It may seem surprising, but the concept of “zero” is actually a relatively recent mathematical innovation. Indeed, the first rudimentary use of a zero-like notation didn’t appear until around 300 BC, when the Babylonians began using a special placeholder symbol to designate the absence of another value in their base-sixty number system. While revolutionary in its own right, the Babylonian null placeholder was still rather limited (for example, it couldn’t be used alone and never appeared at the end of a number), and another millennium passed before gifted Indian mathematicians and astronomers introduced a fully functional “true zero” as part of a formalized system of arithmetic operations. Some 1,500 years later, with this important mathematical foundation finally in place, Apple launched the iPhone on the AT&T wireless network.
Are there any parallels in the animal world, any similarly gifted nonhuman mathematicians that have innovated with the concept of zero?
The answer seems to be yes: Alex, the male African Grey Parrot of book and movie fame (Alex & Me), may go down in history as the parrot equivalent of Albert Einstein, revolutionizing parrot mathematics with his insight into concepts of nothingness.
It was in late 2003, early 2004 that Alex appears to have had his great breakthrough regarding the mathematical usefulness of zero-like concepts. At that time, Irene Pepperberg and Jesse Gordon of Brandeis University, who had been working with Alex over an extended period on a variety of cognitive and communicative studies, decided to conduct some experiments to explore the extent of his numerical competence.
Alex already was adept at tests requiring him to identify numbers of objects – he knew the English words for one through six, and could provide accurate verbal responses to questions about, for instance, how many green blocks were included in a mixed array of blue, red and green blocks and balls. Pepperberg and Gordon now wanted to see whether Alex really understood the numbers he was providing and could grasp the interchangeability of numerical questions.
To do so, they flipped things around: rather than asking Alex to provide the number of objects in particular groupings as he had in prior experiments, they went in the other direction by asking him to indicate which object groups were associated with a particular number. That is, they presented Alex with a tray of objects of various materials, colors and shapes (for example, six green plastic spoons, four yellow tops and three orange wooden sticks), and asked him questions such as “What color six?” and “What toy four?” Alex’s task was to look at the objects on the tray and then respond correctly (in this case, with “green” based on the six green spoons and “top” based on the four yellow tops).
(I know, this all sounds a bit like Jeopardy: “Please be sure to phrase your answer in the form of a question…”)
Perhaps not surprisingly, Alex aced the test, responding correctly to this new battery of questions over 80% of the time. More significant, though, is how Alex – apparently bored with the questioning – spontaneously extended the scope of the experiment:
On the 10th trial within the first dozen, Alex was asked “What color 3?” to a set of two, three, and six objects. He replied “five”; the questioner asked him twice more and each time he replied “five.” The questioner, not attending to the tray, finally said “OK, Alex, tell me, what color 5?” Alex immediately responded “none.”
Now, Alex had previously been trained to use the word “none” in a different context – comparing objects for similarity or difference (for example, to respond to a question about which of two identically-sized objects was bigger) – but he had never been taught to use “none” to describe a quantity that was not present. Fascinated, Pepperberg and Gordon randomly interspersed six more “none trials” into the ongoing experiment. It turned out that Alex’s response was no fluke – he gave the correct “none” response in five out of six of these trials, an accuracy rate of 83.3%.
Here’s a brief video in which Pepperberg describes the experiment and Alex’s unexpected use of the “none” concept:
Thus, it appears that Alex spontaneously used “none” in a zero-like manner to label a null set and designate an absence of objects. As the researchers summarized it, “the notion of none, even if already associated with absence of similarity and difference (and lack of size difference), is abstract and relies on violation of an expectation of presence; that Alex transferred the notion from other domains to quantity, without training or prompting by humans, was unexpected.”
While Alex’s use of “none” may not be as full and robust as the true zero concept that we use today, it nonetheless (no pun intended) is quite impressive. Moreover, Alex’s insight may prove to be quite practical, with the parrot concept of “none” providing helpful guidance as we attempt to answer some of the more pressing questions of our time, including:
- How many neutrinos are able to travel faster than the speed of light?
- How much deep fried batter-covered butter on a stick should you attempt to eat at one sitting (or ever)?
- How many people are surprised at the fact that dinosaurs went extinct after hearing the Barney the Dinosaur “I Love You” theme song?
Pepperberg, I., & Gordon, J. (2005). Number Comprehension by a Grey Parrot (Psittacus erithacus), Including a Zero-Like Concept. Journal of Comparative Psychology, 119 (2), 197-209 DOI: 10.1037/0735-7036.119.2.197.