The Early History of Counting

From an essay by Keith Houston at Lapham's Quarterly:

A 1913 survey of the number words used by several Native American tribes found that many of those words were related to “finger,” “thumb,” and “hand.” Counterintuitively, perhaps, despite the general possession of ten fingers per person, fewer than half of those tribes counted in multiples of ten. About a third used systems that revolved around the number 5, which was often referred to as “fingers finished,” “all finished,” “gone,” or “spent.” A further tenth of the tribes used vigesimal schemes based on the number 20 (“all hands and feet”), while a few contrarian outliers used 2-, 3-, and 4-​based systems with less obvious connections to human anatomy.

Fifteen years earlier, a group of scientists from Cambridge, England, had made a series of visits to the islands of the Torres Straits, strung between Papua New Guinea to the north and Australia to the south. A.C. Haddon, the driving force behind the expeditions, recounted:

"There was another system of counting by commencing at the little finger of the left hand, kotodimura, then following on with the fourth finger, kotodimura gorngozinga (or quruzinger); middle finger, il get; index finger, klak-​nětoi-​gět; thumb, kabaget; wrist, perta or tiap; elbow joint, kudu; shoulder, zugukwoik; left nipple, susu madu; sternum, kosa, dadir; right nipple, susu madu, and ending with the little finger of the right hand."

In this way, Haddon said, starting on one side of the body and traversing over to the other, the islanders could count to nineteen. More recently, a math teacher named Glen Lean catalogued the number words for 883 of the 1,200 known languages from Papua New Guinea and Micronesia and found that the use of fingers for counting was foundational to many of those languages. Like the Torres Strait islanders, the Papua New Guineans then carried on to the forearm, elbow, eyes, nose, ears, and other body parts. A study of Yupno, a language indigenous to Papua New Guinea’s Finisterre Mountain range, recorded that Yupno men added their testicles and penis for good measure, allowing them to count to thirty-​three using body parts alone.

Which is kind of cool, all the different ways people found to count using body parts. But the first people to write numbers down, the Sumerians, used a system based on the number 60, which we still use for seconds and minutes. This almost certainly predates writing, since the early system of keeping track of numbers using clay balls, cones, and ovoids also seems to be based on 60. Why 60?

One clue might be that the Sumerians also had a thing for the number 12, which gave us the 12-hour day and the 12 signs of the Zodiac.

The Mesopotamians’ unique counting method is thought to come from a mix of a duodecimal system that used the twelve finger joints of one hand and a quinary system that used the five fingers of the other. By pointing at one of the left hand’s twelve joints with one of the right hand’s five digits, or, perhaps, by counting to twelve with the thumb of one hand and recording multiples of twelve with the digits of the other, it is possible to represent any number from 1 to 60. However it worked, the Mesopotamians’ anatomical calculator was a thing of exceptional elegance, and the numbers they counted with it echo through history.