* The Maya and their three calendars

* Los mayas y sus tres calendarios

The Maya were undoubtedly the most advanced civilization that existed in the Americas before Columbus and the Spanish arrived. Among its most interesting technologies were its agriculture, its pyramids, and of course, its calendar systems.

Actually, the Maya used three ways of counting the passage of time: there was a civil calendar, a religious calendar and a millennial calendar. The first one was somewhat similar to our own calendar, but the other two were quite different. These calendars were later used by other cultures in Center America, and probably the Maya themselves had inherited it from previous cultures. 

Before continuing, I want to clarify that I will try to avoid as much as possible the different Mayan names and definitions they had for each time period. I would rather leave this to specialists in linguistics and focus on the mechanisms themselves of the  Mayan calendars. Thus, terms such as “Mayan week”, “Mayan groups of ten” and “Mayan century” are not necessarily definitions used by a Maya citizen, in the same way that when the Spanish Conquistadores came and asked some Maya scholars to do a translation of the Mayan “alphabet” to the European alphabet, the natives did not understand well what the foreigners meant, because their hieroglyphs were ideograms and not letters. But I think taking the liberty of finding an equivalent in our culture can help us better understand these calendar systems that are quite different from those we are accostumed.

CIVIL CALENDAR

The civil calendar was basically a calendar that marked the seasons. As these depend on the position of the Sun, the Maya had to look at the sky.

Like so many other cultures around the world, the Maya came to the conclusion that the seasons are repeated over a period of approximately 365 days. They, too, used “months” to divide this year, but unlike our months that initially tried to count the apparitions of the Moon, their “months” counted the amount of numbers of their mathematical base.

Our mathematical system is based on counting to ten, probably because we have 10 fingers. Every ten units we go to a higher level, the group of ten. Every 10 group of tens becomes another level, the hundred. Every 10 hundreds we go to the level of the thousands. And so on. 

But the Maya counted not only with their fingers, but apparently also with their toes. In other words, they counted to 20. Thus, only after every 20 units they passed to the next level, which would be something like "the Mayan group of ten”. Each 20 “Mayan groups of ten” they went to another level, what we would call “the Mayan hundred”. After 20 “Mayan hundreds” they were at the level of the “Mayan thousands”. And so on.

Thus the “month” of the Mayan civil calendar was filled with 20 days. Then, if we continue this logic the civil year may be filled with 20 “months” of 20 days, giving 400 days, but unfortunately they needed something practical: a year of 365 days. The solution was to keep only 18 Mayan “months”, which adds to 360 days in a year. This value was corrected by adding every year a group of 5 days, giving 365.

RELIGIOUS CALENDAR

The religious calendar was totally different from the civil calendar. It was used for rituals, and for casting horoscopes and “predict” the future. Surprisingly, it did not have months to be filled with days, but used two parallel sets of periods similar to "weeks". Thus, one type of “week” was 13 days long and the other type of “week” was a series of 20 days. The strangest thing is that both series were in no way interleaved but simultaneous, as if they were two parallel timelines. So to specify some date in the religious calendar, the Mayans did not struck “today is the day such of the month such”, but invoked both parallel series at the same time relaying something like “today the week of 13 days marks the day such and the week of 20 days marks the day such”. This system made sense because as one “week” was 20 days long and the other only 13, they quickly went out of synchrony and marked different dates for a considerable time. Then, 260 days later, they synchronized again and the cycle restarted. This would be the Mayan religious year.

Apparently the number 260 helped synchronize it with the apparitions of planet Venus or even with eclipses. If there is any astronomical connection we do not know, in part because in 1526 the Franciscan priest Diego de Landa, Bishop of Yucatán, gathered and burned a formidable collection of Mayan texts, a savage show of intolerance towards those who think differently. Today only 3 (three) Mayan books survive.

MARKING THE YEARS

One problem was that both the Mayan civil calendar and the religious calendar did not count the years. No one took the step of placing a “year zero” for the start of these calendars. They rolled continuously, but nobody knew what year it was. 

But, once again, as both calendars were running in parallel, it was possible to indicate a specific date by invoking both at the same time. So you could indicate something like “I was born on the day the civil calendar marked the date such and the religious calendar marked the date such”. This system made sense because as one calendar had 365 days and the other 260, they quickly went out of synchrony and marked different dates during the next 52 years. Then, after 52 years, they synchronized again and the cycle recommenced, with the disadvantage of the occurrence of repeated birth dates. But there was no drama as, anyway, the life expectancy of the average Maya citizen often did not get to 52 years old.

