How Did Ancient Humans Learn to Count?

Feature F. D’ERRICO F. Prehistoric accounting? Markings made on a hyena bone by a Neanderthal might have recorded numerical information. HOW DID ANCIENT HUMANS LEARN TO COUNT? Recent archaeological studies and other analyses have spurred researchers to construct some of the first detailed hypotheses describing the prehistoric development of number systems. By Colin Barras

ome 60,000 years ago, in what is and he thinks that the hyena bone — found he was venturing into territory that few now western France, a Neanderthal in the 1970s at the site of Les Pradelles near scientists had explored: the ancient roots picked up a chunk of hyena femur Angoulême — stands out as unusual. Although of numbers. “The origin of numbers is still a and a stone tool and began to work. ancient carved artefacts are often interpreted relatively vacant niche in scientific research,” When the task was complete, the as artworks, the Les Pradelles bone seems to says Russell Gray, an evolutionary biologist bone bore nine notches that were have been more functional, says D’Errico. at the Max Planck Institute for Evolutionary strikingly similar and approximately He argues that it might encode numerical Anthropology in Leipzig, Germany. Research- parallel, as if they were meant to information. And if that’s correct, anatomi- ers don’t even agree, at times, on what num- Ssignify something. cally modern humans might not have been bers are, although a 2017 study2 defined them Francesco d’Errico, an archaeologist at the alone in developing a system of numerical as discrete entities with exact values that are University of Bordeaux, France, has an idea notations: Neanderthals might have begun represented by symbols in the form of words about the marks. He has examined many to do so, too1. and signs. ancient carved artefacts during his career, When D’Errico published his ideas in 2018, Now the origin of numbers is attracting

increasing attention as researchers from a chicks3 can instantly recognize quantities words and written signs that are used to repre- variety of fields address the problem from up to four, a skill known as subitizing. Some sent them, must be produced by cultural evo- different vantage points. animals are also capable of ‘large-quantity lution — a process in which individuals learn Cognitive scientists, anthropologists and discrimination’: they can appreciate the dif- through imitation or formal teaching to adopt psychologists are looking at contemporary ference between two large quantities if they a new skill (such as how to use a tool). cultures to understand differences among are distinct enough. Creatures with this skill Although many animals have culture, one existing number systems — defined as the could, for example, distinguish 10 objects that involves numbers is essentially unique to symbols that a society uses for counting and from 20 objects, but not 20 from 21. Six- humans. A handful of chimpanzees have been manipulating numbers. Their hope is that month-old human infants also show a similar taught in captivity to use abstract symbols to clues buried in modern systems might illu- appreciation of quantity, even before they represent quantities, but neither chimps nor minate details of their origins. Meanwhile, have had significant exposure to human cul- any other non-human species use such sym- archaeologists have begun looking for evi- ture or language. bols in the natural world. Núñez suggests that a dence of ancient numerical notations, and distinction should therefore be made between evolutionary biologists with an interest in what he has dubbed the innate ‘quantical’ cog- language are