Animals Can Count. What is their number? Do you want to go?

Recent evidence has shown that crows can understand the concept zero. This is just the most recent evidence that animals are capable of numerical abstraction.

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.

However, this is not true. 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. While some ants track their movements, spiders track how many prey they have caught within their web. A particular species of frog bases their entire mating ritual upon number. If a male calls, it will sound like a pew with a short pulsing note known as a chuck. His rival then responds by adding two more chucks to his call. After the first responds, the second replies with three and then four. This continues until they are exhausted.

Scientists have found that almost every species of animal, including insects, cephalopods and amphibians, reptiles, birds, and mammals, can distinguish between the different objects or sounds within a given sequence. Not only do they have the ability to sense “greater than” and “less than”, but also an approximate sense for quantity. For example, two objects are distinct from three while 15 is different from twenty. 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.

Researchers are now discovering more complicated numerical skills in animal subjects. A variety of species has shown a capability to abstract, some even able to perform simple math. However, a few animals have been able grasp the concept of zero. This is a paradoxical idea that can sometimes be difficult for very young children. Experiments have actually shown that honeybees and monkeys can both treat zero as numerosity. They place it on the same mental number lines as numerosities one or two. Researchers also reported in a June paper in Journal of Neuroscience that even crows could do this.

The Content

Male tungaras frogs add one sound to each other’s calls during mating contests. Michale J. Ryan

These three animals are all from different taxonomic categories, including primate, insect, and bird. This suggests that numerical skills have been re-evolved throughout the animal kingdom. Scientists continue to wonder why so many animals have a basic knack for math. What if any clues might that give us about human mathematics’ deep roots? While there are many questions, neuroscientists have enough information to expand their understanding of animal cognition. Brian Butterworth is a Cognitive Neuroscientist at University College London. He wrote the book Can Fish Count?. Butterworth said that even in tiny brains such as those of bees and ants, there’s a mechanism which allows the animal to understand the language of other universes.

Competence in “Number”

Clever Hans, a Berlin-based horse who was nearly 120 years old, became a celebrity. Clever Hans was able to do basic arithmetic with the help of his hoof, adding, subtracting, multiplying, and division. A psychology graduate student quickly realized that the animal wasn’t paying attention to the subtle cues of his trainer, or others who had the answer.

This incident engendered a suspicion about the numerical abilities of animals that continues to this day. For example, some researchers suggest that humans may have an “true understanding” of numerical concepts. However, animals don’t seem to distinguish between objects based upon quantity when they rely on abstract characteristics like size and color.

Crows notice the quantities of items that they see, and have neurons that are tuned to those quantities, allowing them to distinguish a set of four items from a set of three or five.Courtesy of Andreas Nieder

However, rigorous tests over the last two decades have demonstrated that animals even with small brains are capable of performing incredible feats in numerical cognition. All of these mechanisms share a common mechanism for approximating numerosity. It is accurate most of the times, but can sometimes be inaccurate in certain ways. For example, animals are more adept at identifying numerosities that differ in magnitude. So comparing six dots with three is much easier than six to five. It’s much easier to distinguish between different numerosities if they are the same. For example, it is more challenging to discriminate 34 items from 38 than four or eight.

These strengths and weaknesses are reflected in the neural activity of animals. Researchers found that neurons in monkeys’ prefrontal cortex were tuned for different numbers. Researchers found that neurons responding to 3 dots in a screen would also respond weakly to 2 and 4 but not to distant values such as 1 or 5. This is also the case for humans. They also associate numerosities and specific numbers symbols. A different group of neurons is responsible for those quantities.

This observation suggests that animals and humans have a sense of numbers. Vallortigara stated that the fundamental psychophysical law underpinning number sense is an ancient and fundamental one.

You will realize that nearly every animal can do some numerical tasks. Then you’ll want to find out what the threshold is. What’s the limit?” said Scarlett Howard, a postdoctoral research fellow at Deakin University in Australia who studies numerical cognition in honeybees. Scientists wanted to find out if animals could distinguish quantities from their natural and hardwired abilities.

