As children, we learn that numbers can be even or odd. And there are many ways to classify numbers as odd or even.
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 the result of any whole number means that the number is even; otherwise it must be odd.
Similarly, when dealing with real-world objects, we can use matchmaking. If we have an unmatched item left over, that means the number of items was odd.
Until now, even and odd ranking, also called parity ranking, had never been shown in non-human animals.. In a new study, published in the journal Frontiers in Ecology and Evolutionthe authors show that bees can learn to make this categorization.
Why is parity categorization special? Parity tasks (such as categorizing even and odd) are considered high-level, abstract number concepts in humans.
Interestingly, humans demonstrate precision, speed, language, and spatial relationship biases when categorizing numbers as odd or even. 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 at categorizing numbers as even compared to odd.. And research has found that children often associate the word “even” with “right” and “odd” with “left.”
These studies suggest that humans may have learned biases and/or innate biases regarding odd and even numbers, which may have arisen through evolution, cultural transmission, or a combination of both.
It is not clear why parity might be important beyond its use in mathematics, so the origins of these biases remain unknown. It remains to be understood whether other animals can recognize (or can learn to recognize) even and odd numbers and how they can tell us more about our own history with parity.
Training bees to learn even and odd
Studies have shown that bees can learn to order quantities, perform simple addition and subtraction, match symbols with quantities, and relate size and number concepts.
To teach the bees a paired task, the study authors separated the individuals into two groups. One was trained to associate even numbers with sugar water and odd numbers with a bitter-tasting liquid (quinine). The other group was trained to associate odd numbers with sugar water and even numbers with quinine.
Individual bees were trained using odd and even number comparisons (with cards featuring 1 to 10 printed shapes) until they chose the correct answer with 80% accuracy.
Bees were trained to choose even numbers. In this video we see the bee inspect each card on the screen, before making a correct choice. on the card that presents an even number of 12 forms.
Interestingly, each of the groups learned at different rates. Bees trained to associate odd numbers with sugar water learned faster. That is, their learning bias toward odd numbers was the opposite of humans, who categorize even numbers more quickly.
We then tested each bee with new numbers that were not displayed during training. Remarkably, they classified the new 11- or 12-item numbers as odd or even with about 70% accuracy.
The results showed that the miniature brains of bees were capable of understanding the concepts of odd and even.. That means that both a large, complex human brain consisting of 86 billion neurons, and a miniature insect brain with around 960,000 neurons, can classify numbers as odd and even.
Does this mean that the parity task would be less complex than we previously thought? To find the answer, we turned to bio-inspired technology.
Creation of 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 build 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 even or odd. Despite its simplicity, the neural network correctly classified the pulse numbers 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 still don’t know how the bees were able to perform the parity task. Explanations can include simple or complex processes. For example, bees can do tasks such as:
1. Study matched items to find an unmatched item.
2. Perform division calculations, although division had not previously been demonstrated in bees.
3. Count each item and then apply the odd/even categorization rule to the total amount.
By teaching other animal species to discriminate between odd and even numbers, and to perform other abstract mathematics, we can learn more about how mathematics and abstract thinking arose in humans.
Is the discovery of mathematics an inevitable consequence of intelligence? Or is mathematics somehow related to the human brain? Are the differences between humans and other animals less than we previously thought? Perhaps we can gain these intellectual insights, if only we listen correctly.
Reference study: https://www.frontiersin.org/articles/10.3389/fevo.2022.805385/full
Scarlet R Howard
is the first author of the landmark study, along with Adrian Dyer, Andrew Greentree, and Jair Garcia, published in The Conversation.
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