“Two, four, six, eight; Bog in, don’t wait”.
As children, we learn that numbers can be even or odd. And there are many ways to classify numbers as even or odd.
We can remember 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, we can use pairings when dealing with real-world objects. If we have one unpaired element left, it means that the number of items was odd.
Until now odd and even classification, also known as parity classification, had never been shown in non-human animals. In a new study published today in the journal Frontiers in Ecology and Evolution, we show that bees can learn to do this.
Why is equity classification special?
Parity functions (such as odd and even classifications) are considered abstract and high-level numerical concepts in humans.
Interestingly, humans exhibit accuracy, speed, language, and spatial relationship bias when classifying numbers as odd or even. For example, we respond faster to even numbers with our right hand and to odd numbers with our left hand.
We are also faster and more accurate when classifying even numbers than odd. And research has found that children commonly associate the word “even” with “right” and “odd” with “left.”
These studies suggest that humans may have learned bias and/or innate bias about odd and even numbers, which may have arisen either through evolution, cultural transmission, or a combination of both.
It is not clear why the analogy may be important beyond its use in mathematics, so the origin of these biases is unclear. Understanding whether and how other animals can recognize (or learn to recognize) odd and even numbers can tell us more about our own history than we do with analogy.
training bees to learn even and odd
Studies have shown that bees can learn to organize quantities, perform simple addition and subtraction, match symbols with quantities, and combine shape and number concepts.
Read more: Can bees do math? Yes – New Research Shows They Can Add and Subtract
To teach the bees a parity task, we divided 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.
Here we show that a bee is being trained to associate ‘even’ stimuli with a reward of over 40 training options. Scarlett Howard
We trained individual bees using a comparison of odd versus even numbers (with cards containing 110 printed shapes) until they chose the correct answer with 80% accuracy.
Remarkably, the respective groups learned at different rates. Trained bees quickly learned to associate odd numbers with sugar water. Their learning bias towards odd numbers was in contrast to that of humans, who classify even numbers more quickly.
During the experiment, the bees landed on a platform to drink sugar water. Scarlett Howard
We then tested each bee on new numbers not shown during training. Effectively, they classified the new numbers of elements 11 or 12 with an accuracy of about 70% as odd or odd.
Our results showed that the miniature brains of bees were able to understand the concepts of odd and even. So a large and complex human brain containing 86 billion neurons, and a miniature insect brain with about 960,000 neurons, can both classify numbers by analogy.
Does this mean that the parity function was less complex than it was before? To find the answer, we turned to bio-inspired technology.
We trained bees to choose even numbers. In this video we see the bee inspecting each card on the screen before making the correct choice on a card representing an even number of 12 shapes.
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 the parity test. We delivered network signals between 0 and 40 pulses, which he classified as odd or even. Despite its simplicity, the neural network correctly classified pulse numbers as odd or even with 100% accuracy.
it showed us that in principle Equity classification does not require a large and complex brain like a human. However, this does not mean that bees and simple neural networks use the same mechanism to solve the task.
simple or complex?
We don’t yet know how bees can do the same thing. Explanations can include simple or complex processes. For example, bees may have:
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Paired Elements To find an unpaired element
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Display partition count – although the partition has not been previously performed by bees
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Calculated each element and then applied the odd/even classification rule to the total quantity.
By teaching other animal species to distinguish between odd and even 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 mathematics somehow linked to the human brain? Are the differences between humans and other animals smaller than we think? Perhaps we can garner these intellectual insights, if we only listen properly.
Read more: How bees see: Tiny spots on flower petals give them their dark color and help them survive
