Don't wait, two, four, six, eight are all available.

Children learn that numbers can be even or odd. There are many ways to categorize numbers.

The rule is that numbers ending in 1, 3, 5, 7, or 9 are odd while numbers ending in 0, 2, 4, 6, or 8 are even. If the whole number outcome means the number is even, we can divide it by 2.

We can use pairs when dealing with real-world objects. The number of objects was odd if we had an unpaired element.

Parity classification, also called odd and even categorization, had never been shown in non-human animals. A new study shows honeybees can learn to do this.

Why is parity categorization special?

Parity tasks are considered high-level numerical concepts in humans.

Humans demonstrate accuracy, speed, language, and spatial relationship biases when categorizing numbers.

We tend to respond to odd numbers with actions performed by our left hand, and to even numbers with actions performed by our right hand.

We are more accurate when we compare numbers to odd. Children associate the word "even" with the words "right" and "odd", according to research.

Humans may have learned biases and/or innate biases regarding odd and even numbers, which may have arisen either through evolution, cultural transmission or a combination of both.

It is not clear why parity is important beyond its use in mathematics.

Understanding how animals can learn to recognize odd and even numbers could help us understand our own history.

Training bees to learn odd and even

honeybees can learn to order quantities, perform simple addition and subtraction, match symbols with quantities, and relate size and number concepts.

We separated people into two groups to teach bees a parity task. One was trained to associate even numbers with sugar water and odd numbers with a bitter-tasting liquid. The other group was trained to associate numbers with things like sugar water and quinine.

Researchers trained bees to associate stimuli with a reward. The person isScarlett Howard.

We trained individual bees to compare odd and even numbers and then chose the correct answer with 80 percent accuracy.

The groups learned at different rates.

The bees were trained to associate numbers with sugar water.

Their learning bias towards odd numbers was different from humans.

The bees were tested on new numbers not shown during training. The new numbers of 11 or 12 elements were categorized as odd or even with an accuracy of 70%.

The honeybees' brains were able to understand odd and even concepts.

A large and complex human brain with 86 billion neurons, and a miniature insect brain with 960,000 neurons, could both categorize numbers by parity.

The parity task was thought to be more complex. We used bio-inspired technology to find the answer.

Creating a simple artificial neural network

Artificial neural networks were developed for machine learning. These networks can tackle complex recognition and classification tasks using propositional logic.

A simple artificial neural network was constructed to perform a test.

The network signals were either odd or even. The neural network correctly categorized the pulse numbers despite its simplicity.

parity categorization does not need a large and complex brain like a human.

The bees and the simple neural network may have used different mechanisms to solve the task.

Simple or complex?

We do not know how the bees were able to perform the task. Simple or complex processes may be included in the explanation. The bees may have something.

1. An unpaired element can be found by pairs of elements.

2. Although division has not been demonstrated by bees, division was performed.

3. The odd/even categorization rule was applied to the total quantity.

By teaching other animal species to discriminate between odd and even numbers, and perform other abstract mathematics, we can learn more about how mathematics and abstract thought emerged in humans.

Is discovering math a result of intelligence? Is mathematics linked to the human brain? The differences between humans and other animals are less than we thought.

If we listen properly, we might be able to glean these intellectual insights.

Adrian Dyer, Andrew Greentree, and Jair Garcia are research fellows at RMIT University.