exploring the deep origins of nition seen in animals and the learnt ‘numeri- number words. These studies have spurred cal’ cognition seen in humans2. researchers to formulate some of the first “The origin of But not everyone agrees. Nieder argues that detailed hypotheses for the prehistoric devel- numbers is still a neurological studies show clear similarities opment of number systems. between the way in which quantities are pro- And an infusion of funding will stimulate relatively vacant niche cessed in the brains of non-human animals and more studies in this area. This year, an inter- in scientific research.” how the human brain processes numbers. He national research team with a €10-million says that it is misleading to draw too firm a (US$11.9-million) grant from the European line between the two behaviours4, although Research Council will start to test different What all of this suggests, says Andreas he agrees that human numerical abilities hypotheses, as part of a broader effort to Nieder, a neuroscientist at the University of are much more advanced than those of any study when, why and how number systems Tübingen, Germany, is that humans have an other animal. “No [non-human] animal is able appeared and spread around the world. The innate appreciation of numbers. That arose to truly represent number symbols,” he says. project, called the Evolution of Cognitive Tools through evolutionary processes such as nat- D’Errico’s analysis of the Les Pradelles bone for Quantification (QUANTA), might even pro- ural selection, he says, because it would have could help to provide some insights into how vide insights into whether number systems carried adaptive benefits. the earliest stages of number systems took are unique to anatomically modern humans, Others interpret the evidence differently. shape. He studied the nine notches under a or were conceivably present in nascent form Rafael Núñez, a cognitive scientist at the Uni- microscope, and says that their shapes, depths in Neanderthals. versity of California, San Diego, and one of and other details are so alike that all seem to the leaders of QUANTA, accepts that many have been made using the same stone tool, An instinct for numbers animals might have an innate appreciation of held in the same way. This suggests that all Although researchers once thought that quantity. However, he argues that the human were made by one individual in a single ses- humans were the only species with a sense of perception of numbers is typically much more sion lasting perhaps a few minutes or hours. quantity, studies since the mid-twentieth cen- sophisticated, and can’t have arisen through (At some other time, eight much shallower tury have revealed that many animals share the a process such as natural selection. Instead, marks were carved on the bone, too.) ability. For instance, fish, bees and newborn many aspects of numbers, such as the spoken However, D’Errico doesn’t think that this individual intended to produce a decora- tive pattern because the marks are uneven. For comparison, he has analysed the seven notches on a 40,000-year-old raven bone from a site of Neanderthal occupation in Crimea. Statistical analysis shows that the notches on this bone are spaced with the same sort of regularity seen when modern volunteers are given a similar bone and asked to mark it with equally spaced notches5. But this type of analysis also shows that the marks on the Les Pradelles bone lack such regularity. That observation — and the fact that the notches were generated in a single session — led D’Errico to consider that they might have been merely functional, pro- viding a record of numerical information.

