/ 22 June 2018

Is maths any of their beeswax?

(John McCann/M&G)
(John McCann/M&G)

Bees were once thought to be geniuses, natural architects with supernatural mastery over mathematics. This reputation came in for a good kicking a few years ago, when researchers showed they’d been faking it all along. But now they’re making a comeback.

Geometry was their game, and they had all the angles covered. The six sides of a cell in a beehive’s honeycomb make it ideal for tessellation — arrangement in a repeated pattern without gaps or overlapping. And the hexagon provides the optimal shape for storage volume and load-bearing strength using the materials available, in this case wax.

In the fourth century CE, the Greek philosopher Pappus worked out that, of all possible shapes, a repeating hexagon allowed for the strongest honeycomb to be built with the least amount of wax. And the bees were all, like, yes, we already knew that.

However, as the myth-busting apiology-and-engineering trio of Zhang, Wang and Karihaloo noted in a study published in the Journal of the Royal Society Interface in 2013, this geometric perfection is not deliberate. The cells are round when they start off, not hexagonal. But the comb-building worker bees are generating heat as they go about their business. This causes the previously round and now gently warmed waxy walls to collapse —ever so slightly — into their distinctive shape, as a result of the surface tension mechanics of the comb as a whole, and not, as previously suspected, the careful planning of a Euclidean mind, hive or otherwise.

“[Some people] believed the bees had an uncanny ability to measure angles,” said study co-author Bhushan Karihaloo. “But it’s actually much more mundane.”

With their scam exposed, one might have expected bees to retreat to a more suitable subject of study. Spelling, for example.

But they remain active in many fields, and have clearly retained an interest in arithmetic. For it has now been found that they are capable of mathematical feats involving the concept of zero.

Humanity, mind you, has a sketchy track record on the subject of zero. Whereas even our prehistoric ancestors were pretty comfy with the idea of the absence of anything being nothing at all, and ancient Babylonians and Mayans had a symbol for it, it was left to Indian mathematicians of probably the fifth century CE to formally incorporate absence into our understanding of the number zero as an integer for use in calculations. Not as we currently know it, mind you, but rather representing nought with a simple dot.

Carbon-dating of the Bakhshali manuscript, a scroll found in an Indian field in 1881 that features the use of the dotted zero, suggests it may have been used as early as the third or fourth century CE — which was about the time old Pappus of Alexandria was getting all up in his own beeswax.

It was only later, in the ninth century, that zero found its way to Baghdad, where it was so beloved of the Persian mathematician and inventor of algebra Muhammad ibn Musa al-Khwarizmi that he literally put a ring on it — becoming the first person in recorded history to draw a circle around nothing. He corralled the concept of zero into what has since become the de facto numerical framework that underpins modern mathematics, catapulting humanity into an age of marvels.

And now the bees are catching on.

Researchers in Melbourne, Australia, have managed to train bees not only to grasp the idea of zero but also to extrapolate the concept for themselves.

Reporting their results in the journal Science this month, the RMIT University team began by introducing individual bees to the concept of “greater than” and “less than”, by arranging screens, each bearing a certain number of distinguishing elements and an equivalent reward, in the form of sweet nectar. For some of the bees, the rewards increased as the number of elements increased; for others, the rewards increased as the elements decreased. Less, in their case, was more.

What this meant was that the bees were being trained to count.

Then the researchers introduced a screen with no elements all, and the subjects who had been conditioned to associate reward with a decreased number made a, uh, beeline for it. The researchers found that the insects could not only be taught what zero is but could also extrapolate the concept of zero from a numerical sequence.

Once humanity was able to start working with the number zero, great things followed. Algebra and calculus. Equations and algorithms. Physics and astronomy. Construction, economics and technology.

It might be a bit much to expect a universal field theory from your local hive any time soon. But at least now — with sweet nothing dished out as a reward — the honeybee can reclaim its position in nature’s Mathematics Hall of Fame.