Secrets of Math From the Bee Whisperer
Scarlett Howard has taught honeybees how to add, subtract and understand zero. Their ingenuity suggests that all animals may have more mathematical talent than we thought.
Anne Moffat for Quanta Magazine
Introduction
Scarlett Howard teaches math to honeybees. She began with a few hives on a concrete balcony at RMIT University in Melbourne, when she was a doctoral candidate in zoology. Today, at the University of Toulouse, where she is a postdoctoral fellow, her lessons take place in a small field with approximately 50 hives.
It might seem a little strange — bees are insects, after all; what do they know about mathematics? A lot, it turns out. These eusocial flying insects can add, subtract and even comprehend the concept of zero.
“You can see their decision-making process in their movements and flight patterns,” Howard said. While deciding which of two answers is correct, they often fly toward one of the solutions before seeming to think better of it and flying off toward the other.
Howard teaches one bee at a time, placing it next to an apparatus known as a Y maze, a covered box shaped like a block letter Y. The bee enters the bottom leg of the Y and sees a mathematical question, expressed in shapes and colors. In the arithmetic lessons, blue shapes mean “add 1” to the given number of shapes, and yellow shapes mean “subtract 1.” To answer the question, the bee chooses from one of two possible solutions posted at the entrances to the Y’s upper arms. The bee will find a reward — sugar water — in the arm associated with the correct answer, and a punishment — tonic water, which bees find bitter — in the arm with the incorrect answer.
To teach bees about zero, she first trained them to understand the concept of “less than.” As with the addition and subtraction problems, she offered reinforcements for correct choices. Once an individual bee demonstrated it understood “less than,” she advanced that bee to the testing phase of her experiment, where it would decide if any number of shapes is less than zero shapes — a number the bee had never encountered before. Each bee had only one chance to answer. The bees often identified “zero shapes” as smaller than any number of shapes, and Howard concluded that they must possess an innate understanding that zero is smaller than any positive integer.
For each experiment, Howard trains and tests approximately 100 random bees from the thousands in her hives. Handling them is simple enough. After each correct choice, the bee flies back to the hive on its own, to offload its sweet reward. Then, at some point, it’ll come back. That’s because bees are central place foragers, meaning they will remember the experiment and return to it for additional resources. To prepare for her next pupil, Howard changes the stimuli on the Y maze. She has hundreds, possibly thousands of stimuli printed and laminated.
“They’re laminated so we can clean them with ethanol, because bees will scent-mark,” said Howard. “They’ll do anything to cheat the tests. They’re smart! They’ll mark the correct answer. Bees are not as simple as we used to think they are. Or even as some people still think they are.”
Quanta Magazine recently spoke with Howard about her research. The interview has been condensed and edited for clarity.
Scarlett Howard inspects honey bees in a chimney hive at the University of Melbourne’s System Garden. The tiny insects have proven adept at learning many arithmetic concepts.
Anne Moffat for Quanta Magazine
What first inspired you to research bees’ mathematical abilities? Were you a fan of the bugs?
I had always been really scared of bees. But when I was at university in Australia, Adrian Dyer, who works on bees’ cognitive abilities, told me, “Bees can do really cool things. They can recognize human faces and navigate mazes.” I thought, “Really? Is that true? I want to see that for myself.” So I pitched the idea of working on bees’ cognitive abilities to my potential Ph.D. supervisors.
We thought, “We can do something either really high-risk/high-reward, or we can do something less risky but less interesting.” We tried something risky first — whether bees could understand zero at the same level as some primates and birds do.
Most animals know, for example, whether or not they have “some food” or “zero food” in front of them. Do bees really possess more than this basic understanding of zero?
Bees are able to place zero within a numerical continuum. They know that zero is less than 1, it’s less than 2 and it’s less than 3. They also know that zero is more “less than 6” than it is “less than 1.”
Many animals have difficulty with zero. The number 1 might have been the lowest number they’d ever seen. When we got positive results from that experiment showing that they knew zero is lower than any positive integer, it was really exciting to see.
Of course, different bees have different processes of learning. Some do really well from the beginning. Some are really quite bad. You see this moment where they start to get things more and more right. You don’t want to anthropomorphize them too much, but it’s really incredible to watch how they learn.
