Why the Maya used a 260-day calendar

Last night I attended a lecture by Vincent Malmström who, in 1973, published a paper in Science proposing an answer to the mysterious (and still controversial) question: Why did the Maya use a 260-day calendar?

Malmström’s 1997 book Cycles of the Sun, Mysteries of the Moon, which he has also made freely available here, tells the whole story from his point of view. It’s a remarkable tale of geography, religion, culture, computation, science, and human foibles.

The Maya actually used three different calendars. The Tzolk’in ran on a 260-day cycle, and the Haab’ used a 365-day cycle. Then there was the Long Count, which counted days since a mythical beginning of time and also included the other two.

The Long Count’s start date was written, in its full form, like this:, 4 Ahau 8, Cumku

The first five digits measure days in units of 144,000, 7,200, 360, 20, and 1. 4 Ahau is a Tzolk’in day, based on a cycle of 13 numbers with a cycle of 20 days names. 8 Cumku is a Haab’ day, based on 18 20-day months.

Today’s date is, which Wikipedia’s Long Count page helpfully computes for you using this markup:

Today, {{CURRENTDATE}}, in the Long Count is {{Maya date}} (GMT correlation)

(Here GMT doesn’t stand for Greenwhich Mean Time, but rather for Goodman-Martinez-Thompson.)

But today might be, according to this calculator. There has, evidently, been epic confusion and controversy about whether the mythical start date was 584,283 or 584,284 or 584,285 days ago. Thompson originally thought 584,285, then changed his mind and decided on 584,283.

Prof. Malmström likes 584,285, which fixes the start date as August 13, 3114 B.C. Why? Thompson didn’t think there was any astronomical basis for the 260-day calendar, but Malmström figured there had to have been. And he wondered where, in that part of the world, you might observe a 260-day astronomical cycle.

It turns out that at latitude 14.8 º N, the sun is directly overhead on August 13 passing southward, and again on April 30 passing northward, an interval of 260 days. August 13 is also the day after the peak of the Perseid meteor shower. Malmström writes:

The signs were therefore unmistakable. First the heavens would give their notice. All night long the skygazer would watch as stars burst from behind the towering mountains to the northeast and flashed across the sky. And the following morning, as the sun arched higher and higher across the heavens, he would watch as the shadow it cast grew steadily shorter, until, as the sun reached its zenith, its shadow completely disappeared. This then, he decided, was the day for his count to begin.

Why count days? If you’re planting maize, you need to calibrate carefully to the arrival of the monsoon rains. The two solar passages correspond roughly to the beginning of the rainy season at the end of April, and the harvest in mid-August.

Note that these passages, and the associated latitude 14.8 º N, don’t apply to the Maya in the Yucatán Peninsula, but instead to an earlier Olmec civilization to the southwest, on the Pacific coast near what is now the border between Mexico and Guatemala. The Mayan new year was July 26, not August 13. But the 260-day calendar predated the Mayans by a millenium.

Just a few decades after its inception, the 260-day “sacred” calendar was augmented by a 365-day “secular” calendar. The problem was that the sacred calendar didn’t quite work. There were 13 20-day cycles — or 20 13-day cycles — during the sun’s southward passage, and what seemed like 8 more 13-day cycles during the northward passage. So when the calendar started running, things seemed to work out — albeit in a delightfully curious way.

Each time the zenithal sun passed overhead on its way south, a new 260-day cycle would begin on a day numbered “1” but with a different name. Thus, the skygazer watched as the beginning of each successive cycle shifted from “1 Alligator” to “1 Snake” to “1 Water” to “1 Reed” and then to “1 Earthquake.”

That didn’t last long, though.

Where the priest had erred, of course, was in concluding that the cycle of the sun could be measured in 28 “bundles” of 13 days. This meant that he had equated its annual migration through the heavens with an interval of 364 days, when in actuality it took about a day and a quarter longer than that. Thus, after only four years had elapsed his count was already off by 5 days. This might go unnoticed by the commoners at first, but certainly, as the error increased with each passing year, it wouldn’t be long before “the cat was out of the bag.”

What a colossal screwup! I like to imagine the priests furiously backpedaling.

OK, wait, I know we said 260, but it’s really 365, but we’ll keep both, don’t worry, it’ll work out, trust us, we know what we’re doing.

Of course the fun never stops. We’re less than two years away from Y That’s in 2012, on Dec 23. Or on Dec 22, or Dec 21, depending on which correlation constant you choose. On one of those dates the world will end. Or not. Prof. Malmström suggests you choose 584,285. That’ll give you two extra days to put your affairs in order.

For more on the endlessly weird human reckoning of time, see A literay appreciation of the Olson/Zoneinfo/tz database.