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In the late 19th Century, German math teacher Wilhelm von Osten became convinced that animals could do math. To prove this, he took a horse, and taught it to solve basic math equations by pawing the ground with its hooves to represent numbers. One stroke–one. Two strokes–two. Von Osten would take the horse, named Clever Hans, from town to town to tell it math equations, which it would solve to the public's amazement. It turned out, though, that, unbeknownst to von Osten, Clever Hans didn't know math. He merely pawed the ground until his master looked overjoyed, and knew then that he had done his job.
Science has evolved beyond von Osten's famous demonstrations, yet the question rages on. Are animals capable of higher-level thinking? Several studies are proving now that, not only can animals do math, but a lot of them do it on a regular basis.
Dogs Counting Treats
While we may take counting for granted, we must understand that quantification and calculations of this nature are the most basic forms of math, and, in accordance, any animal that can count is mathematically inclined. So the first step in figuring out if animals can do math is to ask "can they count and quantify?"
A 2002 English study done on dogs indicated that, while dogs may not be able to do calculate angular momentum, they can count. The study placed eleven pet dogs in front of a screen. On the other side of the screen sat a doggy bowl with a large treat in it. They would show the dog the treat, then make a big show of placing a single treat in the bowl behind the screen–but, on occasion, slip a third treat in there. The dogs would stare at the bowl, as if confused that the human had put down one extra treat, but two appeared instead.
While this does not for sure prove that all dogs can count, it does indicate that canines in general are capable of quantitive reasoning.
Sedona–a Counting Collie
Another experiment offered even more substantial evidence that canines could count. Krista Macpherson, a professor at Canada's University of Western Ontario in London, performed a well-documented experiment to test canine counting abilities that received some degree of acclaim when she published her results. She took a young collie named Sedona, and set up an interesting experiment. She set up two magnetic screens, and placed an assortment of magnets on the board. Sedona had to knock over the board with more magnets on it to earn a treat. The magnets were of assorted sizes, so Sedona could not judge the boards based only on how much surface area the magnets occupied.
After 700 tests, Sedona had provided Macpherson enough evidence to justify her hypothesis. After some initial issues, Sedona managed to knock over the correct board time and time again–too often for it to be merely random chance. Though Sedona had difficulties telling apart eight magnets from nine, she could time and time again sort out seven from five or three from four. And, more remarkable, Sedona became better at it with each test. Not only could Sedona do math, but she demonstrated that animals can improve their mathematical skills with experience.
In a similar story to the bit about dogs counting snacks, birds have well-documented counting abilities. In experiments similar to the one where scientists gave dogs treats with the expectation that they'd notice when one extra treat slipped in, scientists in New Zealand held a study with New Zealand robins to see if they would notice if a worm went missing in their meal. The experiment tested many things, but one thing of note was how the robins reacted when they received more or less worms than expected. When robins received extra worms, they seemed eager and excited. When they found less worms than expected, they went into a rage.
This indicates more than just comprehensive math skills. This demonstrates that birds are also capable of remembering quantity, and expecting certain numbers to appear at a consistent rate. Pattern recognition is an advanced form of quantitive reasoning. And this isn't like Sedona–a specific animal that did math. This is a species that all can do math.
But it turns out that this is not unusual.
Lions on the Prowl
Lions are territorial creatures. They are known to strike down rival prides in order to spread their dominion across the Savana. Many scientists noted, however, that the lions tend to strike prides smaller than their own. Knowing they had the advantage in numbers, they would strike hard and fast on more susceptible targets.
Karen McComb of the University of Sussex took five Tanzanian lionesses together to perform a little experiment. She placed the lionesses in a faux-environment, and, from behind an underbrush, played the sound of three lions of the same species roaring. The five lionesses, assured of their superior numbers, attacked. The experiment was repeated, and they found that, when the lionesses heard more than five roars, they went on guard. Though the experiment also noted that more than five roars became harder to discern and separate from one another. The experiment was repeated successfully for hyenas, monkeys, and chimps.
This establishes that these creatures are capable of comparative thinking–simultaneously able to compare their own numbers to enemy numbers. So the lionesses used math to assure themselves of militaristic victory. So they can do math...and they can certainly kill.
"Croak math for me"
Frogs do math in order to procreate. Didn't see that one coming, did you? Frogs, most often dismissed as unintelligent amphibians, are capable of counting–and require it in order to reproduce.
