Dogs Not Great at Math (Wolves Are Better)

By Elizabeth Preston | December 19, 2014 9:40 am


Even a brilliant dog may not be able to count as high as the number of feet she has. In a cheese cube counting challenge, dogs struggled to prove they have any number sense at all. Embarrassingly for the dogs, some wolves took the exact same test and passed it. This may be a hint about what dogs lost when they moved to a cushy life of domestication.

At the Wolf Science Center in Austria, Friederike Range and her colleagues raise both wolves and dogs by hand, then train them to take part in cognition research projects. Their interest in canine counting skill isn’t totally trivial. In nature, a little bit of number sense might help animals choose the best food source or hunting spot. It also helps to know whether another pack of animals is bigger than yours before getting in a fight.

If dogs have any grasp of numbers, they should be able to judge two sets of food items—say, three versus four Milk-Bones—and pick the bigger snack. Earlier research found that dogs are OK at this, but only if they can see both food piles. This means they might just be judging which pile takes up more space, not the actual amounts.

One way to get around this is to drop food items into opaque containers, one by one, while a dog is watching. If the dog understands numbers, it should know which container you dropped more food into. (For low numbers, anyway. No one’s asking a dog to count to 100, or even 10.) But if the dog can’t count, the opaque containers should stump it. A 2013 study found that dogs failed this kind of test.

The Wolf Science Center researchers decided to try a counting experiment with both wolves and dogs. Like a canine math league meet, they’d pit the two species against each other.

First they had to chase off the ghost of Clever Hans, a German horse who haunts all animal cognition research. Hans gained fame in the early 20th century for his apparent mathematical genius. In the end, it turned out the horse had been merely reading his handler’s body language to judge when he reached the right answers.

Range and her colleagues set up an elaborate experimental apparatus to prevent dogs and wolves from getting any human hints. When a researcher stood behind it, the device hid her whole body. She looked out at the dog through a slit, but wore sunglasses just in case the animal saw her eyes.

dog setup

While a dog or wolf watched, an experimenter extended her hand through a hole and dropped some number of Gouda cubes into an opaque tube below. The number was always between one and four cubes, and she held up her empty hand afterward. She repeated this in a second tube, with some other number of cubes between one and four. Then the dog or wolf had to step on a buzzer to show which side had more cubes. If it chose correctly, those cheese cubes dropped out for the animal to eat.

The study’s 10 wolves passed this test for every possible ratio of cheese cubes. They chose correctly between two and four cubes, three and four, two and three, and so on. The wolves weren’t perfect, but they got the right answer more often than not. Dogs, on the other hand, only passed the test when one tube had at least twice as much cheese as the other.

The animals couldn’t judge the cheese piles by size, but it was still possible they were getting clues without counting. They might be keeping track of the time it took to drop the cheese cubes, for example. So the researchers tried the test again, spacing out the smaller numbers of cheese cubes so they took the same amount of time to drop as the larger numbers. They also tried adding rocks to the experiment: an experimenter dropped the same number of items on each side, but some of the items were small stones, and the dog still had to pick the side with more cheese.

Even with these controls in place, wolves picked the correct side more often than not. But dogs failed. They performed no better than if they’d been guessing.

This was a small study, with only 8 dogs participating, but the results agreed with previous studies. And the researchers actually started out with 13 dogs. One was eliminated because it couldn’t figure out how to work the buzzers. The other four failed out of training because they couldn’t choose between one cheese cube and four cheese cubes in plain sight. So those dogs aren’t making a strong case for dog math skills, either.

The researchers think that when humans domesticated wolves, we may have taken away certain evolutionary pressures on their brains. With us sheltering and feeding them, it was important for dogs to be hyper-smart socially; other cognitive skills may have faded. Earlier research at the Wolf Science Center suggested that dogs may also be worse than wolves at learning things from each other.

