## Pages

### Top 10 Greatest Moments in Math History: A Written Counting System

Moment 2: Developing a Written Counting System
The natural numbers, or counting numbers, have been expressed verbally throughout all cultures for thousands of years to keep mental track of how many: how many days, how many sheep, how many people are coming for a meal. Over the years, cultures developed intricate languages that describe these numbers, and the first ten numbers of our counting system are tied to our ten fingers.

In South America, the Kamayura tribe’s word for “three” translates to “peak-finger”, or “middle-finger”, or the third finger used for counting in the Kamayura language. The Mandingo tribe in West Africa created a word for “nine” that translates to “the one in the belly”, referring to the length of a woman’s pregnancy [4, page 3). Though it is amazing to think that humans developed oral language to keep count of things, it is even more extraordinary, and warranting of the tag “Greatest Moment in Mathematical History” that humans even developed a written numerical system.

37,000 years ago, someone scratched 29 notches on a baboon bone in present day Swaziland, a small country located between South Africa and Mozambique, that represented the moon cycle. Similar “calendar sticks” are still used in Namibia [3, page 10]. Found in 1960 in modern day Democratic Republic of the Congo, the Ishango Bone was carbon dated to have come from an animal that died 25,000 years ago [5], and was made by an early human recording a count of some sort [2, page 26]. It is still uncertain what the count represented, but the bone contains three columns of markings: one with four groups of 11, 13, 17, and 19 notches, one with three groups of 11, 21, 19, and 9 groups of notches, and one with eight groups of 3, 6, 8, 10, 5, 5, and 7 notches.

Some archaeologists believe the Ishango Bone was made by a person using base 10 who was familiar with prime numbers because of the first set of numbers are the primes between 10 and 20. Some scientists believe that the Ishango bone was a recording or the ancient sky or even a record of an ancient woman’s menstrual cycle [6, pages 158-160; 2, page 26). No one really knows for absolute certainty what the Ishango Bone was a record of, but it’s clear that people 25,000 years ago were keeping a written count of some kind.

Cultures throughout time have developed their own written number systems, in different bases, with and without zero, for keeping track of counts. Possibly the most used, and the one we use today, is a written count of base 10 that stemmed long ago from our ten fingers.

And interestingly, base 12 counting systems come from the inner knuckles on one hand (here's an awkward video of me explaining it). Merchants would collect payments with one hand and keep count on the other.

Works Cited:

[2] Pickover, Clifford A., The Math Book, Sterling Publishing, New York, 2009

[3] Weidenfeld & Nicolson, The Science Book, London, United Kingdom, 2003

[4] Eves, Howard, Great Moments in Mathematics Before 1650, The Mathematical Association of America, 1983

[5] Murdin, Paul, “Secrets of the Universe: How We Discovered the Cosmos”, Science Magazine, December 17, 2009

[6] Krupp, Edwin C., Echoes of the Ancient Skies: The Astronomy of Lost Civilizations, Harper & Row, New York, 1983