“Two, four, six, eight…”
As children, we learn that numbers can be even or odd. And there are many ways to classify them.
We can memorize the rule that numbers ending in 1, 3, 5, 7, or 9 are odd, while those ending in 0, 2, 4, 6, or 8 are even. We can also divide a number by 2: if the result is an integer, it means that it is even, otherwise, it must be odd.
Similarly, in the real world, we can use matching when working with objects. If one element remains unpaired, we have an odd number of objects.
Until now, equal and odd categorization, also called parity classification, has not been proven in non-human animals. In a new study recently published in the journal Frontiers in Ecology and Evolutionwe show that honey bees can learn to do this.
Why is sorting by parity special?
Consistent tasks (such as categorizing odds and evens) are considered abstract, high-level numerical concepts in humans.
Interestingly, people show accuracy, speed, language, and spatial relations biases when classifying numbers into even or odd categories. For example, we tend to respond faster to even numbers with actions performed with our right hand, and to odd numbers with actions performed with our left hand.
We are also faster, and more accurate, when ranking even numbers versus odd numbers. And research shows that children typically associate the word “even” with “right” and “odd” with “left.”
These studies suggest that these biases may be learned or innate in the case of even and odd numbers, and may be the result of evolution, cultural transmission, or a combination of both.
The significance of parity, beyond its use in mathematics, is unclear. The sources of the biases therefore remain unclear. We can learn more about our own relationship to equality by understanding why and how other animals recognize (or learn to recognize) even and odd numbers.
Training bees to learn similarities and differences
Studies have shown that bees can learn to order quantities, perform simple addition and subtraction, associate symbols with quantities, and associate the concepts of size and number.
To teach the bees a consistent task, we separated the individuals into two groups. One of them was trained to associate even numbers with sugar water and odd numbers with a bitter liquid (quinine). For the other group, odd numbers are associated 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.
Surprisingly, the two groups learned at different rates. Bees trained to associate odd numbers with sugar water learned faster. Their learning bias in favor of odd numbers is in contrast to that of humans, who categorize even numbers more quickly.
We then tested each bee with other numbers that were not presented during training. Impressively, they classified the new 11- or 12-element digit as odd or even with about 70% accuracy.
Our results showed that bees, with their small brains, understand the concepts of uniqueness and similarity. So a large, complex human brain with 86 billion neurons, and a small insect brain with about 960,000 neurons can sort numbers by parity.
So the task of parity is less complicated than we thought? To find the answer, we turned to biomimetic technology.
Construction of Simple Artificial Neural Networks
Artificial neural networks were one of the first learning algorithms developed for machine learning. Inspired by biological neurons, they 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 the parity test. Between 0 and 40 pulses are sent to the network, classifying them as odd or even. Despite its simplicity, the neural network correctly classified the pulse as odd or even with 100% accuracy.
This showed us that, in principle, parity sorting does not require a large and complex brain like that of a human. However, it should not be assumed that the bees and the simple neural network used the same mechanism to solve the task.
Simple or complex?
We still don’t know how bees accomplish the parity task. Explanations may relate to simple or complex processes. For example, bees can have:
match elements to get mismatched elements
performed division calculations – even though division had not been demonstrated in bees
each item is counted, then the even/odd sorting rule is applied to the total quantity.
By teaching other animal species to distinguish between even and odd numbers and perform other abstract mathematical operations, we can learn more about how mathematics and abstract thinking originated. to people.
Is the discovery of mathematics an inevitable consequence of intelligence? Or is mathematics bound to the human brain? Are the differences between humans and other animals less important than we once thought? Perhaps we can gain an intellectual understanding from this; you just listen
The original version of this article was été published on The conversationa news site à dédié to the sharing of ideas between academic experts and the general public.
Adrian Dyer received funding from the Australian Research Council.
Andrew Greentree has received funding from the Australian Research Council, Defense Science and Technology Group, SmartSat CRC, US Air Force Office of Scientific Research, Asian Office of Aerospace Research and Development, United States Office of Naval Research, and Foundation for Australia- Pag -studying in Japan.
Jair Garcia does not work for, consult with, own shares in or receive funding from any company or organization that would benefit from this article, and has disclosed no relevant affiliation beyond their academic appointment.