# Dogs Understand Math, Sort Of

Give a dog its choice of a single treat or a whole handful, and it’ll go for the latter every time. It’s simple dog math: More treats equals better.

Not so simple, though, is the question of what more means to a dog: Can they understand quantity in terms of numbers? It’s easy to tell the difference between one treat and five, but what if the ratio were, say, three to four?

As Susan Milius recently wrote for Science News, a small but growing body of research suggests that dogs do have something like number sense. In one 2002 study, for example, the authors showed a dog a single treat in a bowl, then either pretended to drop in a second one or actually did it for real; when they showed the bowl again, the animals stared at it longer if things didn’t add up — if they’d seen the second treat added, and yet there was just one in front of them. The same thing happened when the authors snuck in an extra treat, and the dogs saw three when they were expecting two.

As Milius noted, though, it’s possible that the dogs were responding to something besides the numbers:

Dogs could in theory recognize funny business by paying attention to the number of treats — or the treats’ “numerosity,” as researchers often call a quantity recognized nonverbally. But, depending on the design of a test, dogs might also get the right answers by judging the total surface area of treats instead of their numerosity. A multitude of other clues — density of objects in a cluster, a cluster’s total perimeter or darkness and so on — would also work. Researchers lump those giveaways under the term “continuous” qualities, because they change in a smooth continuum of increments instead of in the discrete 1, 2, 3.

To determine whether something else was going on, Krista Macpherson, a psychology researcher at the University of Western Ontario who studies dog cognition, devised a slightly different study: In 2013, she trained her collie to scrutinize two magnetic boards and knock over whichever one had more geometric magnets stuck to it. In a paper published earlier this year, researchers unaffiliated with the study called it “only evidence of dogs’ ability to use numerical information.” It’s small, but it’s something — at the very least, it’s an indication that those “wet-nosed conundrums,” as Milius put it, can grasp something kind of like counting, even if they have no concept of numbers themselves.