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, (AMPM), 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.

That does sound simpler than ours. And thanks for explaining it. I knew almost nothing about it.
ReplyDeleteOther calendars I know almost nothing about:
* The metric calendar imposed after the French revolution.
* A couple of calendars created by Tolkein (specifically the Shire calendar, which had the same day names for every date every year, managing this by having some holiday dates which didn't have a weekday name).
* Ancient Indian calendars, which also make use of very long time periods.
TRiG.