Arithmetic was first. Numerous species have shown that they are able to add and subtract. In 2009, researchers led by Rosa Rugani, a psychologist and Marie Sklodowska-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. After obscuring the objects, the team moved the pieces from one side to another while watching the chicks. No matter how many items were moved, the chicks consistently chose the screen that hid more of them. The chicks seemed to be doing computations similar to adding or subtracting to track each group’s change in numerosity. They were able to perform this work without any training. Rugani stated that they deal with numerosities spontaneously.

From left to right chick with plastic objects hanging and Rosa Rugani
The imprints of newly hatched chicks are created on any object presented to them. Rosa Rugani, a psychologist at the University of Padova (right), has demonstrated that chicks imprinted with objects can use math to track the number of them.Photograph by Rosa Rugani

Wild monkeys can do something similar. Scientists placed several slices of bread into a sealed box and then removed one or two of them each time. Monkeys were watching. Although they couldn’t see the number of pieces remaining, the monkeys continued to look at the box until they found the final piece. This suggests that subtraction was used to aid in their foraging.

Simple arithmetic can also be taught to honeybees. In 2019, Howard and her colleagues trained the insects to note the colors and numbers of objects they saw, and then to add one to numbers of blue objects or subtract one from numbers of yellow objects. If the maze contained three different blue shapes and the bees were presented with the option of choosing between four or two items, the latter they chose.

Howard stated that the bees are able to perform these tasks in natural settings because they learn so much. It is not known if the bees can add or subtract without being trained. Scientists have not had any reason to investigate this behavior until now. The bees have everything they need to do arithmetic. Howard said that the environment could be a training ground for its members.

Honeybees were shown to understand the numerosity of zero in behavioral research. Honeybees can also be trained to do simple arithmetic tasks, but it’s not clear if they actually use that ability in nature. Photo by Anne Moffat/Quanta Magazine

Researchers were motivated by these findings to search for more abstract representations of numbers in animals. In 2015, a few years after their arithmetic study in chicks, Rugani and her colleagues found that the animals associated smaller numerosities with the left and larger ones with the right–much as humans spatially represent ascending values on a number line. “That was thought to be our human invention,” said Adrian Dyer, a vision scientist at the Royal Melbourne Institute of Technology who works with honeybees and was Howard’s doctoral adviser. It could “just be something that is within some brains. Part of how we process data.” Dyer is currently testing the possibility.

Birds, insects, and primates can also be trained to connect symbols with numbers of elements. Dyer explained, “We took bees and trained them as though they were at primary school. This symbol represents that number.” They got the association. Chimpanzees who have been taught to connect numerosities and number symbols can also be trained to touch the numbers in ascending order.

Researchers are now exploring new types of numerical tasks. Rugani’s team is currently studying whether monkeys are capable of counting and comparing the elements of two lines to determine the concept of “middle.” So far, she said, “the results are kind of impressive.”

She and other researchers continue to find evidence that animals have a simple and universal sense of numerosity. However, there is also growing evidence for more complex and abstract forms of numerical cognition. For neurobiologists, this is why the great challenge lies in understanding whether animals can grasp numerical abstractions beyond the abstract concept of “nothing”.

An Extraordinary Quantity

All numerosities can be described as abstractions. A group consisting of three or more people, three dots, three chairs, or three people can be called “three”. Butterworth explained that having a sense for numbers means being able to evaluate or assess the size of a set regardless of their members. Even if you have bees that count petals, every flower differs from other flowers in certain respects: its exact location and the conformation of its petals.

One numerosity, however, is distinct from all the others. Rugani stated that zero is very special and unique. It’s more than an abstract of perceiving, it also includes perceiving the absence.

Zero is a difficult number for humans. Very young children, for instance, don’t seem to regard the empty set as a numerical quantity at first. They view it as an absence and a separate category, independent of other values. Although children can usually understand the numbers at age 4 and often grasp them by age 5, it takes two more years to learn zero.

