The Unit of Time and the Mesoamerican Calendar

Abstract

A hypothetical rational process of establishing a unit of time with a meaningful connection to both, the length of the day and that of the tropic year, would lead to a natural candidate which represents the average error per year in a cycle of 365,2422 x 128 = 46751.0016 days, that is: 0.0016/128 = 1/80,000. However, if we multiply that unit by the number 1.08 we obtain: 80,000 x 1.08 = 86,400, that is the actual unit of time. The odds are that such a process was done by an ancient unknown civilisation which influenced on one side the Eurasian continent, where the second and a trigonometric system on base 60 were adopted and the number 108 and its multiples and submultiples (54, 108, 216, 432, 86400 etc) represent the scientific, mythological and sacred numerology of all ancient civilisations. On the other side central America, where a numerical system on base 20 was adopted and a calendar based on the cycle of 128 years. It can be demonstrated that it belongs to a family of 18 calendars, characterised by an ever rolling week and an auxiliary year which together with the solar year are submultiples of an auxiliary century. There are precise relations between all these units, allowing to design astronomical “clocks” with the same characteristics of the central American calendar for whatever length of the week.