Bees can learn the difference between odd and even numbers, just like us
“Two, four, six, eight; get bogged down, don’t wait”.
As children we learn that numbers can be even or odd. And there are many ways to categorize numbers as even or odd.
We can memorize the rule that numbers ending in 1, 3, 5, 7 or 9 are odd while numbers ending in 0, 2, 4, 6 or 8 are even. Or we can divide a number by 2 – where any integer result means the number is even, otherwise it must be odd.
Similarly, when dealing with real-world objects, we can use pairing. If we are left with an unpaired element, it means that the number of objects was odd.
Until now, odd and even categorization, also called parity classification, had never been demonstrated in non-human animals. In a new study, published on friday in the magazine Frontiers in Ecology and Evolutionwe show that bees can learn to do this.
Why is gender categorization special?
Parity tasks (such as odd and even categorization) are considered abstract and high-level digital concepts in humans.
Interestingly, humans exhibit biases in precision, speed, language, and spatial relationships when classifying numbers as even or odd.
For example, we tend to react faster to even numbers with actions performed by our right hand, and to odd numbers with actions performed by our left hand.
We are also faster and more accurate when categorizing even versus odd numbers. And research has shown that children typically associate the word “even” with “right” and “odd” with “left”.
These studies suggest that humans may have learned innate biases and/or biases regarding even and odd numbers, which may stem either from evolution, cultural transmission, or a combination of the two.
It is not clear that parity could be important beyond its use in mathematics, so the origins of these biases remain unclear.
Understanding if and how other animals can recognize (or can learn to recognize) odd and even numbers could tell us more about our own history with parity.
Training bees to learn odd and even
To teach the bees a parity task, we separated the individuals into two groups. We learned to associate even numbers with sugar water and odd numbers with a bitter-tasting liquid (quinine). The other group learned to associate odd numbers with sugar water and even numbers with quinine.
We trained individual bees using odd and even number comparisons (with cards showing 1 to 10 printed shapes) until they chose the correct answer with 80% accuracy.
Remarkably, the respective groups learned at different rates.
Bees trained to associate odd numbers with sugar water learned faster.
Their learning bias toward odd numbers was the opposite of humans, who categorize even numbers faster.
We then tested each bee on new numbers not displayed during training. Impressively, they classified the new 11- or 12-element numbers as odd or even with about 70% accuracy.
Our results showed that the miniature bee brains were able to understand the concepts of odd and even.
Does this mean that the parity task was less complex than we previously thought? To find the answer, we turned to bio-inspired technology.
Creating a Simple Artificial Neural Network
Artificial neural networks were one of the first learning algorithms developed for machine learning. Inspired by biological neurons, these networks are scalable and can tackle complex recognition and classification tasks using propositional logic.
We built a simple artificial neural network with only five neurons to perform a parity test.
We gave the network signals between 0 and 40 pulses, which it classified as odd or even. Despite its simplicity, the neural network correctly classified pulse counts as odd or even with 100% accuracy.
This showed us that in principle parity categorization does not require a large and complex brain like that of a human.
However, this does not necessarily mean that the bees and the simple neural network used the same mechanism to solve the task.
Simple or complex?
We don’t yet know how the bees were able to perform the parity task. Explanations can include simple or complex processes. For example, bees may have:
matched items to find an unmatched item
performed division calculations – although division had not previously been demonstrated by bees
counted each item, then applied the even/odd categorization rule to the total quantity.
By teaching other animal species to distinguish between even and odd numbers and by performing other abstract mathematics, we can learn more about how mathematics and abstract thought emerged in humans.
Is the discovery of mathematics an inevitable consequence of intelligence? Or is math somehow tied to the human brain? Are the differences between humans and other animals less than we previously thought?
Perhaps we can glean these intellectual insights, if only we listen properly.
Scarlett HowardLecturer, Monash University; Adrian DyerAssociate Professor, RMIT University; Andrew Green Treeprofessor of quantum physics and Future Fellow of the Australian Research Council, RMIT Universityand Jair GarciaResearcher, RMIT University.