Frog species sometimes can look very similar to one another. It's hard for them to find compatible partners to reproduce with just by looking at other frogs in the area. So, instead, the frogs identify each other based on the pulses in their croaks. They can count up to ten, but, based on the number of pulses, frogs can identify compatible mates of the same species.
Bees Count Their Way Home
Ever wonder how bees find their way back to their hives? When worker bees go out to find food, they always seem to know the way back to their location, no matter how far and twisty their path has been up until that point. Surely they look for landmarks, but what kind of landmarks? How so?
A study done by the State University of New York at Stony Brook performed an experiment to uncover the mystery behind this, and found that bees counted landmarks they passed by to find their way home. To test this, they set up multiple tents that the bees would fly past to reach their food. However, the scientists would remove a tent before the bees could fly back–or, in some cases, add an extra tent. The bees had trouble returning back, either traveling too far or stopping short. If four tents sat between them and their goal, they'd travel back four tents–invariably. Which proves they navigated thanks to their mathematical skills.
Guppies Travel for Safety
A 2012 study on guppies found that even guppies–really small fish known for traveling in groups–can do math. And not only can they do math, but, to survive, they need to comprehend math, for, after all, safety comes in numbers if you're a tiny fish in a huge sea.
The study placed individual guppies in an open tank, and tried to see which shoal of fish it would join. Logically, when the whole shoal of fish appeared at once, the guppies would go toward the obviously larger shoal. However, when the fish passed the guppy by one at a time--one by one--the guppy had to count each passing fish on either side. Invariably, the guppy, even when unable to see the whole shoal in one massive unit, could sort out the larger shoal from the smaller one, and joined the larger one. By counting and remembering. For an animal with a brain as small as a guppy's, this is remarkable. It completely revolutionizes everything scientists believed previously about the intelligence levels of such small creatures.
Ai, the Chimp who could Add
Tetsuro Matsuzawa from Kyoto University has spent several years working with a chimpanzee named Ai. This female chimpanzee has spent many years stunning the world with her incredible talent for counting. For several decades now, Ai has sat in front of a monitor, and associated a series of dots with the numeric value representing the quantity of dots. Three dots? She clicks "3." Four? "4." It started with being able to differentiate between "1" and "2," but has evolved into something much more.
This long-term study has proven in so many ways the capabilities of our closest relatives on the evolutionary chain, and how comprehension of math isn't a concept exclusive to humanity. But counting is one thing...animals can do more than just count. They can do math.
Alex–One Smart Bird
For thirty years, a parrot named Alex, property of animal psychologist Irene Pepperberg, stood as the greatest example of avian intelligence observed by scientists. Irene formed a close bond with her bird, and, over the bird's over thirty year lifespan, taught Alex language, reading, and, yes, mathematic skills that no one believed birds could be capable of learning.
Most well-known is Alex's method of counting. Irene would place a group of different colored, different shaped blocks in the cage with Alex, and ask Alex to identify the number of a specific type of blocks. Alex could count up to six. To be able to identify by name different categories of shape and color is remarkable, but to add the number–even more remarkable.
But if that isn't enough, he could also comprehend basic addition. In one of the final studies released about Alex, it was revealed that Alex was capable of addition problems. Toward the end of his life, he could comprehend Arabic numerals up to "8" in the form of giant multi-colored magnets. He performed too well for it to be chance.
Alex was one of a small number of animals who could do math, demonstrating his remarkable ability in public numerous times before his eventual death. This parrot demonstrated a sense of intelligence and meta-cognition unrecorded in avians before. Before dying from heart failure, Alex told his master, "Be good. See you tomorrow. I love you."
Monkeys vs College Students
Perhaps the most definitive proof that animals can do math came in 2007, when a study in Duke University presented a math challenge. They took fourteen college students, and put them in a room with two rhesus monkeys. The two groups both took a number test. A series of dots would appear on a monitor, then be followed by a second number of dots. Then, they would be offered two options to indicate the sum of the prior screens. If the monkeys answered a question correctly, the scientists rewarded them with Kool-Aid.
The college students answered 94% of the questions correct. The monkeys answered 76%.
While this doesn't prove that monkeys are ready to take the ACTs, it did prove that their math skills are similar to a human's capabilities in many results. The processes are not that far apart. While it still remains exceptional, animals are capable of math. We are a far way from the days of ol' Clever Hans, but we still have much to learn.