Wait — some bees are better at math than other bees?
We actually have quantified it. We’ve got a theoretical physicist on our team who is working on bee numerical ability. He ran some Bayesian analysis on my results. We were hoping to find a moment where we could say, “OK, bees switch from not being very good at the arithmetic task to understanding it at this certain point.” But we found no consistency between the individuals. The moment when an individual bee switched from doing really poorly to doing really well happened at a different stage for each bee.
Honeybee brains have less than 1 million neurons, but they can still perform complex numerical tasks, suggesting that number sense may be inherent in animals.
Anne Moffat for Quanta Magazine
Just like people, in other words. So, are there other connections? In understanding bees’ numerical abilities, do we gain insight into humans’ numerical abilities?
Humans and bees are separated by over 600 million years of evolution. If both species are able to do similar numerical tasks, we might gain insight into the evolution of numerical ability. Is this evolution divergent? Convergent? Parallel?
There is a big debate about numerical ability in animals. One side argues that numerical cognition — complex tasks like addition, subtraction, multiplication and division — is only possible because of language and culture, specifically human abilities to write things down and speak. The other side argues that animals have an evolutionary need to process numerical information.
Our work supports the second argument. We’re seeing an insect doing addition and subtraction and learning “greater than” and “lesser than.” Scientists have observed numerical abilities across many different species. These abilities appear to be evolutionarily ancient — something that occurred in a common ancestor long ago. My hypothesis is that bees and other animals can process numerical information without culture and without language because they have a need that has persisted through time.
What kind of need? Why would bees benefit from these numerical skills?
We’re working on this question. We’re trying to see how useful number discrimination and number sense might be in their foraging activities. Perhaps numbers help them determine which flower patch might be more beneficial for them. They care about the quantity of flowers. Being able to count landmarks could be really useful for navigation between their hive and places with resources. There’s also an older paper that suggests bees use petal number to differentiate between species of flowers.
This research differs from what we’ve done previously, because the task the bee does needs to be ecologically relevant to them in their natural environment. We want to look at how they make choices in the absence of training, if they still want or need to process numbers without the pressure to learn a [possibly irrelevant] task to receive sugar. It’s more a question of “What would they do on their own?”
So if you’re right that number sense really does transcend language and culture, what does that mean for our own understanding of numbers?
We’re only beginning to ask about the implications. Still, my team just got a paper accepted in a teaching journal. Our paper suggests that the way we train bees to develop numerical abilities has implications not only for human learning but also for artificial intelligence and design. But I don’t recommend feeding kids a bitter-tasting substance for wrong answers!
For each experiment teaching them math, Howard worked with approximately 100 random bees from the thousands in her hives.
Anne Moffat for Quanta Magazine
Our thinking is that we could base a computer model on a bee brain. A bee brain consists of less than 1 million neurons, compared to ours, which have over 100 billion. They’re able to do these really complex tasks with a very small processing system and not much in the way of energy consumption — drops of sugar water. If we could work out how they learn in such an efficient way, we could apply it to computer learning. Our computers use a lot of energy, so looking at how bees learn and do complex tasks could improve the efficiency of computing solutions.
What about higher math? Do bees understand negative numbers, or operations such as multiplication and division?
We plan to look at some of those concepts. I’d like to try division, such as “divide this number in half.” We could look at whether they prefer to round the result up or down. Is there consistency, or is it just random?
There’s been a lot of talk about negative numbers in the team, but we haven’t nailed down the details. There are challenges. What stimulus could represent a negative number? How do you ensure that the bee considers it negative?
With insects, a lot of work goes into ensuring you asked the question in the right way. You can’t give them a human test. They need the right motivation. They need to understand the question to be able to answer it.
So it’s safe to say you’re not scared of bees anymore?
If there’s an insect in my house, I’m not killing it. I make sure it gets outside. A really special part of my job is talking to the public, to strangers, to friends, to everyone about bees. I hear about bees in places like Flinders Street Station in Melbourne or on the rooftop of Notre Dame. Family and friends come up to me and say, “I saw a bee the other day!” or “I saw a bee flying by!” or “There are bees in my garden at the moment!” I reply, “That’s great!” It’s normal to see a bee, but they want to tell me about it.
