Australasian Science: Australia's authority on science since 1938

## Chasing the Meaning of Zero

By Scarlett Howard, Jair Garcia & Adrian Dyer

**It took early mathematicians until 400 BC to determine the concept of zero, yet the simple bee brain can be trained to recognise an “empty set” within a few hours.**

Mathematics allows us to count, add, subtract, and perform complex numerical operations. Understanding the concept of zero as an empty set is not a trivial task, even for mathematicians.

There are four levels of developing an understanding of zero:

- understanding zero as the absence of something;
- understanding zero as “nothing” versus “something”;
- understanding that zero can have a quantitative value that belongs at the low end of the positive number line; and
- understanding that zero can be assigned a symbolic representation that can be used in modern mathematics and calculations.

So far, level 4 is only known to be possible in humans. For example, we can write and understand the equation 3–3 = 0.

Zero has been a very important conceptual leap in how humans have developed technology and culture. Think of how important binary coding is as a backbone to how almost all of our current computers and technology work.

The ability to use zero as a quantitative number with its own value actually took a long time to develop in human culture, and until recently it was thought to be such an advanced concept that it required a large human brain. Indeed, several ancient human civilisations did not have a representation for zero, but by around 400–500 BC in China counting rods were used with a blank space to represent zero.

A formal sign for an empty column in positional notation appears to have been first used around 400 BC in ancient Mesopotamia by the Babylonians, who used two slanted wedges as a placeholder to represent zero. In 628 AD the Indian mathematician Brahma Gupta wrote formal rules for the use of zero in calculations that provides a link to the way we currently understand it in modern mathematics.

This revolution in our thinking of how to represent nothing as something in an ordered sequence enables calculations, accountancy, and is important to how our sophisticated societies so quickly developed. Can non-human animals also understand such concepts?

Interestingly, some animals have previously demonstrated level 3 of understanding zero by assigning a quantitative value to an empty set. Chimpanzees, rhesus monkeys, vervet monkeys and an African grey parrot named Alex have learned and demonstrated an understanding of zero to some extent.

But what about an insect? Could an animal such as the honeybee demonstrate an understanding of this complex number concept? We asked whether a miniature insect brain, such as the honeybee brain, could learn number rules and apply them to an empty set. Our findings were recently published in Science (https://goo.gl/VTsoEQ).

To test if honeybees could achieve a conceptual understanding consistent with level 3, we individually trained marked honeybees to learn the rule of “less than”. In order to receive a reward of sugar water, bees would need to choose the lower of two quantities presented to them on a rotating screen. For example, if a bee was presented with a choice of three versus four elements in an image, the quantity of three would be correct. However, if the bee was shown two or three elements in an image, the quantity of two would be correct.

Quantities and element shapes and configurations were randomly varied for each choice made by the bee, and shapes were controlled for black and white surface area, size and perimeter. Over the course of several hours, a bee learned this rule to achieve a level of accuracy above 75%.

In non-rewarded tests, bees were presented with a novel choice between blank empty set images and images containing elements similar to the ones they had experienced during training. The bees preferred to choose the blank stimulus, and did so more accurately when the empty set stimulus was presented against higher numbers (six versus zero) compared with lower numbers (one versus zero).

Control experiments also showed that bees didn’t just innately choose a blank empty set image. Their choices were consistent with bees placing an empty set at the lowest end of a number continuum.

Thus honeybees were able to learn an advanced numerical concept within a few hours of training. The brain of bees contains less than a million neurons compared with our 100 billion neurons, demonstrating that a miniature and seemingly simple brain can also learn and apply complex number rules.

The evidence that such a miniature brain can learn complex problems suggests that new artificial intelligence solutions might be created from the bio-inspired solutions of bees. Thus, the rules behind complex mathematical thinking may be much more accessible than previously thought.

**Scarlett Howard, Jair Garcia & Adrian Dyer are part of the Bio-inspired Digital Sensing Lab at RMIT University.**