Solution of the Mayan Calendar Enigma
Résumé
The Mayan Codices, bark-paper books from the Late Postclassic period (1300 to 1521 CE) contain many tables correlating ritual practices to astronomical cycles. This demonstrates the achievements of Mayan mathematics as applied to time measurements characterized by the use of a unique time reckoning system: the Mayan Calendar. Despite many myths, the origin of the Mayan Calendar and its connection to Mayan religion remains unknown, due to the few clues left for us by the Maya. In this study, we propose a solution to this enigma. A pseudo-astronomical calendar supernumber is calculated by computing the least common multiple of 8 canonical astronomical periods. The three major calendar cycles are shown to derive from this supernumber: the Calendar Round (the 260-day religious year Tzolk'in and the 365-day civil year Haab'), the Long Count Calendar (the 360-day Tun, the 7200-day Katun and the 144000-day Baktun) and the 3276-day Kawil-direction-color cycle. My calculations explain certain aspect of Mayan religion notably the existence of the Maya Era, a cycle of 13 Baktun. Modular arithmetic considerations on the calendar supernumber give the position of the Calendar Round at the Mayan origin of time, the Long Count Calendar date 0.0.0.0.0 4 Ahau 8 Cumku. Various Long Count numbers present on Mayan Codices and monuments are explained by my approach. In particular, the results provide the meaning of the Xultun numbers, four enigmatic Long Count numbers deciphered in 2012 by Saturno et al. [Science 336, 714 (2012)] in the Mayan ruins of Xultun, Guatemala, dating from the IX century CE.
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