telling quantities apart, scientists wanted to determine what other abilities might emerge with it.

First up was arithmetic. Several species have demonstrated that they can essentially add and subtract. In 2009, researchers led by Rosa Rugani, a psychologist and Marie Skłodowska-Curie Actions global fellow at the University of Padova in Italy, found that when newly hatched chicks were presented with two groups of items on which they had imprinted, the days-old birds tended to approach the larger group. Then the team obscured the groups of objects with screens, and moved some of the items from behind one screen to the other while the chicks watched. No matter how many items were moved, the chicks consistently chose the screen that hid more of them. They seemed to be performing computations akin to addition or subtraction to keep track of each hidden group’s changing numerosity. No training was required for them to do this. “They deal spontaneously with these kinds of numerosities,” Rugani said.