What led humans to counting and when?

Before an intelligence can turn to counting it must first have some concept of numbers. When and how did our ancient ancestors  first develop a concept of numbers and then start counting?

Some claim that:

Two possibilities for the origin of counting have been posited. One is that counting spontaneously arose throughout the world more or less independently from place to place, tribe to tribe. The other is that counting was invented just once and it spread throughout the world from that source. The latter view, maintained by Abraham Seidenberg, is based upon a remarkable number of similarities of number systems throughout the world.

But both  Abraham Seidenberg’s belief in the spread by rituals or the belief that counting started simultaneously around the world leave something wanting. They seem to me to bypass actually considering the origin and address instead the spread of counting. They don’t really address the “when” and the “what” of how it all started.

It seems clear that many animals do distinguish – in a primitive and elementary way – between “more” and “less, and “few” and “many”,and  “bigger” and “smaller”, and even manage to distinguish between simple number counts. They show a sophisticated use of hierarchy and precedence. However it is much less certain that animals have any real concept of number or of mathematical operations.  Marc Hauser’s observations on animal cognition are still valid (and not I think disqualified by his recent transgressions in the Hausergate affair).

It is clear that animals have need for certain basic arithmetic calculations. We know little, however, about how they represent those calculations, and the corresponding numbers, in their heads. ……

…….  Rhesus monkeys appear to understand that 1 + 1 = 2. They also seem to understand that 2 + 1 = 3, 2 – 1 = 1, and 3 – 1 = 2—but fail, however, to understand that 2 + 2 = 4. ……

……. These results suggest that rhesus monkeys have a system of spontaneous quantification that translates to something like one, two, three and many.

There have been primitive and isolated tribes of anatomically modern humans (AMH) contacted in the 19th and 20th centuries who are not much more numerate (having no need to be numerate) but whose concept of number is significantly advanced from that of the rhesus monkeys. Humans separated from chimpanzees about 8 million years ago. It would be reasonable to conclude therefore that by the time archaic humans had come down from the trees and started walking upright (c. 6 million years ago) they already had concepts of number and counting at least as advanced as that exhibited by rhesus monkeys today. As early as 6 million years ago we can reasonably assume that our ancestors had at least a rudimentary (1,2, many) concept of number and could perform some simple arithmetic operations.

Further development of numeracy would – I think – have been only in response to specific needs. I speculate that it was the need to co-operate which needed such feats of counting or numeracy to be communicated to others.

The earliest evidence we have of humans having counting ability are ancient tally sticks made of bone and dating upto 50,000 years ago. An ability to tally at least upto 55 is evident. One of the tally sticks may have been a form of lunar calendar. By this time apparently they had a well developed concept of time. And concepts of time lead immediately and inevitably to the identification of recurring time periods. By 50,000 years ago our ancestors counted days and months and probably years. Counting numbers of people would have been child’s play. They had clearly developed some sophistication not only in “numbering” by this time but had also progressed from sounds and gestures into speech.  They were well into the beginnings of language.

Marks on a tally stick tell us a great deal. The practice must have been developed in response to a need. Vocalisations – words – must have existed to describe the tally marks. These marks were inherently symbolic of something else. They are evidence of the ability to symbolise and to think in abstract terms. Perhaps they represented numbers of days or a count of cattle or of items of food or of number of people in the tribe. But their very existence suggests that the concept of ownership of property – by the individual or by the tribe – was already in place. Quite probably a system of trading with other tribes and protocols for such trade were also in place. At 50,000 years ago our ancestors were clearly on the threshold of using symbols not just on tally sticks or in cave paintings but in a general way and that would have been the start of developing a written language.

So while it was less than 6 million years ago, we need to go further back in time than 50,000 years ago to identify when counting took off – when “1, 2, 3, many” advanced to something else. But this is in an age where evidence will be hard to come by and I can only speculate.

By some 2 million years ago our ancestors were making stone tools. By the time of Neanderthals – around 400,000 years ago – they had the physiology necessary for the production of speech. Neanderthals may well even have had the so-called “language gene” (FOXP2). This would suggest that sometime earlier than 200,000 years ago, all the members of the genus Homo of that time (Archaic Humans, Neanderthals, Denisovans …) had evolved the physiological and genetic wherewithal necessary for speech. Having the capability of speech, of course, was merely a precursor for the long slow journey from sounds through gestures to speech. It would have been the need to cooperate among members of an increasing tribe, in increasingly complex survival and social situations, which could have provided the impetus for communication and the development of speech. Cooperation needed not only within the members of a tribe but also between tribes. I speculate that the need to communicate to others lies not only behind speech but also behind the development of counting. Words for “ten” or a “hundred” or a “million” would have been invented only when it was necessary to communicate them. Trading and the need to “reach agreements” would have led to the need for principles of equivalence and for simple arithmetic operations. The needs of trading by barter which in turn would need equating dissimilar things would have led to the abstractions and generalisations that numbers allow. I further speculate that it was the increasing complexities of cooperation with outside tribes and their necessary requirements for communication that drove the parallel – and inter-linked – development of speech and numerology starting some 150,000 years ago.

My time-line then becomes:

• 8 million YBP           Human Chimpanzee divergence
• 6 million YBP           Rudimentary counting among Archaic humans (1, 2, 3 many)
• 2 million YBP           Stone tools
• 600,000 YBP          Archaic Human – Neanderthal divergence
• 400,000 YBP          Physiological and genetic capability for speech?
• 150,000 YBP           Speech and counting develop together
• 50,000   YBP           Verbal language, counting, trading, calendars in place (tally sticks)
• 30,000   YBP           Beginnings of written language?

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