MILLENNIAL CALENDAR

Of course, the leaders who built the giant Mayan monuments had other needs: their exploits were to be remembered by future generations. Then, they devised a “millennial calendar”, known as the Long Count.

They had to seek a “year zero”, and as in many other cultures around the world, apparently decided that it should be a very presumptuous point in time described as nothing more and nothing less than the beginning of the world. This occurred, according to what the Maya calculated (we do not know how they did this!), around the year 3114 before Jesus.

Surprisingly, they were using an accounting system very similar to what exists today in spacecrafts. Although it seems that this was reversed and those who chose not to complicate their lives are today's engineers: they just program the computers to add up the days one after another. So did the Maya, just not using the binary code nor our base-10 system, but their base-20 system.

In this system the “creation of the world” occurred as of 00.00.00.00.00. The days are numbered starting by the box to the right and when reaching 20 skipping to the next field, always to the left. Here the Maya took two liberties: the second box did not reach 20, counting until 18, something that remembers the second period of the Mayan civil calendar (which we call “month”), and the “Mayan centuries” did not reach 20 but added to 13 (a number apparently sacred, remember the "week" of 13 days). Otherwise, this calendar counts the days very much like the odometer does with the mileage a car has on it. The last date that fits into this "odometer of time" is 12.19.19.17.19 days (Mayan numbers) since the "creation of the world". After this date, if we go over 1 day all boxes are reset to zero, as in the odometer of an old car. (Although purist researchers used 13 instead of zero in the box to the left). 

And a datum for the anecdote: this Mayan “end of days” was apparently going to fall on 21 September 2012. So it is no surprise that the usual doomsayers were already profiting over this issue. Cheers!

A. L.

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First published in ABC Color, on 1 April 2007. Illustration: Freehand copy of a Mayan inscription carved on the underside face of the lintel over the door of the "Temple of the Initial Series" (structure 5C4), in Chichén Itzá, one of the greatest pre-Columbian centers in the Yucatán peninsula. This is the only inscription in that important archaeological site containing a date in the Long Count system. In Maya hieroglyphs, a shell means "zero", each dot represents 1 unit and each bar equals 5 units. Therefore here in the second row, first column of the illustration, there is a "10", in the second column there is a "2", in the third row, first column, there is a "9", in the second column there is a "1" and in the fourth row, first column, there is a stylized "9" inside a head, less clear. Signs from the religious calendar follow: a perfect "9" can be seen in the the fourth row, second column, and there is a "7" in the fifth row, first column, both being dates from the parallel "weeks" mentioned in the article. The millennial calendar date here is therefore "10.2.9.1.9". This Mayan date could be equivalent to 30 July 878 C.E. in our Gregorian calendar, well within the Classic period of that remarkable civilization. Credit: Sylvanus Morley, "An introduction to the study of Maya hieroglyphs", Bulletin No. 57 of the Bureau of American Ethnology, Smithsonian Institution, U.S. Government Printing Office, Washington, D.C., 1915, page 197, figure 75 B, and text from page 199. Courtesy of the Biodiversity Heritage Library, http://www.biodiversitylibrary.org, made possible by a contribution from the Smithsonian Institution Libraries. With permission from the Biodiversity Heritage Library.

A scientific, very respectful and well-thought reply to the popular question "Do you believe in UFOs?"  This book evolved as a reply to one of the most frequent questions that I used to hear from the public when I was working in an astronomical observatory: "Do you believe in UFOs?". That seems an odd question to ask to scientists, but after researching conscientiously for about a full year, I discovered, to my surprise, that mainstream Science has a few things to say about the topic.  This book is not about conspiracy theory, "NASA is hiding the truth", or much less, that flying saucers have already landed on the lawn of the White House. Rather, it is a book about what is the most rational reply that a scientist, or in my case, a science writer, can offer when people insist on asking that question.  Of course, "Do you believe in UFOs?" is, understandable, one of the most popular questions that common people ask (even if silently, to themselves) when they raise their eyes and look at the stars. So it has to be treated respectfully, and why not, given a well-thought reply.

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