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When a Number System Loses Uniqueness: The Case of the Maya - Conclusion and About the Authors

Pedro J. Freitas (Universidade de Lisboa) and Amy Shell-Gellasch (Beloit College)


The natural question that Amy asked, being a math historian, is “Did the Maya have a preference for one encoding over the other? In fact, were they even aware of this duality of their number system?'' Given the limited number of Mayan texts remaining, this question may never be answered. A by no means exhaustive survey, as well as conversations with Dr. Ed Barnhart of the Maya Exploration Center (see [8]), indicate that no Mayan numbers with an \(18\) or \(19\) in the second place appear on known monuments or documents. This makes sense when you think again of the world view of the Mayans. As noted at the beginning, these numbers are Long Count dates used on stelae and in codices to record significant events. It would make sense to record dates using the largest units of time possible. For example, it would seem natural to record a date as one Haab (rounded to 360 days) as opposed to 18 months of 20 days.

Finally, Amy is happy to conclude that Isabel's birthday, written as a Mayan number, is \(,\) which is a unique expression! Could you imagine the hassles with the IRS if the expressions of our birth dates were not unique?

In conclusion, we would just like to say: regardless of the number system you use,

All Your Base Are Belong to Us.*


About the Authors

Pedro Freitas, of Lisbon, Portugal, and Amy Shell-Gellasch, originally from Birmingham, Michigan, became dear friends during graduate school at the University of Illinois at Chicago in the late 1990s. Pedro studies matrix theory and is a professor at the FCUL Universidade de Lisboa. Amy is a historian of mathematics and will join the Hood College faculty in September of 2012. During a visit by Pedro from Lisbon to Amy’s home in Madison, Wisconsin in 2011, teaching math history came up in conversation. This led to the topic of different number bases, which in turn led to a comment by Pedro about the non-uniqueness of the Mayan numbers. This in turn led to several fun hours investigating all the implications of that and finally this article.


*Google it!

Pedro J. Freitas (Universidade de Lisboa) and Amy Shell-Gellasch (Beloit College), "When a Number System Loses Uniqueness: The Case of the Maya - Conclusion and About the Authors," Convergence (June 2012), DOI:10.4169/loci003883