Marks of sophistication The Les Pradelles bone is not an isolated find. For instance, during excavations at Border Cave in South Africa, archaeologists discovered an approximately 42,000-year-old

MATTHEW HORWOOD/GETTY MATTHEW baboon fibula that was also marked with Some researchers suggest the mind extends beyond the brain to fingers and other objects. notches. D’Errico suspects that anatomically modern humans living there at the time used

Feature the bone to record numerical information. In QUANTA will use data from anthropology, cog- are still in use around the world. For example, the case of this bone, microscopic analysis nitive science, linguistics and archaeology to linguists Claire Bowern and Jason Zentz at of its 29 notches suggests they were carved better understand those social factors, says Yale University in New Haven, Connecticut, using four distinct tools and so represent four D’Errico, who is one of the project’s four prin- reported in a 2012 survey that 139 Aboriginal counting events, which D’Errico thinks took cipal investigators. Australian languages have an upper limit of place on four separate occasions1. Moreover, ‘three’ or ‘four’ for specific numerals. Some of he says that discoveries over the past 20 years Bones of contention those languages use natural quantifiers such show that ancient humans began producing However, QUANTA researcher Núñez, along as ‘several’ and ‘many’ to indicate higher val- abstract engravings, which hint at sophisti- with some researchers who are not involved ues9. There is even one group, the Pirahã peo- cated cognition, hundreds of thousands of in the project, cautions that ancient artefacts ple of the Brazilian Amazon, that is sometimes years earlier than was once thought. such as the Les Pradelles bone are challenging claimed not to use numbers at all10. In the light of these discoveries, D’Errico has to interpret. Karenleigh Overmann, a cognitive Overmann and other researchers stress that developed a scenario to explain how number archaeologist at the University of Colorado in there’s nothing intellectually lacking about systems might have arisen through the very Colorado Springs, highlights those difficulties societies that use relatively simple number act of producing such artefacts. His hypothe- by citing the example of message sticks used systems. But she wondered whether such sis is one of only two published so far for the by Aboriginal Australians. These sticks, which societies might provide clues about the social prehistoric origin of numbers. are typically flattened or cylindrical lengths of pressures that drive the development of more It all started by accident, he suggests, as wood, are adorned with notches that might elaborate number systems. early hominins unintentionally left marks look as though they encode numerical infor- on bones while they were butchering animal mation — but many do not. Counting on possessions carcasses. Later, the hominins made a cogni- Piers Kelly, a linguistic anthropologist at In a 2013 study11, Overmann analysed anthro- tive leap when they realized that they could the University of New England in Armidale, pological data relating to 33 contemporary deliberately mark bones to produce abstract Australia, who conducted a review of message hunter-gatherer societies across the world. designs — such as those seen on an approxi- sticks8, agrees with Overmann’s point. He says She discovered that those with simple number mately 430,000-year-old shell found in Trinil, that some message sticks are carved with systems (an upper limit not much higher than Indonesia6. At some point after that, another tally-like marks, but these often act as a visual ‘four’) often had few material possessions, leap occurred: individual marks began to memory aid to help a messenger recall details such as weapons, tools or jewellery. Those take on meaning, with some of them perhaps of the message they are delivering. “They call with elaborate systems (an upper numeral encoding numerical information. The Les to mind the act of recounting a narrative rather limit much higher than ‘four’) always had a Pradelles hyena bone is potentially the earliest than accounting a quantity,” says Kelly. richer array of possessions. The evidence known example of this type of mark-making, Wunyungar, an Aboriginal Australian who is suggested to Overmann that societies might says D’Errico. He thinks that with further a member of the Gooreng Gooreng and Wakka need a variety of material possessions if they leaps, or what he dubs cultural exaptations, Wakka communities, says that the sticks might are to develop such number systems. such notches eventually led to the invention transmit one of any number of distinct mes- In societies with complex number systems, of number signs such as 1, 2 and 3 (ref. 7). sages. “Some are used for trading — for foods, there were clues to how those systems devel- D’Errico acknowledges that there are gaps tools or weapons,” he says. “Others might carry oped. Significantly, Overmann noted that it in this scenario. It isn’t clear what cultural or messages of peace after war.” was common for these societies to use quinary social factors might have encouraged ancient Overmann has developed her own hypothe- (base 5), decimal or vigesimal (base 20) sys- hominins to begin marking bones or other sis to explain how number systems might have tems. This suggested to her that many number artefacts deliberately, or to then harness emerged in prehistory — a task made easier by systems began with a finger-counting stage. those marks to record numerical information. the fact that a wide variety of number systems This finger-counting stage is important, according to Overmann. She is an advocate of material engagement theory (MET), a frame- work devised about a decade ago by cognitive archaeologist Lambros Malafouris at the Uni- versity 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 conceptualiza- tion 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 VIA GETTY RUPETA/NURPHOTO OLEKSANDR A number line echoes some of the numerical tools that were used by ancient humans. are necessary for the elaboration of number systems. An artefact such as a tally stick also

F. D’ERRICO & L. BACKWELL D’ERRICO F. Researchers think that people cut notches into this baboon bone some 40,000 years ago as an early form of counting.

