By Eleanor Heydt

“Come here!” calls Meno to a boy. Socrates shows the boy a square. “Now boy, you know a square is a figure with all sides equal?” he asks, drawing a square. The boy responds, “Yes.” “And these lines which go through the middle of it are also equal?” The boy agrees. Socrates proceeds in this way, asking the boy simple questions until the boy solves a complex geometry problem. Looking at Meno, he says, since the boy had never been taught math, “he must always have known” and therefore, knowledge of math is innate.

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Counting and numbers feel so natural and fundamental to human existence, similar to language. When we see something, one of the first ways we describe it is with numbers—“there are four pencils,” “she is 30 years old.” But recent evidence from archaeology and anthropology raises questions about how natural counting and numbers themselves really are.

In 1973, archaeologists sifting through a cave in South Africa discovered the Lebombo bone, a 40,000 year old baboon fibula with notches scratched on it. The ecstatic archaeologists rushed to tell the world about their find. This boring-seeming bone with tally marks was the earliest-known instance of counting among humans. While 40,000 years may seem like forever, hominids have been building fires for 1,000,000 and using stone tools for 2,600,000, meaning, based on our current evidence, hominids have been counting for less than 1% of their existence.

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Even once we started counting, we didn’t do it in a uniform way. For example, look at base-10 (a base is the amount of unique number symbols we use (ex: 0-9)). Base-10 appears to us as the obvious way to count. Of course we count in 10s instead of 12s or 83s because we have 10 fingers. Science fiction writers copy this logic, making their 6-fingered alien species count in base-12, etc. But why only count fingers? The Mayans had base 20 because they counted fingers and toes. The Mountain-Ok of Papua New Guinea and the Aboriginal Wimmera use bases like 13, 15, and 27 because, once they finish their fingers on one hand, they move up to their palm, elbows, shoulders, throat, nose, and down to the other hand. While base-10 was developed independently by several civilizations, like the Egyptians, Indians, and Chinese, there is nothing special about 10, or any other base, for counting.

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In fact, there are still groups that don’t count at all. In 2005, anthropologist Daniel Everett published a controversial paper claiming he found a group, the Pirahã (an Amazonian tribe), without number concepts. Anumeric groups exist throughout the globe, from the Amazon to Botswana to Australia, but are rapidly disappearing as they assimilate to other cultures. Everett, one of the few people who speak the Pirahã language, sprang to take advantage of his fleeting opportunity. First, he performed an experiment where he strung beads into a necklace and asked volunteer tribesmen to make an identical necklace. While for strings of two or three beads, they were entirely correct, as the number got higher, they started making estimations, usually being off by a couple beads for a string of 7 compared to the 100% accuracy of people from numerate societies. 

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How did humans function without a concept of, say, the number 4? How could they trade, keep track of their chickens, and remember how much fish they’ve stored? There have been many stories of frustrated anthropologists trying to glean information off these tribes. John Peters, who studied the Xilixana, complained that when he asked how many people lived in a nearby village, they responded, “more than two,” which might mean “the population was 16 or 80.” An explorer in southern Africa recalls trying to buy two sheep for four sticks of tobacco from a man in the Damara tribe and watching as the befuddled herdsman tried to figure out the arithmetic. As strange as it seems to us, though, hunter-gatherer societies can operate perfectly well without numbers. According to Everett, when the Pirahã are piling into a canoe, they wouldn’t say, “It has a 3-person capacity,” but instead yell “STOP” when it starts sinking. The Damara manage to keep track of their oxen by faces. They’ve never needed numbers, so they never developed them.

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However, now tribesmen living in the middle of the Amazon or Outback can be found wearing mass-produced T-shirts and sandals. As their isolation comes to an end, so too does the practicality of anumericy. Youths in remaining anumeric tribes are picking up counting. The Pirahã once asked Everett to teach them counting so they wouldn’t be so easily cheated by Portuguese traders during exchanges of Brazil nuts for tobacco.

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Our society revolves around numbers—dates, money, populations, age. It can be tempting to think they are a universal feature of human communities, but really they started as a simple tool we invented instead of an inherent part of human thought.

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Sources:

1. https://en.wikipedia.org/wiki/Australian_Aboriginal_enumeration.

2. https://www.newscientist.com/article/mg21028081-500-one-two-many-the-prehistory-of-counting/.

3. https://www.laphamsquarterly.org/roundtable/early-history-countin

4. https://en.wikipedia.org/wiki/Ishango_bone.  

5. https://www.scientificamerican.com/article/dont-count-on-it/.

6. O'Shaughnessy, David M., et al. “The Cultural Origins of Symbolic Number.” American Psychological Association, vol. 129, no. 0033-295X, 2022, pp. 1442-1456.  

7. Plato. Meno.

8. https://news.mit.edu/2008/language-0624.