Monday Morning Math: Number Systems


For today’s Monday Morning Math, we’ll do some counting!

In the Indo Arabic number system we have ten digits: 0123456789 grouped by tens, so the number 23 can be thought of as 2 tens and 3 ones.  But in Mesopotamia (modern day Iraq) 4000 years ago they grouped numbers by 60s.  In that system the number 2 3 would be 2 60s and 3 ones, or what we would think of as 123.  That grouping by 60s, incidentally, has passed down to us in how we count time: it is the reason we have 60 seconds in a minute and 60 minutes in an hour.

For an example closer to home, the Mayans 2000 years ago, in modern-day Mexico, Guatemala, Belize and Honduras, grouped numbers by 20s.  In this number system the number 2 3 would be 2 20s and 3 ones, or what we could think of as 43. Numbers below numbers less than 20 were formed using dots for 1s and lines for 5s, with a shell like oval for the number 0, as in the image below.

Some Mayan numbers in the thousand year old Dresden Codex, named after where it was taken away to.

Several indigenous tribes in North American group numbers by 4s and 8s, particularly the Yuki in northern California, and the Chumash people along the central and southern coast.

(From “Numeral Systems of the Languages of California” by Roland B. Dixon and A. L. Kroeber, published in American Anthropologist in Oct-Nov 1907 (p. 665)

Grouping numbers by 5s and 10s is often attributed to fingers on the hand, but the interesting (to me) thing is that grouping numbers by 4s and 8s is also based on the hands:  the Yuki used the spaces between the fingers to count.  As Dixon and Kroeber wrote above, “It does not follow that because people count by their fingers they count by fives.”

November 1 marks the beginning of National Native American Heritage Month!  Visit the website for Indigenous Mathematicians to learn about more mathematicians!

 I first read about the Yuki in Ethnomathematics: A Multicultural View of Mathematical Ideas by Marcia Ascher. 

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