Counting seems so obvious. As infants, adults count our fingers and toes, the pieces of food on our trays, the colored blocks we play with. We learn to count from the beginning of our lives.
And then we move on to numbers. They must be memorized. We have symbols for 0 to 9 whose names and symbols must be memorized for immediate recall. It is so intrinsic a skill that we no longer consider their purpose or origin.
What did people do before symbolic language?
They made tick marks on sticks. That’s what they did. And that is such an effective method of counting that we still do it. We make groups of five marks. Four marks up and down and then a fifth across to complete the bunch.
The oldest known example of these kinds of marks is …
The Lebombo Bone.
The Lebombo bone is a baboon’s fibula with 29 distinct notches, discovered within the Border Cave in the Lebombo Mountains of Swaziland.
The number of notches suggests that the bone was used to mark the days of a lunar or menstrual calendar.
It has been dated to about 35,000 years ago (Middle Paleolith) in the excavation report of 1973. (Wikipedia; Pegg, Ed Jr. “Lebombo Bone.” From MathWorld; The oldest mathematical artefact by Bogoshi, Naidoo, and Webb)
Consider that it is thought that humans only began to migrate from Africa 50,000 years ago.
The Lebombo bone is about as old as the oldest known piece of vigurative art, the Venus of Hohle Fels, found in southern Germany.
The Ishango Bone
The Ishango bone is similarly a fibula of a baboon but dating from much later, the Upper Paleolithic era, about 18,000 to 20,000 BC.
It has a series of tally marks carved in three columns running the length of the tool.
This gets a little detailed in the description of the markings, but it’s interesting to read how archaeologists attempt to decipher them.
There are three rows around the bone containing sets of tally marks:
First row: 19, 17, 13, 11
Second row: 7, 5, 5, 10, 8, 4, 6, 3
Third row: 9, 19, 21, 11
Some believe the three columns of asymmetrically grouped notches imply that the implement was used to construct a numeral system.
The central column begins with three notches, and then doubles to 6 notches.
The process is repeated for the number 4, which doubles to 8 notches, and then reversed for the number 10, which is halved to 5 notches.
These numbers may not be purely random and instead suggest some understanding of the principle of multiplication and division by two.
The bone may therefore have been used as a counting tool for simple mathematical procedures.
Furthermore, the numbers on both the left and right column are all odd numbers (9, 11, 13, 17, 19 and 21). The numbers in the left column are all of the prime numbers between 10 and 20 (which form a prime quadruplet), while those in the right column consist of 10 + 1, 10 − 1, 20 + 1 and 20 − 1. The numbers on each side column add up to 60, with the numbers in the central column adding up to 48. In the book How Mathematics Happened:The First 50,000 Years, Peter Rudman argues that the development of the concept of prime numbers could only have come about after the concept of division, which he dates to after 10,000 BC, with prime numbers probably not being understood until about 500 BC. He also writes that “no attempt has been made to explain why a tally of something should exhibit multiples of two, prime numbers between 10 and 20, and some numbers that are almost multiples of 10.”
(Wikipedia; Williams, Scott W.: “Mathematicians of the African Diaspora” The Mathematics Department of The State University of New York at Buffalo.; Rudman, Peter Strom (2007). How Mathematics Happened: The First 50,000 Years. Prometheus Books. p. 64.)
It’s just amazing to me to imagine a person sitting in the forest or next to a modest living space, and deciding that because he or she uses these numbers so often, or these numbers are so important, he needs to mark them on something sturdy so he can use it again. It isn’t incredibly easy to carve markings into a bone. It takes some intention. And a sharp tool.