Will the Mayan calender enter the 14th Baktun at Dec. 22. 2012 or will it start over at 1.0.0.0.0?

Most experts seem to go with “13th” (There was no baktun number 0). On December 20 to 21, the count goes from 12.19.19.17.19 to 13.00.00.00.00 and, on the 22nd, it simply goes to 13.00.00.00.01

Your question would apply to the year we call 2407: what happens on the day after 13.19.19.17.19?

Many experts believe that it goes to 14.00.00.00.00 while some still believe that it goes to 1.00.00.00.00 (with the next level, the piktun, going up by 1)

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It now appears that baktun (and all higher levels) go up to 20, which was their major base for mathematics.

The one element that favors it ending at 13 is that
13*20*20*18*20 = 1,872,000 days
which is roughly the closest you can get to 1/5 of the precession period, when you cannot use fractions.

The Mayan’s mathematics system did not use fractions, That is why the Long Count calendar appears to use a “year” of 360 days.

This would mean that they used a precession cycle of 25,627 years (relatively close to the modern value of 25,800 years) which is not that surprising — the Ancient Greeks had found a similar result a thousand years BEFORE the Mayans.

However, since the Long Count calendar’s main utility was as a day-count calendar for long intervals (specially useful in astronomy), topping the baktun at 13 instead of 20 would just have made calculations harder, without any real benefit.

Plus, there is no real evidence that they did stop at 13. And there is no real evidence (other than ‘recent’ interpretations) that the Mayans paid any more attention to the precession cycle than other civilizations of that era.