Dec 20, 2012

Thoughts on the Origins of the Mayan Calendar

The sacred Mayan calendar based on cycles of 260 days and 360 days can be traced back to the Olmecs living in 800 BCE but the cycles themselves have no known counterparts in the real world today. The nearest naturally occurring cycles are the Earth year of 365.2422 days which is approximated as 365.2425 days in the Gregorian calendar; and the orbital period of Venus of 224.7 days.

Many early civilisations based their calendars on a 360-day year but in the case of the Maya this cannot be ascribed to ignorance of the true length of the year. They knew the year was 365.2420 days long, which is closer to the real value than our Gregorian calendar approximation!

So why would the Maya have used values which they knew to be inaccurate? Or were they?

In today’s clockwork astronomy the thought that the planets might have had different periods in the past is anathema. But in these pages it is accepted that there are more things in Heaven and Earth than are dreamt of in mainstream philosophy. So let’s speculate a little and see if we can begin to understand the Mayan obsession with 260-day and 360-day cycles.

But first we need to understand how the Mayan calendar worked in today’s system.

Mayan dates are expressed as glyphs on monuments and the like. One glyph gives the date in the sacred 260-day tzolkin cycle made up of 13 day numbers and 20 day names, linked together like two gear wheels. Every single day that passes, the ‘gears’ turn and both the day number and the day name advance by one day. After 260 days, both the 13-day sequence of day numbers and the 20-day sequence of day names are back to the same position they started in.

Another glyph expresses the date in the civil calendar which, in the later Maya period, has 18 months of 20 days each plus an extra 5 ‘days of nothing’ which had been added to the original 360 days and were considered to be extremely unlucky. Nothing was done on those extra days and they didn’t even count in the calendar. It’s as though the Maya kept a 360-day clock which they stopped after 360 days, waited until the 260-day tzolkin calendar had clicked on another 5 days, and then re-started the clock on what they then called New Year’s Day.

So how would the system have worked before the extra 5 ‘days of nothing’ were added, i.e. in the ‘old’ year of 360 days?

The 260-day sacred cycle would be the same as described above; it never changed. But a new civil year would start after 360 days, without waiting 5 days. On every New Years’ Day in the civil calendar the tzolkin day-number and day-name would be different to the year before. Only after 13 years would New Year’s Day have the same dates in the tzolkin calendar that it started with.

So the two calendars would have repeated their combined cycle every 13 years.

The Maya were as equally obsessed with the worship of Venus as they were with the 260-day tzolkin calendar, and perhaps for good reason.

The diagrams above show how the current orbit of Venus looks as seen from the Earth in the centre, and what the orbit would have looked like for Earth and Venus periods of 360 days and 260 days respectively. Today, 5 cyclings of Venus equal 8 Earth years; Venus’ synodical period is 1.6 years or 584 days. Every 1.6 years, Venus is closest to the Earth in inferior conjunction at one of the inner loops in the pattern on the left. It takes 8 years to complete the whole pattern, at which time the two planets return to the same positions relative to the fixed stars.

In the hypothetical diagram on the right, the synodical period is 2.6 years of 360 days or 936 days. The interesting thing is that it still needs 5 cyclings of Venus to complete the pattern and return Earth, Venus and the stars to the same locations they started in. But this time it takes 13 Earth years to achieve it – which is exactly how long it would have taken for the two calendars to repeat their cycle without the extra 5 days of ‘nothing’!

Is it possible that the 260-day and 360-day calendars were based on earlier values of the orbital periods of Venus and the Earth? It could explain the link between the sacred calendar and the worship of Venus. Venus’ closest approach to Earth would always occur on the same sacred day number and the same month of the civil year; the tzolkin day name and civil day number, each based on a cycle of 20, would drop back 4 days every Venus cycle; after 5 cycles = 13 years, they would be back in sync too and the same arrangement in the Heavens would occur on the same day in both calendars.

It would have been a simple system for keeping track of the movements of Venus. It would have given a regular pattern of dates in the civil calendar which repeated every 13 years.

So what would have happened when the orbits changed to their present values? We can expect that the astronomer-priests would become aware of the new 365-day year and the new 1.6 year cycle of Venus (synodical period) fairly quickly. And it probably didn’t take long to discover that it still needed 5 cyclings of Venus to complete the pattern and for Earth, Venus and the stars to get back to the same position. But now it only took 8 new years for the pattern to be completed!

The similarity of the old and new patterns, the same 5 cyclings and the inherent conservatism of any sacred system would have been strong incentives to retain the 260-day and 360-day calendars and adapt them to the new world order. What would have been the easiest way to do this? Well, just keep the old system but stop the civil clock during those extra 5 days each year. Then all that was needed was a bit of adjustment from the 13-year cycle to the new 8-year cycle and there you have it!

Except it wasn’t quite that simple. With the stopping of the civil clock every new year for 5 days while the tzolkin calendar kept time, the day names, day numbers and months didn’t repeat in the way they used to. After one Venus cycle of 1.6 new years, nothing matched up any more. After 8 new years, only the 20-day cycle was complete. And after 13 new years, or 4,745 days, the tzolkin calendar had advanced 18.25 cycles.

They had to wait 4 x 13 years for the fractions to sort themselves out. Only after 52 years did the two calendars finally get back to where they had both started. And that period of 52 years became known as the Calendar Round, completion of which was a cause for general celebration.

And that’s what the Dresden Codex is based on. One of only four texts known to have escaped Bishop Diego da Landa’s bonfire of all the Mayan sacred books, the Dresden Codex lists the start dates in the tzolkin calendar for each phase of the Venus cycle – the 8 days of invisibility at inferior conjunction, the 236 days as morning star, the 90 days of invisibility at superior conjunction and the 250 days as evening star – for two compete Calendar Rounds of 52 years each. Two complete Calendar Rounds?

Those of you who have been following closely will have realised that even 52 years is not enough! The calendars both return to their starting points after 52 years, but unfortunately Venus isn’t back to its starting position. Each circuit takes 8 years so 52 years = 6.5 circuits of the new pattern. So the scribes had to write out two Calendar Rounds to get the two calendars and the planets all back to their starting positions relative to the stars. After which they probably had a celebration!

But what a complicated system this is now, compared to the original! The pattern of dates is much less obvious and it takes 104 years, not 13, for everything to get back to square one at the same time. It’s not the sort of thing one can easily imagine being invented. But if it had developed as a response to the change from an earlier, simpler, system based on actual orbital periods of 360 and 260 days, then it becomes easier to understand what the Maya were thinking.

It’s not evidence for a previously different system but it is food for thought. Maybe the orbits really were different previously.

So does all this mean that the world will end when the Mayan calendar runs out on Friday 21 December 2012? Probably not!

You see, one Calendar Round isn’t really long enough to record historical dates so the Mayan system uses another series of glyphs as well. This series shows the Long Count, or the total number of days since a mythological starting point in 3114 BCE in our calendar. The highest digit recorded in the Long Count represents a baktun, or nearly 400 years. Now the Long Count counter will ‘click over’ to the next number in the baktun column on 21 December 2012, but it isn’t the highest digit available for counting the baktuns. Even if it was, there are higher place-numbers in the Mayan counting system for 8,000 years and so on. They just didn’t bother carving them because they would have been zeros every time.

The baktun digits run out in 4772. We’re probably all right until then.

Bob Johnson

December 2012. Based on an article which appeared in the SIS Review, 2001:1