A Possible Solution to the Mayan Calendar Enigma

Abstract

The Mayan calendar is proposed to derive from an arithmetical model of naked-eye astronomy. The Palenque and Copan lunar equations, used during the Maya Classic period (200 to 900 AD) are solution of the model and the results are expressed as a function of the Xultun numbers, four enigmatic Long Count numbers deciphered in the Maya ruins of Xultun, dating from the IX century AD, providing strong arguments in favor of the use of the model by the Maya. The different Mayan Calendar cycles can be derived from this model and the position of the Calendar Round at the mythical date of creation 13(0).0.0.0.0 4 Ahau 8 Cumku is calculated. This study shows the high proficiency of Mayan mathematics as applied to astronomy and timekeeping for divinatory purposes. a arXiv:1601.03132v7 [math.HO]

Non-power positional number representation systems, bijective numeration, and the Mesoamerican discovery of zero

“…Enumerating rather than just labelling time permits one to know how long ago in the past something occurred, or how far into the future it will occur. The Maya used their calendar to record astronomical events for astrological purposes [1] , [8] and there continues to be much interest in understanding the Maya concepts of time and on what astronomical observations it may have been based [9] . It has been asserted that the Maya numeration system would be superior to today's, at least for the ease of recognizing small divisors of large numbers [10] .…”

“…A significant characteristic of the Maya calendar is the concurrent use of three separate number systems: the Haab, the Tzolk'in and the Long Count; the former two formed the Calendar Round, in which all dates are repeated every 52 years [9] , [15] . This combination of calendars is similar to our use today, without a second thought, of a year-month-day calendrical system together with an incommensurate week system, where repetition comes after 28 years.…”

Non-Power Positional Number Representation Systems, Bijective Numeration, and the Mesoamerican Discovery of Zero

“…Enumerating rather than just labelling time permits one to know how long ago in the past something occurred, or how far into the future it will occur. The Maya used their calendar to record astronomical events for astrological purposes [1,5] and there continues to be much interest in understanding the Maya concepts of time and on what astronomical observations it may have been based [6]. It has been asserted that the Maya numeration system would be superior to today's, at least for the ease of recognizing small divisors of large numbers [7].…”

“…A significant characteristic of the Maya calendar is the concurrent use of three separate number systems: the Haab, the Tzolk'in and the Long Count; the former two formed the Calendar Round, in which all dates are repeated every 52 years [12,6]. This combination of calendars is similar to our use today, without a second thought, of a year-month-day calendrical system together with an incommensurate week system, where repetition comes after 28 years 1 .…”

“…Now let us move to the Long Count, for which the earliest evidence is several hundred years later than the two preceding calendars. It is tantalizing that in none of the eight known inscriptions that show the earliest development of positional notation in the Long Count can we find the full range of digits that were necessarily then in use 6 , which would enable us to understand whether the calculations behind the Long Count were being performed with digits 1-20, 0-19, or 0-20. Neither 0 nor 20 appears in any of the earliest examples written from 36 BCE to 162 CE.…”