The History of Mathematics
Early Counting and Numbers
What are some examples of how early peoples counted?
There were several different ways that early civilizations recorded the numbers of things. Some of the earliest archeological evidence of counting dates from about 35000 to 20000 B.C.E., in which several bones bear regularly-spaced notches. Most of these marked bones have been found in Western Europe, including the Czech Republic and France. The purpose of the notches is unclear, but most scientists believe they do represent some method of counting. The marks may represent an early hunter’s number of kills; a way of keeping track of inventory (such as sheep or weapons); or a way to track the movement of the Sun, Moon, or stars across the sky as a kind of crude calendar.
Not as far back in time, shepherds in certain parts of West Africa counted their flock by using shells and various colored straps. As each sheep passed, the shepherd threaded a corresponding shell onto a white strap, until nine shells were reached. As the tenth sheep went by, he would remove the white shells and put one on a blue strap, representing ten. When 10 shells, representing 100 sheep, were on the blue strap, a shell would then be placed on a red strap, a color that represented what we would call the next decimal up. This would continue until the entire flock was counted. This is also a good example of the use of base 10. (For more information about bases, see “Math Basics.”)
Certain cultures also used gestures, such as pointing out parts of the body, to represent numbers. For example, in the former British New Guinea, the Bugilai culture used the following gestures to represent numbers: 1, left hand little finger; 2, next finger; 3, middle finger; 4, index finger; 5, thumb; 6, wrist; 7, elbow; 8, shoulder; 9, left breast; 10, right breast.
Another method of counting was accomplished with string or rope. For example, in the early 16th century, the Incas used a complex form of string knots for accounting and sundry other reasons, such as calendars or messages. These recording strings were called quipus, with units represented by knots on the strings. Special officers of the king called quipucamayocs, or “keepers of the knots,” were responsible for making and reading the quipus.