Andreas Nieder
Andreas Nieder, a neurobiologist at the University of Tubingen, studies how the brains of monkeys and crows represent numerosities — including zero.Courtesy of Andreas Nieder

That’s because using zero in this way “requires some transcending of the empirical world,” said Andreas Nieder, a neurobiologist at the University of Tubingen in Germany–a recognition that the empty set can be considered a quantity, and that “nothing” can be represented as something. He said that “we don’t go out to purchase zero fish.”

He also said, “When we look at history of mathematics it turns out zero is an extrem latecomer to our culture.” Historical research has shown that humans didn’t use zero in mathematical calculations before the seventh century.

“From this human perspective,” said Aurore Avargues-Weber, a cognitive ethologist at the University of Toulouse in France who works with Howard and Dyer on honeybees, “zero seems not to be biological but much more cultural.”

Nieder thought otherwise. Nieder thought that animals might have the ability to view zero as a quantity even though they don’t possess a symbolic meaning of it like humans. His group proved in 2016 that monkeys had neurons in their prefrontal cortex which were tuned for zero preference over other numerosities. It was also revealing that the animals mixed up zero more frequently than they did with numerosity 2. Nieder stated that the animals perceive empty sets, or nothing as quantities next to one in this number line.

In 2018, Howard, Avargues-Weber, Dyer, and their colleagues found behavioral evidence of this in honeybees as well. These findings, Howard called it, “this mathematical cognition” or the ability to understand abstract numbers, were innate. Understanding zero may be more common than previously thought.

series of yellow tents in a field
Honeybees can count landmarks — in this study, a series of yellow tents — to help them navigate toward a food source.Photograph: Lars Chittka

The honeybee study caused eyebrows not only because of the fact that it revealed that a bee with less than one million neurons (compared to the human brain’s 886 billion), could consider zero a quantity but also because mammals and bees diverged 600 million years ago in evolutionary terms. Avargues Weber stated that their last common ancestor was “unable to perceive any thing” and even less capable of counting. According to Nieder, who was not involved with the insect work, this implied that the ability to grasp the empty set and other numerosities evolved independently in the two lineages.

“A whole different neural substrate produced such high-level cognitive capacity,” said HaDi MaBouDi, a cognitive scientist at the University of Sheffield in England. Researchers have not been able to examine the neural activity in honeybees performing numerical tasks. This makes it hard to compare their representations with monkeys. Scientists realized that they needed to study the brain of an animal to find out how or why “nothing” became possible.

An Parallel History

Nieder and his colleagues turned to the crows. They have had no ancestors with primates in more than 300,000,000 years and have evolved very different brains. Nieder explained that birds do not possess a prefrontal cortex. Instead, their “intelligence brain centers” have distinct structures, wiring and developmental paths.

However, despite the differences in their results, researchers discovered a common numerical understanding of zero. The crows were more likely to mix up blank screens with images of one dot, than with those of three or four dots. The brain activity of the crows during the tasks was recorded and revealed that the neurons of the pallium, a part of the brain responsible for zero representations it as an quantity along with other numerosities. This is similar to what can be found in primate’s prefrontal cortex. Nieder stated that this is a natural result. “We can see the exact same response, and the same code in both the monkey and crow brains.”

The same neural structure can be explained in different brains by the fact that it is an efficient solution for a common problem. Avargues Weber stated, “It is actually thrilling because it suggests it’s just best.” There may be physical and/or other limitations on the way that the brain processes zero and other numerosities. Vallortigara stated that there could be very few ways to encode numbers.

Giorgio Vallortigara
Giorgio Vallortigara, a neuroscientist at the University of Trento, and his colleagues have seen indications that zebra fish have an area in their brains that corresponds to numerosity.Courtesy of Giorgio Vallortigara

However, the fact that monkeys and crows encode an abstract concept such as zero the same way doesn’t mean it is the only way. Vallortigara stated that it is possible different algorithms have been developed during evolution and natural history to accomplish similar computations. To find out, researchers will need to examine other animals. For instance, in Cerebral Cortex, Vallortigara with his collaborators identified a brain area in Zebra Fish that appears to correlate to numerosity. However, they have not yet assessed the animal’s ability to determine zero.

