# Have leap days confused the calculated date for the “end of the Mayan calendar”?

At the beginning of the 2012, I predicted that we would see a number of false debunkings of the Mayan Calendar Apocalypse, which would depend on their own misunderstandings of the Mesoamerican Long Count Calendar. I believe my prediction has already come true!

I have now seen several viral claims that the cycling of the Mayan calendar has already happened, and that those who think it will be happening in December have forgotten to take into account leap days.

So, the world's going to end December 21st, 2012, huh....?

Since Ceasar introduced leap years in 45BC, there have been 515 leap years including this year(so im told). Without those extra days, the date would be the 2nd of September, 2013.

Since the Mayan Calendar didn't use leap years, and today's date (without leap years) is the 2nd of the 9th 2013, the apocalypse (21st of the 12th 2012) was 9 months ago... So congratulations on surviving

^_^ God I love maths

• Source: PressCore blog

Leap Year has resulted in a miscalculation wherein the Mayan calendar’s December 21, 2012 end date actually ends this year, in 2011.

Have the people who have calculated the mapping of the end of the Long Count cycle to occur on December 21st, 2012 failed to take into account leap days?

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Confused who? I am not confused. I know my left from up and Down from right. – Chad Mar 6 '12 at 14:04
This has got to be wrong. Looking for a good explanation why. +1 – NickC Mar 6 '12 at 14:36
@Chad: Your comment has confused me! In the question title, the "confused" refers to the people who have calculated the date mapping, whoever they are. Does that answer your question? – Oddthinking Mar 6 '12 at 14:46
Sounds plausible, however, when you really think about it there have only been 511 leap years. After 1582, fourth years that fell on century changes were omitted as leap years unless they were a four hundredth year--for example, 1600 and 2000 were leap years but 1700, 1800, and 1900 were not. So we’ve skipped 3 leap years since then, making it only 511.25 leap years.. How? Ok here’s the math, add 45 (which is 45 BCE) to 2012, that gives you 2057, (which is 2057 years since Cesar started the leap year rule) divide that by 4 and you get 514.25, subtract 3 and you get 511.25, so there, there have – user6325 Mar 6 '12 at 18:28
Apparently Snookie's due date is 21 DEC 12... Well played Mayans. Well played! – JasonR Mar 6 '12 at 21:32

No.

The Mayan long count calendar is based on days, not solar cycles.. Because of that, leap days are irrelevant.

### Mayan calendar basics

The long count calendar is based on a series of 5 numbers each representing a number of the previous period — usually 20, except for the tun period:

image from Wikipedia

### 2012

The 2012 Phenomenon is based on the idea that Mayans believed their current world (the fourth world) ended after 13 b'ak'tuns:

The Popol Vuh describes the gods first creating three failed worlds, followed by a successful fourth world in which humanity was placed. In the Maya Long Count, the previous world ended after 13 b'ak'tuns, or roughly 5,125 years.

0.0.0.0.0 is the beginning of the first b'ak'tun and 12.19.19.17.19 is the last day of the thirteenth b'ak'tun.

The full size of 13 b'ak'tuns — thirteen multiplied by 144,000 days — is 1,872,000. (This is 5128.8 periods of 365 days, so you can already see that the information cited by Wikipedia for a rough translation of solar years has taken leap days into account.)

To use this number of days to figure out the "end date", in other words, the day that corresponds to 12.19.19.17.19, all we need to know is what equivalent Gregorian calendar date corresponds to the Mayan date 0.0.0.0.0. And to know if December 21, 2012 is that date, all we need to do is figure out 1,872,000 days from the start date.

For that, we turn to this well-sourced article by John Major Jenkins, a student of Mayan time:

But how are we to relate this to a time frame we can understand? How does this Long Count relate to our Gregorian calendar? This problem of correlating Mayan time with "western" time has occupied Mayan scholars since the beginning. The standard question to answer became: what does 0.0.0.0.0 (the Long Count "beginning" point) equal in the Gregorian calendar? When this question is answered, archeological inscriptions can be put into their proper historical context and the end date of the 13-baktun cycle can be calculated. After years of considering data from varied fields such as astronomy, ethnography, archeology and iconography, J. Eric S. Thompson determined that 0.0.0.0.0 correponded to the Julian date 584283, which equals August 11th, 3114 B.C. in our Gregorian calendar. This means that the end date of 13.0.0.0.0, some 5125 years later, is December 21st, 2012 A.D.1

This same start date was also cited in Wikipedia

Assuming, of course, that the start date is correct, there is no way a lack of leap days in the Mayan calendar could confuse this at all. Leap days must be taken into consideration in the conversion, but historians have known to do that since the leap day was invented.

1,872,000 days since August 11, 3114 B.C. is a calculation that can be made safely with the calendar information we have. The best calculator I could find was this one, in which you can enter the dates and come up with a close (too close for leap days to affect it) but not exact result of 1,872,026.

You can also try this calculator which comes up with the same calculation using August 11, 3114 B.C., but if you enter the Julian date 584283, you get the exact period of 1,872,000 days until December 21, 2012.

### Conclusion

So, there you have it — yes, the Mayan calendar did not include leap days. But, it didn't need to, since they didn't have anything to do with solar years. In fact, as you can see, the closest equivalent Mayan period to a solar year, a tun, is only 360 days — already five days off.

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Is it a coincidence that the Mayan calendar rolls over at (or very near) the day of the winter solstice? – starblue Mar 6 '12 at 18:52
I'd have to do some more research to answer that for certain, though it would have to be unless the Mayans did know exactly how to measure a solar year and simply didn't include it with any significance in their calendar otherwise. – NickC Mar 6 '12 at 19:52
@NickC the Tikal twin pyramids form a solar calendar, so they knew about solstices and equinoxes. – Jader Dias Mar 19 '12 at 13:42

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