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The Mayan and Other Ancient Calendars

Lawrence Shirley (Towson Univ.)


The Mayan and Other Ancient Calendars, Geoff Stray, 2007.  58 pp., $12.00 hardbound.  ISBN 0-8027-1634-2.  Walker Publishing Company, Inc., New York,



At first glance, The Mayan and Other Ancient Calendars looks like a children’s book—it’s only about 6’’x 7’’ and has only 58 pages, many of which are illustrations.  Actually, it might appeal to middle-school math/science whiz-kids.  However, it is packed with detailed and complex content, so its appeal is certainly not limited to 13-year-olds.


Calendar designs were stimuli for a variety of ancient mathematical developments and probably much of the start of the field of astronomy.  The cycles of days, lunar months, and even the seasons of the year were obvious to peoples throughout the ancient world, and an understanding of these cycles was often essential to their livelihood of herding and farming.  It was apparent to all that time-keeping depended on observing, counting, and calculating these cycles.  Unfortunately, none of the cycles fit together nicely.  There are three basic solutions: a purely solar calendar that ignores the moon’s movement (the current civil calendar), a lunar calendar that ignores the seasons of the solar calendar (the Islamic calendar), and a calendar that uses a system of extra “leap-months” to follow the lunar pattern but keep adjusted to the solar year (the calendars of both the Hebrews and the Chinese).   Also, to handle cycles that don’t fit, various societies essentially used least common multiples of days—supercycles of many years--to find times when the astronomical cycles do correspond.  This led not only to patterns of annual calendars but also to measurements of much longer eras.  Arranging the interaction of these long cycles led to very precise measurements of the movements of the planets, in addition to the moon and sun.


Geoff Stray starts with astronomical cycle statistics and reports on the bigger cycles when solar and lunar patterns match.  Then, still in an introductory mode, he describes the calendars of several ancient civilizations in words, numbers, and diagrams.  Finally, after about a third of the book, he gets to his main title group, the Mayans.  He gives a brief history of the Mayans; he explains their base twenty counting systems and their idiosyncrasies; and then uses the counting to lead to the calendars.  The Mayans had many calendar cycles, including an unusual ritual 260-day year, and the complex cycles of cycles of cycles led to consideration of incredibly long time periods.  Stray goes into much detail, both numerical and cultural—so much that it becomes overwhelming!  It’s amazing how much factual material he fits into fifty-eight pages.


In addition to a main text, Stray includes a useful glossary and additional material on calendars, month names, eras, calendar conversions, and special dates.  Perhaps the most crucial date is 21 December 2012, which he reports to be the end of a major Mayan calendar cycle and—perhaps—the end of time!! Yikes!


Lawrence Shirley, Professor of  Mathemathics, Towson University


Lawrence Shirley (Towson Univ.), "The Mayan and Other Ancient Calendars," Convergence (February 2010), DOI:10.4169/loci003264