becomes an extension of the mind, and the number words could have a history stretch- languages. Don Ringe, a historical linguist at act of marking tally notches on the stick helps ing back at least tens of thousands of years. the University of Pennsylvania in Philadelphia, to anchor and stabilize numbers as someone Evolutionary biologist Mark Pagel at the says it isn’t clear that the stability of low- counts. These aids could have been crucial to University of Reading, UK, and his colleagues er-number words can just be projected far the process through which humans first began have spent many years exploring the history back into prehistory, regardless of how stable counting up to large numbers13. of words in extant language families, with the they seem to be in recent millennia. Eventually, says Overmann, some societies aid of computational tools that they initially That all adds up to a slew of open questions moved beyond tally sticks. This first happened developed to study biological evolution. about when and how humans first started in Mesopotamia around the time when cities Essentially, words are treated as entities that using numbers. But despite the debate swirl- emerged there, creating an even greater need either remain stable or are outcompeted and ing around these questions, researchers for numbers to keep track of resources and replaced as languages spread and diversify. agree it’s a topic that deserves a lot more people. Archaeological evidence suggests that For instance, English ‘water’ and German attention. “Numbers are just so fundamental by 5,500 years ago, some Mesopotamians had to everything we do,” says Gray. “It’s hard to begun using small clay tokens as counting aids. conceive of human life without them.” According to Overmann, MET suggests Numbers might even have gained this that these tokens were also extensions of the “No non-human animal importance deep in prehistory. The notched mind, and that they fostered the emergence baboon bone from Border Cave is worn of new numerical properties. In particular, the is able to truly represent smooth in a way that indicates that ancient shapes of tokens came to represent different number symbols.” humans used it over many years. “It was clearly values: 10 small cone tokens were equivalent an important item for the individual who pro- to a sphere token, and 6 spheres were equiv- duced it,” says D’Errico. alent to a large cone token. The existence of ‘wasser’ are clearly related, making them cog- Not so for the Les Pradelles specimen, large cones, each equivalent to 60 small cones, nates that derive from the same ancient word which lacks this smooth surface. If it does allowed the Mesopotamians to count into the — an example of stability. But English ‘hand’ record numerical information, that might thousands using relatively few tokens. is distinct from Spanish ‘mano’ — evidence of not have been quite as important at the time. Andrea Bender, a psychologist at the Uni- word replacement at some time in the past. By In fact, although D’Errico and his colleagues versity of Bergen in Norway and another assessing how frequently such replacement have spent innumerable hours analysing the leader of the QUANTA project, says that the events occur over long periods, it is possible bone, he says it’s possible that the Neanderthal team members plan to gather and analyse to estimate rates of change and to infer how who chipped away at that hyena femur some large amounts of data relating to the world’s old words are. 60,000 years ago spent very little time using numeral systems. That should allow them to Using this approach, Pagel and Andrew it before tossing the bone aside. test Overmann’s hypothesis that body parts Meade at Reading showed that low-value num- and artefacts might have helped societies to ber words (‘one’ to ‘five’) are among the most Colin Barras is a science journalist in Ann develop number systems that ultimately count stable features of spoken languages14. Indeed, Arbor, Michigan. into the thousands and higher. But Bender says they change so infrequently across language she and her colleagues are not presupposing families — such as the Indo-European family, 1. D’Errico, F. et al. Phil. Trans. R. Soc. B 373, 20160518 that Overmann’s MET-based ideas are correct. which includes many modern European and (2018). Others are more enthusiastic. Karim Zahidi, southern Asian languages — that they seem 2. Núñez, R. E. Trends Cogn. Sci. 21, 409–424 (2017). a philosopher at the University of Antwerp in to have been stable for anywhere between 3. Rugani, R. Phil. Trans. R. Soc. B 373, 20160509 (2018). 4. Nieder, A. Trends Cogn. Sci. 21, 403–404 (2017). Belgium, says that although Overmann’s sce- 10,000 and 100,000 years. 5. Majkić, A., Evans, S., Stepanchuk, V., Tsvelykh, A. & nario is still incomplete, it has real potential This doesn’t prove that the numbers from D’Errico, F. PLoS ONE 12, e0173435 (2017). to explain the development of the elaborate ‘one’ to ‘five’ derive from ancient cognates that 6. Joordens, J. C. A. et al. Nature 518, 228–231 (2015). 7. D’Errico, F. & Colagè, I. Biol. Theory 13, 213–227 (2018). number systems in use today. were first spoken tens of thousands of years 8. Kelly, P. J. Mater. Cult. 25, 133–152 (2020). ago, but Pagel says it’s at least “conceivable” 9. Bowern, C. & Zentz, J. Anthropol. Linguist. 54, 133–160 Linguistic leads that a modern and a Palaeolithic Eurasian (2012). 10. Everett, D. L. Curr. Anthropol. 46, 621–646 (2005). Overmann acknowledges that her hypothe- could have understood one another when it 11. Overmann, K. A. Camb. Archaeol. J. 23, 19–39 (2013). sis is silent on one issue: when in prehistory came to such number words. 12. Malafouris, L. How Things Shape the Mind: A Theory of human societies began developing number Pagel’s work has its fans, including Gray, Material Engagement (MIT Press, 2013). 13. Overmann, K. A. J. Cogn. Cult. 17, 354–373 (2017). systems. Linguistics might offer some help another of QUANTA’s leaders, but his claims 14. Pagel, M. & Meade, A. Phil. Trans. R. Soc. B 373, 20160517 here. One line of evidence suggests that are challenged by some scholars of ancient (2018).