Now there’s a lot to savour in such a visit. I wanted to ask if he had seen any signs of Chicxulub, the enormous crater formed about 65 million years ago when a large asteroid slammed into Yucatán. After all, this impact is commonly thought to have wiped out the dinosaurs. But Ajay brought up something else that stopped me in my tracks. The guide they had there, said Ajay, told him that the Mayans invented the number zero.
“What?” sputtered Ajay, as I might have, too. After all, in India we’ve grown up believing zero was invented here. In a sense, both those are true, for different peoples in different parts of the world came up with the idea independently. Here’s how a scientist once explained this in Scientific American (https://t.ly/sqBHd):
“The first recorded zero appeared in Mesopotamia around 3 B.C. The Mayans invented it independently circa 4 A.D. It was later devised in India in the mid-fifth century, spread to Cambodia near the end of the seventh century, and into China and the Islamic countries at the end of the eighth.”
So yes, India can still lay claim to the invention. But claims apart, why was zero a significant mathematical advance, to the extent that we try to trace its origins? Probably two major reasons. One, it stands for the concept of nothing, which, in a world full of things, is not simple at all. Two, it is a placeholder in our number system, which makes numbers easy to grasp and manipulate. Consider the conniptions ancient Romans would have gone through in adding CCCVII and MMXLIII to produce MMCCCL, and then compare it with how you’d do the same thing: Add 307 and 2,043 to produce 2,350.
That’s the power of zero. That’s also all I’ll say on those lines in the rest of this column. Because in the rest of this column, I want to focus on bees. Specifically, on pretty strong evidence that bees can understand the idea of zero.
As you scoff at that, I’ll remind you that I’ve written in this space before about a team of Australian scientists who taught bees to add and subtract (https://t.ly/yUIk7). The same team extended their research to show that “bees could…extrapolate the concept of ‘less than’ to order zero numerosity.” And in doing so, they “demonstrated an understanding that parallels animals such as the African grey parrot, non-human primates, and even preschool children.” (Numerical ordering of zero in honey bees, Scarlett R. Howard et al., Science, 8 June 2018, https://t.ly/ngycI).
How they did this is, to me, even more compelling than addition and subtraction.
To begin, though, think about how we come to understand all that zero actually means. The scientists suggest four stages in this process of understanding. First, we learn to define zero as nothing. Second, the contrast between “nothing” and “something”. Third, the position of zero at the low end of the positive numbers, meaning it is less than all of them. Fourth, and perhaps most complex, the way zero is represented and then used in numbers and mathematics (as a placeholder, for example).
Keep those in mind as we walk through some of the experiments the scientists subjected the bees to.
The first experiment prompts bees to grasp the ideas of “less” and “greater”. They were shown white squares that contained between one and four shapes and tasked with distinguishing between them. Selecting right was rewarded with a sweet treat, wrong led to mild bitterness (a charmingly-named “appetitive-aversive” protocol). After a number of repetitions, the bees showed they had learned these ideas, to the extent that they even used them to deduce that five was more shapes than two or three. But they also seemed to have understood that zero “lies at the lower end of the numerical continuum”—they could both choose an empty square as “less than” a square with some shapes, and choose a square containing some shapes as “greater than” an empty one.
In the second experiment, bees that had shown an understanding of “less” when working with the numbers two to five were then offered one and zero, numbers they had not seen. They chose zero as a lower number than one, which choice, the scientists note, “is challenging for some other animals.”
Note here that in their training, two—being less than the other numbers the bees worked with—was always rewarded. When they were later tasked with choosing between two and zero as possible answers to what’s “less than” one, they chose zero only about half the time. No better than chance. That showed that the potential reward for choosing two—a choice always rewarded in this experiment, remember—also weighed on the insects’ minds.
But then there was the third experiment. This one measured the effect of numerical distance from zero on bee behaviour. If bees really do see zero as another number, but lower than all the rest, then how would they consider zero versus six compared with zero versus smaller numbers? That is, compare an empty plate with one with a lone peanut on it. Then compare it with a plate with six peanuts. If asked in each case to point out the plate with fewer peanuts, which of those two comparisons would be easier to decide? If you think about it, you’ll agree that zero versus six peanuts makes a more obvious difference than zero versus one.
Turns out that the bees were reasonably good in deciding that zero was less than the other numbers on offer. But their choices grew noticeably more accurate as the gap widened: “There was a significant effect of numerical distance on accuracy.” Number magnitudes, clearly, made sense to these bees.
To sum up: The scientists showed that their bees used “less than” and “greater than” to understand that zero means nothing. But they also placed zero correctly relative to other numbers; in particular, as less than one.
Those are truly impressive achievements. The ancient Romans could have taken note, you’d think.
(Today is Srinivasa Ramanujan’s birthday, National Mathematics Day. Find a nearby circle and walk around it. Then walk across its diameter. Think of Ramanujan as you do.)
Once a computer scientist, Dilip D’Souza now lives in Mumbai and writes for his dinners. His Twitter handle is @DeathEndsFun.
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Published: 21 Dec 2023, 10:43 PM IST
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