Dogs may have lost their wolfish number sense when they moved in with humans. On the other hand, they gained the opportunity to eat cheese. Who’s smart now?

Images: top, Kimberly Martin-Sprickman (via Flickr); bottom from Utrata et al. (2012).

Range F, Jenikejew J, Schröder I, & Virányi Z (2014). Difference in quantity discrimination in dogs and wolves. Frontiers in psychology, 5 PMID: 25477834

  • zlop

    Malamutes are considerably more aware than regular dogs. The house mutt excels in paying attention to you, without trying to count.

    • Racer X

      I was wondering if dogs would perform differently by breed.

      • zlop

        My guess, Malamute Huskies are the toughest and smartest. I used to take one along for protection, while camping. It would chase the bears away. Dominated a German Shepherd.

        Supposedly, about 15% are in the wild and interbreed occasionally, with the domesticated Malamute Huskies.

  • Vincent A Kennard

    Fascinating stuff..

  • Uncle Al

    Hold out your hands, Many people can uniquely count to ten in one pass using their thus displayed fingers. If you cannot uniquely count to 1023 in one pass, you are the dog not the wolf. Answering questions is simple. Thinking is not simple.

    • Jack McCauliffe

      Far more is revealed about the idividual casting aspersions than those who may or may not be familiar with binary counting systems.

      • Uncle Al

        If not familiar, invent it. Social advocacy tells us that objective intelligence does not exist, cannot be measured, and makes no difference. Its absence does exist, can be measured, and makes a huge empirical difference – as above.

        • Jack McCauliffe

          Social advocacy tells us that objective intelligence does not necessarily correlate to success, well-being or happiness for the individual, or society.

          • Uncle Al

            Parse the White House any way you like re recent US unconditional surrender to North Korea.

            This article shows discrete quantitation is very different form “keeping a journal ” or “telling stories,” or any other excuse for being innately or voluntarily smartless. If you beleve Intelligence is interchangeable with stupidity, you are successfully arguing against yourself.

          • Marge

            So what kind of dogs were in this study? Beagles or Border collies? We have selected to strengthen certain traits and diminish others as dogs diverged from wolves. Just curious as these two breeds, as examples of this selection, would perform most tests very differently, I think.

          • Elizabeth Preston

            The dogs at the Wolf Science Center are all mixed-breed.

          • Hard–Truth

            Incorrect. High correlation between intelligence and success. Terman’s longitudinal study proved that long ago.
            (Stupid people do not win Nobel prizes in physics.)

  • larrybudwiser

    My dog can drive an SUV and paint with watercolors. He speaks French, Yiddish and Manderin

    • connie

      Hopefully he can SPELL Mandarin, too

      • TecumsehUnfaced

        Only when larry shares his budwiser.

  • daqu

    “. . . the dog or wolf had to step on a buzzer to show which side had more cubes.”

    This does not strike me as the best experimental design in order to conclude that dogs can’t count as well as wolves.

    It is not clear at all what the dogs may be using to make their “choice”. It may well be just their sense of smell. It would be easy to believe that dogs sense of smell has deteriorated since domestication, if they don’t need to hunt their own food. Maybe the dogs and wolves are both trying to go by which side smells better (stronger).

    If that is the case — and I don’t see how to exclude that possibility — then this experiment has not shown anything about dogs’ or wolves’ counting abilities.

    • Elizabeth Preston

      The authors did address the question of smell. They thought it was probably not a confounding factor for a few reasons: they didn’t clean the tubes between trials, so both tubes would have smelled strongly of cheese; another study showed that dogs used their sense of smell in a visual task more than wolves did; etc.

      You can read the whole paper here:

  • CR

    But they learn from us, know how to train and manipulate us into giving them what they want (cheese!), thus creating a billion dollar pet economy with their innate and learned charms, and clearly express a wide range of empathetic emotions that resemble our own. Dogs are multicultural and bilingual, understanding both dog and a select range of human communication.(just don’t discuss algebra concepts with your dog, he’ll get bored and fall asleep, you know, just like teenagers).

