Posts Tagged ‘origins of counting’

Counting was an invention

March 19, 2017

A new book is just out and it seems to be one I have to get. I am waiting to get hold of an electronic version.

Number concepts are a human invention―a tool, much like the wheel, developed and refined over millennia. Numbers allow us to grasp quantities precisely, but they are not innate. Recent research confirms that most specific quantities are not perceived in the absence of a number system. In fact, without the use of numbers, we cannot precisely grasp quantities greater than three; our minds can only estimate beyond this surprisingly minuscule limit.

Numbers fascinate me and especially how they came to be.

The earliest evidence we have of humans having counting ability are ancient tally sticks made of bone and dating up to 50,000 years ago. An ability to tally at least up to 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. …….

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?
Clearly our counting is dominated by the base of 10 and our penchant for 12-based systems. The joints on the fingers of one hand allows us to count to 12 and that together with the five fingers of the other clearly led to our many 60-based counting systems.

I like 60. Equilaterals. Hexagons. Easy to divide by almost anything. Simple integers for halves, quarters, thirds, fifths, sixths, tenths, 12ths, 15ths and 30ths. 3600. 60Hz. Proportions pleasing to the eye. Recurring patterns. Harmonic. Harmony.

The origins of the use of base 60 are lost in the ancient past. By the time the Sumerians used it about 2,500 years ago it was already well established and continued through the Babylonians. But the origin lies much earlier. ……

Why then would the base 60 even come into being?

image sweet science

The answer, I think, still lies in one hand. Hunter-gatherers when required to count would prefer to use only one hand and they must – quite early on and quite often – have had the need for counting to numbers greater than five. And of course using the thumb as pointer one gets to 12 by reckoning up the 3 bones on each of the other 4 fingers. 

My great-grandmother used to count this way when checking the numbers of vegetables (onions, bananas, aubergines) bought by her maid at market. Counting up to 12 usually sufficed for this. When I was a little older, I remember my grandmother using both hands to check off bags of rice brought in from the fields – and of course with two hands she could get to 144. The counting of 12s most likely developed in parallel with counting in base 10 (5,10, 50, 100). The advantageous properties of 12 as a number were fortuitous rather than by intention. But certainly the advantages helped in the persistence of using 12 as a base. And so we still have a dozen (12) and a gross (12×12) and even a great gross (12x12x12) being used today. Possibly different groups of ancient man used one or other of the systems predominantly. But as groups met and mixed and warred or traded with each other the systems coalesced.

If we had 4 bones on each finger we would be using 5 x 16 = 80 rather than 60.


 


%d bloggers like this: