Those with simple number systems (an upper limit not much higher than ‘four’) often had few material possessions, such as weapons, tools or jewellery; those with elaborate systems always had a richer array of possessions

How did Neanderthals and other ancient humans learn to count? Colin Barras. Nature 594, 22-25, Jun 2 2021. https://www.nature.com/articles/d41586-021-01429-6

Archaeological finds suggest that people developed numbers tens of thousands of years ago. Scholars are now exploring the first detailed hypotheses about this life-changing invention.

Counting on possessions

In a 2013 study11, Overmann analysed anthropological data relating to 33 contemporary hunter-gatherer societies across the world. She discovered that those with simple number systems (an upper limit not much higher than ‘four’) often had few material possessions, such as weapons, tools or jewellery. Those with elaborate systems (an upper numeral limit much higher than ‘four’) always had a richer array of possessions. The evidence suggested to Overmann that societies might need a variety of material possessions if they are to develop such number systems.

In societies with complex number systems, there were clues to how those systems developed. Significantly, Overmann noted that it was common for these societies to use quinary (base 5), decimal or vigesimal (base 20) systems. This suggested to her that many number systems began with a finger-counting stage.

This finger-counting stage is important, according to Overmann. She is an advocate of material engagement theory (MET), a framework devised about a decade ago by cognitive archaeologist Lambros Malafouris at the University of Oxford, UK12. MET maintains that the mind extends beyond the brain and into objects, such as tools or even a person’s fingers. This extension allows ideas to be realized in physical form; so, in the case of counting, MET suggests that the mental conceptualization of numbers can include the fingers. That makes numbers more tangible and easier to add or subtract.

The societies that moved beyond finger-counting did so, argues Overmann, because they developed a clearer social need for numbers. Perhaps most obviously, a society with more material possessions has a greater need to count (and to count much higher than ‘four’) to keep track of objects.

Overmann thinks MET implies that there is another way in which material possessions are necessary for the elaboration of number systems. An artefact such as a tally stick also becomes an extension of the mind, and the act of marking tally notches on the stick helps to anchor and stabilize numbers as someone counts. These aids could have been crucial to the process through which humans first began counting up to large numbers13.

Eventually, says Overmann, some societies moved beyond tally sticks. This first happened in Mesopotamia around the time when cities emerged there, creating an even greater need for numbers to keep track of resources and people. Archaeological evidence suggests that by 5,500 years ago, some Mesopotamians had begun using small clay tokens as counting aids.

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According to Overmann, MET suggests that these tokens were also extensions of the mind, and that they fostered the emergence of new numerical properties. In particular, the shapes of tokens came to represent different values: 10 small cone tokens were equivalent to a sphere token, and 6 spheres were equivalent to a large cone token. The existence of large cones, each equivalent to 60 small cones, allowed the Mesopotamians to count into the thousands using relatively few tokens.

Andrea Bender, a psychologist at the University of Bergen in Norway and another leader of the QUANTA project, says that the team members plan to gather and analyse large amounts of data relating to the world’s numeral systems. That should allow them to test Overmann’s hypothesis that body parts and artefacts might have helped societies to develop number systems that ultimately count into the thousands and higher. But Bender says she and her colleagues are not presupposing that Overmann’s MET-based ideas are correct.

Others are more enthusiastic. Karim Zahidi, a philosopher at the University of Antwerp in Belgium, says that although Overmann’s scenario is still incomplete, it has real potential to explain the development of the elaborate number systems in use today.

Linguistic leads

Overmann acknowledges that her hypothesis is silent on one issue: when in prehistory human societies began developing number systems. Linguistics might offer some help here. One line of evidence suggests that number words could have a history stretching back at least tens of thousands of years.

Evolutionary biologist Mark Pagel at the University of Reading, UK, and his colleagues have spent many years exploring the history of words in extant language families, with the aid of computational tools that they initially developed to study biological evolution. Essentially, words are treated as entities that either remain stable or are outcompeted and replaced as languages spread and diversify. For instance, English ‘water’ and German ‘wasser’ are clearly related, making them cognates that derive from the same ancient word — an example of stability. But English ‘hand’ is distinct from Spanish ‘mano’ — evidence of word replacement at some time in the past. By assessing how frequently such replacement events occur over long periods, it is possible to estimate rates of change and to infer how old words are.

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Using this approach, Pagel and Andrew Meade at Reading showed that low-value number words (‘one’ to ‘five’) are among the most stable features of spoken languages14. Indeed, they change so infrequently across language families — such as the Indo-European family, which includes many modern European and southern Asian languages — that they seem to have been stable for anywhere between 10,000 and 100,000 years.

This doesn’t prove that the numbers from ‘one’ to ‘five’ derive from ancient cognates that were first spoken tens of thousands of years ago, but Pagel says it’s at least “conceivable” that a modern and a Palaeolithic Eurasian could have understood one another when it came to such number words.

Pagel’s work has its fans, including Gray, another of QUANTA’s leaders, but his claims are challenged by some scholars of ancient languages. Don Ringe, a historical linguist at the University of Pennsylvania in Philadelphia, says it isn’t clear that the stability of lower-number words can just be projected far back into prehistory, regardless of how stable they seem to be in recent millennia.

That all adds up to a slew of open questions about when and how humans first started using numbers. But despite the debate swirling around these questions, researchers agree it’s a topic that deserves a lot more attention. “Numbers are just so fundamental to everything we do,” says Gray. “It’s hard to conceive of human life without them.”

Numbers might even have gained this importance deep in prehistory. The notched baboon bone from Border Cave is worn smooth in a way that indicates that ancient humans used it over many years. “It was clearly an important item for the individual who produced it,” says D’Errico.

Not so for the Les Pradelles specimen, which lacks this smooth surface. If it does record numerical information, that might not have been quite as important at the time. In fact, although D’Errico and his colleagues have spent innumerable hours analysing the bone, he says it’s possible that the Neanderthal who chipped away at that hyena femur some 60,000 years ago spent very little time using it before tossing the bone aside.