As we know, numbers can become very large very quickly. The diameter of the universe is about 8.8×1023 kilometres, and it’s dwarfed by the largest known number – googolplex, 1010100.
These colossal concept numbers were reached by brilliant mathematicians, but humans are still pretty limited when it comes to assessing quantities at a glance.
“Humans have a threshold limit for instantly processing one to four elements accurately,” says Adrian Dyer, from RMIT University, Melbourne. And it seems that we’re not alone.
A number of apparently simple animals show a bit of form when it comes to counting.
Scarlett Howard from RMIT University and the Université de Toulouse, France, says that guppies, angelfish and even honeybees are capable of distinguishing between quantities of three and four.
But bees come unstuck at finer differences – they fail to differentiate between four and five. Which got Howard thinking.
Howard says bees are quite accomplished mathematicians: “Recently, honeybees were shown to learn the rules of ‘less than’ and ‘greater than’ and apply these rules to evaluate numbers from zero to six,” she says.
Howard and Dyer posited that numeracy wasn’t the bees’ problem: it was how the question was being posed.
The duo has just published their discovery that bees can discriminate between four and five if the training procedure is correct in the Journal of Experimental Biology.
Dyer explains that when animals are trained to distinguish between colours and objects, some training procedures simply reward the animals when they make the correct decision.
In the case of the honeybees that could distinguish three from four, they received a sip of super-sweet sugar water when they were right, but just a taste of plain water when they were wrong.
However, Dyer, Howard and their colleagues knew there was an alternative strategy: the bees would be given a bitter-tasting sip of quinine-flavoured water when they got the answer wrong.
Would the unpleasant flavour help the honeybees to focus better and improve their maths?
“[The] honeybees were very cooperative, especially when I was providing sugar rewards,” says Howard, who moved to France each April to study them during the northern summer, when Australian bees are dormant.
Howard trained the bees to enter a Y-shaped maze, where she presented the insects with a choice: a card featuring four shapes in one arm of the maze, and a card with a different number of shapes (ranging from one to 10) in the other arm.
During the first series of training sessions, Howard rewarded the bees with a sugary sip when they alighted correctly before the card with four shapes. Those selecting the wrong card got a sip of water.
Then Howard trained a second set of bees. Those choosing incorrectly copped a bitter-tasting sip of quinine; those that selected the card with four shapes were rewarded with sugar water.
Once the bees had learned to pick out the card with four shapes, Howard tested whether they could distinguish the card with four shapes when offered a choice between it and cards with eight, seven, six or – the most challenging comparison – five shapes.
The bees that had only been rewarded during training struggled; they couldn’t even pick between four and eight shapes.
But when Howard tested the honeybees that had been trained more rigorously – receiving a quinine reprimand – their performance was considerably better. They consistently picked the card with four shapes when offered a choice between it and cards with seven or eight shapes.
Even more impressively, the bees succeeded when offered the more subtle choice between four and five shapes.
So, it seems that honeybees are better mathematicians than had been credited. Unlocking their ability was simply a matter of asking the question in the right way.