The mathematical concept of zero is, today, something completely intuitive. However, this was not always like that. Although in ancient times there were already civilizations that used a specific symbol to mark a null value, such as the Babylonians, they only used it as a punctuation mark. However, it seems that they failed to understand the true value of the number zero. The Mayans had a specific glyph to designate zero , but it never made it out of the Americas. Everything seems to indicate that the use of zero as a mathematical concept as we use it today has its origin in what is now Cambodia, and dates back to the 6th century . Although it is also true that cultures that lack zero as a form of notation are capable of using the concept of the empty set without a symbol to indicate it, it is one of the numerical quantities that takes the longest to understand during childhood .
With this background, we understand that understanding zero as a mathematical value is not as simple as intuition invites us to think. This fact puts into perspective the incredible capacity that the animals that are the protagonists of this article have shown to have.
Primates, ravens and parrots
This list could not be headed by others than our cousins, the primates . Among them, and aside from the human being, there are numerous species that dominate the concept of zero, of which the chimpanzee stands out. But they are by no means the only ones.
Let’s talk about ravens. It is well known that these animals are extraordinarily intelligent, and that they have some mathematical ability. In fact, we know that corvids are not only capable of distinguishing different quantities and understanding which ones are greater than others, something that many other animals do, but that they can even understand concepts such as addition.
With this knowledge, a group of researchers trained crows —a kind of raven— to identify different numbers. They were shown images with one, two, three, four dots, or none, while their brain activity was monitored . They not only confirmed what was already known—that there were certain neurons associated with the different positive values—but also that there was a specific signal for the empty set. The zero.
But they did not stop there. In a subsequent test, the animals were invited to compare two images showing certain quantities, including zero, so that they would indicate when the quantities were the same in said images . Many times the ravens were right, but what was truly significant was when they missed. And it is that frequently they confused images that showed close quantities —3 and 4, for example—, but it did not happen with clearly different quantities —4 and 1, for example—. When the crows were wrong with the zero, they always mistook it for the one. According to the researchers, this proves that animals recognize not only the concept of zero, but that they have a mental number line, in which zero is the smallest value , it is next to one, and on the opposite side of two. Like ours.
But these clever birds aren’t the only ones who can grasp the complex mathematical concept of zero. In 2005, the ability of a non-primate animal to recognize zero as a mathematical concept was described for the first time; It was Alex , a gray parrot who had been taught the word “none” —none in English— to answer which object was bigger between two identical objects. Alex also used it to indicate the absence of differences in other features such as shape or color. But, although he had never been taught to use that term to indicate the absence of objects, the animal abstracted the notion of the absence of differences to the absence of quantity .
Of course, as we have said, there are also primates — apart from humans — such as chimpanzees, capable of distinguishing the concept of zero. In our case, that of primates, it is a capacity that seems to be in the parietal zone of the neocortex , the most recent layer of the brain in our evolutionary history. However, birds do not have this cerebral cortex , which indicates that the ability to recognize the value of the empty set as a numerical quantity has emerged independently in different animal groups, obtaining a similar result. We call this phenomenon evolutionary convergence .
The convergence expands
This trait seems indeed to have arisen multiple times in the history of life, in very different animals. But not only in birds and mammals. Not only, in fact, in vertebrates. Among invertebrates, a few years ago the discovery that bees also have the ability to understand the concept of zero stood out. Today we know that some species of ants also have the notion of the null quantity and that, like us and the crows, they locate it at the lower end of their mental number line.
It would not be surprising if, as this type of capacity is investigated in more animals, new cases emerge. Outside of insects, cephalopods , the group to which cuttlefish and octopuses belong, seem like good candidates for recognizing the value of zero. After all, these fascinating animals are so extraordinarily intelligent that they have even shown the ability to foresee and plan for the future.
References
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Cammaerts, M.-C., & Cammaerts, R. (2020). Ants Acquire the Notion of Zero through Experiences. International Journal of Biology, 12(2), p13. https://doi.org/10.5539/ijb.v12n2p13
Howard, S. R., Avarguès-Weber, A., Garcia, J. E., Greentree, A. D., & Dyer, A. G. (2018). Numerical ordering of zero in honey bees. Science, 360(6393), 1124-1126. https://doi.org/10.1126/science.aar4975
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Schnell, A. K., Boeckle, M., Rivera, M., Clayton, N. S., & Hanlon, R. T. (2021). Cuttlefish exert self-control in a delay of gratification task. Proceedings of the Royal Society B: Biological Sciences, 288(1946), 20203161. https://doi.org/10.1098/rspb.2020.3161
