The humble honey bee can use symbols to perform basic mathematics, including addition and subtraction, shows new research published today in the journal Science Advances.

Although a brain contains less than a million neurons, honey bees have recently shown that it can cope with complex problems – such as understanding the concept of zero.

Honey bees are a high value model for exploring neuroscience issues. In our latest study, we decided to test whether they could learn to perform simple arithmetic operations such as addition and subtraction.

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## Addition and subtraction operations

As children, we learn that a plus symbol (+) means that we must add two or more quantities, while a minus sign (-) means that we must subtract quantities.

To solve these problems, we need both long-term and short-term memory. We use working (short-term) memory to control the numerical values during the execution of the operation, and we store the rules to add or subtract in long-term memory.

Although the ability to perform arithmetic like addition and subtraction is not simple, it is crucial in human society. The Egyptians and the Babylonians show signs of using arithmetic around 2000BCE, which would have been useful – for example – to count living stocks and calculate new numbers when cattle were sold.

But does the development of arithmetic thinking require a large primate brain, or are other animals exposed to similar problems that allow them to treat arithmetic operations? We explored this using the honey bee.

## How to train a bee

Honey bees are central forages – which means that a headland bean will return to a place if the location provides a good food source.

We deliver bees with a high concentration of sugar water during experiments, so individual bees (all women) continue to return to the experiment to collect nutrition for the hive.

In our setup, when a bee chooses a correct number (see below) she gets a reward of sugar water. If she makes the wrong choice, she will receive a bitter tasting quinine solution.

We use this method to teach individual bees to learn the task of addition or subtraction over four to seven hours. Each time the bee became full, she returned to the hive and then returned to the experiment to continue learning.

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## Addition and subtraction in bees

Honey bees were individually trained to visit a Y-maze shaped appliance.

The bee would fly into the entrance to the Y maze and see a series of elements consisting of one and five shapes. The shape (for example: square shapes, but many form options were employed in actual experiments) would be one of two colors. Blue meant that the bee had to perform an addition operation (+ 1). If the figures were yellow, the bee should perform a subtraction operation (- 1).

For the task of either plus or minus one, one side would contain a wrong answer and the other side would contain the correct answer. Side of stimuli was changed randomly during the experiment so that bee would not learn to visit only one side of the Y maze.

After seeing the initial number, each bee would fly through a hole in a decision chamber where it could either be chosen to fly to the left or right side of the Y maze depending on the operation to which she was trained.

At the beginning of the experiment, bees made random choices until they could figure out how to solve the problem. Finally, bees over 100 learning attempts learned that blue meant +1, while yellow meant -1. Bees can then apply the rules to new numbers.

During testing with a new number, bees were also correct and subtraction of an element 64-72% of the time. Bees performance on samples was significantly different than what we would expect if bees chose randomly, called chance level performance (50% correct / incorrect)

Thus, our bee school in the Y maze allowed the bees to learn to use arithmetic operators to add or subtract.

## Why is this a complex issue for bees?

Numerical operations such as addition and subtraction are complex issues because they require two levels of treatment. The first level requires a bee to understand the value of numerical attributes. The second level requires that the bee mentally manipulates numerical attributes in working memory.

In addition to these two processes, bees also had to perform the arithmetic operations in the working memory – the number "one" to be added or subtracted was not visually present. Instead, the idea of plus one or less "one" was an abstract concept that bees had to solve during the training.

Shows that a bee can combine simple arithmetic and symbolic learning has identified many areas of research that can be extended to, such as whether other animals can add and subtract.

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## Implications for AI and neurobiology

There is great interest in AI, and how well computers can make it possible to learn new problems.

Our new results show that learning symbolic arithmetic operators to enable addition and subtraction is possible with a miniature brain. This suggests that there may be new ways to incorporate interactions between both long-term rules and work memory in design to enhance rapid AI learning of new issues.

Also, our results show that the understanding of mathematical symbols as a language with operators is something that many brains are likely to achieve and helps explain how many human cultures independently developed speech capabilities.

*This article has been published simultaneously in Spanish at The Conversation Espana.*

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