Apocalypse in 2012! Wait, shouldn't it be 4772?

After quickly losing interest in the movie 2012, I found myself reading about some of the claims for the 2012 phenomenon instead of paying attention to the film. For me the most interesting part was learning more about the Mayan long count calendar. The long count works in a similar way to Unix time in that it is a count from a fixed starting point known as the epoch. Unix time counts the number of seconds since January 1, 1970. The Mayan system counts the number of days since August 11, 3114 BCE.

I had always been under the impression that the 2012 fears were because it represented the end of the Mayan calendar. It turns out this isn't true. Some do seem to think it is the end of the calendar, but others just describe it as the end of a period. It is true that on December 21, 2012 the most significant digit, called the b'ak'tun, will increase by one and the least significant digits will be zero just like hitting 100,000 miles on the odometer of a car. Regardless of whether they think it is the end of the calendar or just of a given cycle, many do go on to claim the date represents the time when some catastrophic event will occur such as galactic alignment, solar flares causing geomagnetic reversal, Nibiru crashing into Earth, etc. Insane nonsense aside, the interesting thing to me was there is an overflow problem with the way the Mayan calendar, at least as I saw it described on Wikipedia, represents dates. Considering the recent problems with overflow such as Y2K and the coming year 2038 problem the obvious question is when will it overflow?

Overflow occurs because of limits in how the values are represented. For Y2K the problem was that many systems used two digits to represent the year. So the year 1900 would be recorded as "00" and 1970 would be recorded as "70". The problem is then how do you represent the year 2000? For Unix systems the time is typically stored as a signed 32-bit integer value. With one bit used for the sign, this means that there are 31-bits for the value to represent the number of seconds since the epoch. Do the math and you find: 231 / (60 s/min * 60 min/hr * 24 hr/day * 365.25 day/yr) = 68.05 years. With an epoch of January 1, 1970 the overflow will occur in 2038.

So how are Mayan dates represented? The Mayan date is represented with five digits. Each digit is base 20, except for the middle digit that is base 18. The Mayan's had symbols for representing quantities from 0 to 19, similar to how we use 0 to 9 with the decimal system. Do the math and you find that the Mayan encoding can represent 2,880,000 distinct values. As mentioned earlier it was used to count the number of days since the epoch of August 11, 3114 BCE. Using 365.25 days per year the encoding will overflow after around 7885 years, on October 13, 4772 CE. For the purposes of media fear mongering I suppose the more imminent date is useful, but you would think for a movie they could exploit interesting aspects of the actual calendar system for the plot. Of course, with my particular proposal you would have to find some reason why the date rolling over and going back to zero in a calendaring system that nobody uses would cause harm.