About the Mayan Calendar Part 1: Our Calendar and the Long Count

I've written and rewritten this post several times because there's so many possible places to start and so many ways to approach this. I'm still not sure what the best one is.

I've heard it said that our calendar is linear while the Mayan calendar is cylindrical. That's an oversimplification in various ways.

It's easy to see why people say our calendar is linear, just look at the years. 2011 will not be coming back around. No matter how much time passes it won't come back. It just gets further in the past. But Thursday will come back around.

So will 5 AM, and half passed the hour, and the '20s. These things all happen in regular and predictable intervals. We have a Thursday every seven days, we have a 5 AM every day (assuming you limit yourself to one time zone), we have a half passed the hour every hour, and we have a '20s every century. There are definitely cycles.

I bring this up in part because I think it's important to note that cyclical and linear things kind of go together. If you look at a cycle (say the days of the week) it looks perfectly linear until it starts repeating. If you look at the units that make a linear count they're almost certainly going to be cyclical.

The digits of numbers are cyclical, for example. You can count up and up forever and never repeat the same number, but the ones' digit is going to cycle through the same ten numbers over and over again.

Our method of time keeping is largely like that, but with a truly bizarre hodgepodge of bases. If we wrote the time like we write a number, with the smallest unit on the right and the largest on the left, we'd write it as:

millennium, century, decade, year, month, day, (AM-PM), hour, minute, second.

Whether AM or PM is included depends on whether you prefer 12 or 24 hour time.

Part of the reason that I'm bringing this up is because, for everyone who uses the same calendar and clock system as I do, this is the system you're used to. This is something that probably makes sense to you without even thinking about it. This is probably what you consider easy. Yet here is how it works:

A millennium is 10 centuries, each of which is 10 decades, each of which is 10 years, each of which is 12 months, each of which is [28, 29, 30, or 31] days, each of which is 24 hours each of which is 60 minutes, each of which is 60 seconds. If you use 12 hours with AM and PM then it's slightly different and I'm not sure what you call the periods designated "AM hours" and "PM hours" perhaps?

If you work on 24 hour time you're essentially working in a mix of bases 10, 12, 24, 28, 29, 30, 31, and 60. If you use 12 hour time it's 2, 10, 12, 28, 29, 30, 31, and 60.

Given that I'm just planning on talking about the Mayan calendar, not their way of dividing up a day, perhaps I should leave out the hours minutes and seconds. In that case it's just 10, 12, 28, 29, 30, and 31. Still an odd mix.

I bring this up because when I say that the Long Count is incredibly simple to the point that I don't find it interesting, I want you to have our system fresh in your mind.

So, the Long Count calendar. It's probably the most famous of the Mayan calendars, it's the one that ends in 2012 and thus something that you've probably heard a lot about lately. I don't find it interesting.

I find it interesting that it's in base 20 and 18, I find it interesting that they do have an apparently linear calendar, I find it interesting that they decided to date it's beginning to a time that might have been about 3,000 years in their past when they created the calendar. I think it's interesting in that, according to certain sources that might not be reliable, it might have been set up to correspond to certain astronomical alignments. I don't think it's very interesting as a calendar.

That might be a complement. The interesting things about our calendar are the ones that make it harder to use. Screwy things are interesting. Difficult things are interesting. Well ordered simple ones are not.

The long count has five pieces to it, so you could think of it as being equivalent to “century, decade, year, month, day” in our calendar but where in our calendar you end up sort of working in bases 10, 12, 28, 29, 30, and 31 to make sense of those things, with 28, 29, 30, and 31 all applying to the same digit, in the Mayan calendar you only need to to work in bases 20 and 18. And you never have something like our months where the length varies depending on which one you're talking about.

The five things are “B'ak'tun, K'atun, Tun, Winal, K'in” where a B'ak'tun is 20 K'atuns, a K'atun is twenty Tuns, a Tun is 18 Winals, a Winal is 20 K'ins, and a K'in is a day. Other than the unfamiliar names, that's immediately easier to understand than our our calendar.

A Winal is 20 days, where a month for us is … how many again? Just not having cause to have the, “30 days has September,” rhyme is a sign of how much simpler it is. A Tun is 18 Winals where a year is 12 months. I'd say the switch to 18 is confusing, but it's not as if the numbers of months in our years are the same as the number of days in our months. After that you switch back to 20.

Now, as it turns out, they only have 13 B'ak'tuns. After that it's like the odometer runs out and everything sets back to zero. (Except that the B'ak'tun's don't have a zero so they go to 13, sort of like how in 12 hour time midnight and noon are represented by 12 instead of 0.) And that, they say, is how the world will end. Except for the fact that the Maya had ways of indicating dates that occurred after that and none of those indications came with footnote stating, “By the way, there won't be a world when this happens.”

From what I'm seeing it looks like the way that the Maya would indicate a date after the Long Count had cycled through if they wanted to is the same way we'd indicate a date after 9999, they'd add another digit. Actually, if I'm reading things right, first they'd expand the B'ak'tuns so there were 20 instead of 13. Then, once they finished all of those, they'd add another digit. (And at that point there would be a zero in the B'aktuns' place.)

So it's all pretty straightforward and simple. And long. They're not kidding when they call it the Long Count. It starts in the 32^nd century BCE, the normal version of it ends this year. That's a long time. According to the internet the Maya once used an extended version to indicate a date 400 million years from now. If they ever had need to add another digit after that, I'm sure they could have managed it.

Sorry to ruin the end of the world.

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I'll talk about the calendars that I do find interesting in the next post third and fourth posts.

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