Number Games



One of the most fascinating aspects of mathematics is that of unexpected results. For example there is the way things multiply with astounding speed once you start.

The Longest Count

Stela One, Coba, Yucatan, Mexico

In a previous posting I discussed the Mayan calendar and of course the Mayan long count.1 Since the supposed ending of the world in 2012 was supposedly predicted by the Maya perhaps exactly what the Mayan long count was about should be examined. Now in the Mayan long count dates were given by giving the number of days that had passed since August 11, 3114 B.C.E., (B.C.).2 This was the so called long count which is usually transcribed into 5 numbers as in 13.0.0.0.0. The number given is in fact the beginning of the Mayan long count.

Mayan Math

The Mayan mathematical system was both sophisticated and different from the one we use today. The following is brief overview of that system.

The Maya used a "vegistmal" or 20 based math system unlike our 10 based system. The Maya also used a zero within that system. Place notation was vertical rather than horizontal. The following is a list of the basic Mayan numbers. Note Mayan numbers could be written in a number of different ways including as complicated Glyphs.

Thus the figure of 8,456 would be written.

The figure 1, 576,234 would be written.

The system works in the following way.

Sixth line = etc.

Fifth line = 160, 000’s

Fourth line = 8,000’s

Third line = 400’s

Second line = 20’s

First line = 1’s

In each line the base amount is twenty times greater than the base amount of the previous line. It is important to note that in Mayan Calendrics a Tun does not equal 400 but 360, i.e., 18 x 20 not 20 x 20, and this effects all the numbers above it which work out as for example 7,616 days:

This was done apparently to round off a Tun so it was approximately 1 year long, even though the Maya recorded dates by the total number of days since particular events not in years.

Bibliography

Coe, Michael D., The Maya 6th Edition, Thames and Hudson, London, 1998.

Hagen, Victor W. World of the Maya, Mentor Books, New York, 1960.

Schele, Linda, Freidel, David, Parker, Joy, Maya Cosmos, William Morrow Company Inc., New York, 1993.

Schele, Linda, Freidel, David, A Forest of Kings, William Morrow Company Inc., New York, 1990.

Foster, Lynn V., Handbook to Life in the Maya World, Oxford University Prtess, Oxford, 2002.

Martin, Simon, Grube, Nikolai, Chronicle of the Maya Kings and Queens, 2nd Edition, Thames and Hudson, London, 2008.

Longhena, Maria, Maya Script, Abbeville Publishers, New York, 2000.

Pierre Cloutier