  • Jean Guarr

    Interesting. I’m going to try a variation of this with my dogs. I did something similar with a cat, years ago, and catnip mice. She could count up to 7, but after that became confused. I’m aware that smell could have been involved and not just counting skills, and of course I didn’t have an experimental setup. Her brother, BTW, refused to play the counting game and just attacked the mice . . . .

  • Henry Smallwood

    I wonder if dogs lack the ability to focus on numbers of food items, since they always eventually “get the cheese,” and if they want more, use their social skills to influence us to feed them again. Would their apparent cognitive deficit be less if they were counting those who they consider members of their dog family, beings who are important to them and not directly replaceable later? And if they can do a head count, do they tally the overall number of members or check their mental inventory against each individual present (or missing?) Whatever else we can say for them, dogs know how to get us to talk and think about them.

  • JR

    I wonder if a street dog or feral dog would fare better.

    Why is the language so vague ? Dogs ‘performed no better than if they’d been guessing’ – meaning say, 50% right – while wolves
    ‘got the right answer more often than not’ meaning what, 51% ?

    • Elizabeth Preston

      These dogs live in packs with other dogs, so cognitively I wouldn’t think they’d be too different from street dogs. They’re not sitting in laps and being fed table scraps.

      As for the numbers, it depends which part of the study you’re looking at. In both the experiment that was controlled for time (spacing out the smaller numbers of cheese cubes) and the one with rocks mixed in, wolves got 67% correct and dogs got around 50%. Statistical tests said that the dogs may as well have been guessing, but that wolves’ results differed significantly from chance.

  • Don’t Even Try It!

    Maybe the dogs weren’t as hungry as the wolves< therefore didn't fare as well in this test ;-]

  • nik

    Perhaps dogs just dont like cheese?

  • Overburdened_Planet

    Interesting article, which reminded me of this study regarding the differences between dogs and wolves:
    “Dogs’ unusual ability and motivation to observe, imitate, and communicate with people appears to be with them from birth. Two years ago, Csanyi’s graduate students were given either a puppy or a wolf cub to raise. They fed the animals by hand, coddling and doting on them.

    At five weeks, each cub was placed in a room containing an adult and the student who had raised the cub. Both sat motionless. But while the wolf cubs merely sniffed both humans before climbing into the student’s lap to sleep, the puppies yipped at their caregivers, licking their hands and trying to establish contact.

    Three months later, the canines were given the opportunity to try to remove a piece of meat from under a cage by pulling on a rope in the presence of their caregiver. Dogs and wolves both mastered this promptly. Then the rope was anchored, making it impossible to obtain the meat. The dogs tried a couple of times, then turned to their masters for assistance or cues. The wolves ignored their caregivers, yanking on the rope until exhausted.

    “The wolves … were only interested in the meat,” notes Miklosi. “The dogs were of course interested in the meat, but knew that one way to get it might be to figure out what the human wants them to do.”

    To Csanyi, this proves that dogs have acquired an innate ability to pay attention to people, and thus to communicate and work with them. This is a skill that wolves don’t assume even when raised from birth to learn it.

    Dogs are “very motivated to cooperate with and behave like people,” says Csanyi. “That’s why dogs can do things no other animal can do.”

  • Great First Sentences

    But, when a dog gives birth to more than 4 pups, does she regularly forget one pup?



Like the wily and many-armed cephalopod, Inkfish reaches into the far corners of science news and brings you back surprises (and the occasional sea creature). The ink is virtual but the research is real.

About Elizabeth Preston

Elizabeth Preston is a science writer whose articles have appeared in publications including Slate, Nautilus, and National Geographic. She's also the former editor of the children's science magazine Muse, where she still writes in the voice of a know-it-all bovine. She lives in Massachusetts. Read more and see her other writing here.


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