As the basis for bees’ numerosity is better understood, there may also be some surprising results. In a study published last year, MaBouDi and his colleagues “showed that the bumblebee counts by a fundamentally different strategy” when presented with up to four objects, he said. Their findings suggest that honeybees might have different mechanisms than what has been previously observed.

Perhaps the most fundamental question regarding numerical abstraction in brains diverse animals is not how it works, but why. Animals shouldn’t have to be able to identify specific numbers. Evolution has repeatedly ensured that animals understand that not only is four less than five, but also that “four squares”, conceptually speaking, is the same thing as “four circles”.

Vallortigara believes that one reason could be the fact that arithmetic is so essential. Animals have to perform arithmetic every day. He said that even simple animals can do arithmetic. He said, “If there is an abstract representation for numerosity it’s very simple to do.” The brain can perform more efficient computations by abstracting numerical data.

This is where perhaps zero also fits in. The area will remain dangerous if there are two or more predators in the environment. Rugani suggests that animals must be able subtract and also interpret zero to indicate the result of previous numerical subtractions. This can help them associate specific environmental conditions. Rugani stated that the environment is considered safe if it reaches the lowest value (zero). Zero can indicate a need for foraging in another location when searching for food.

Nieder is not convinced. Nieder isn’t convinced. He says there’s no pressing need that animals understand zero, as it should be understood as an absence. He said that he doesn’t believe animals are using numerosity zero in their daily lives.

Another possibility is that the brain’s ability to identify visual objects in its environment may have led to an understanding of zero and numerosity. In 2019, when Nieder and his colleagues trained an artificial network to recognize objects in images, the ability to discriminate numbers of items arose spontaneously, seemingly as a byproduct of that more general task.

Math’s Building Blocks: A Look at the Details

Nieder says that the existence of mathematical abstraction talents in animals suggests “that something is already laid out in these brains that could constitute an evolutionary basis to what can be developed in us humans into a complete understanding of zero.”

He stressed that while the animal’s achievements are impressive, there were important differences in how they conceptualize numerosity. It’s not enough to understand numbers; we also link them with arbitrary numeric symbols. Nieder stated that a set of five objects does not equal the number 5. The empty set, on the other hand, is different from 0.

Dyer stated that even though animals are able to identify two items using the symbol 2, and three with 3, Dyer noted, “that doesn’t mean they could combine those symbols to get 2 + 3 = 5,”. Dyer said that this is a trivial problem for elementary-school students. However, experiments to prove that animals can use symbolic reasoning to their advantage have not been done.

This step was taken beyond numerosity, creating a symbolic system for enumeration allowed humans to create a precise concept of numbers, manipulate them according to certain rules and build an entire science around the abstract use of these quantities–what we call mathematics.

Nieder hopes his research on zero will help to show how an abstract understanding of numbers might arise from a practical and more precise one. His current research focuses on the relationships between symbolic and non-symbolic numbers.

Vallortigara, Butterworth, and some of their colleagues are now collaborating with Caroline Brennan, a molecular geneticist at Queen Mary University of London, to pin down the genetic mechanisms underlying numerical ability. The team has already discovered genes associated with dyscalculia (a mathematical learning disorder) in people and are now manipulating similar genes in Zebra Fish. Vallortigara stated, “I believe that the genetic portion of this story, in a way, is the future of the field.” It would be truly a breakthrough to identify genes that are number-based.

Reprinted original story with permission of Quanta Magazine. This independent, editorially-controlled publication is part of the Simons Foundation and aims to increase public knowledge of science. It covers research trends and developments in math and other life and physical sciences.

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Publiated at Sun, 15 August 2021 12:27.24 +0000

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