Tuesday, December 4, 2012

On the accuracy of the Mayan Calendar

My watch does not display the correct time.  The time it has is about two and a half minutes ahead of actual time.  Slightly less.

I know this, and since I know this I can tell the correct time fairly accurately.  If I were to reset my watch to the correct time I'd risk forgetting that I reset and assuming it's about two and a half minutes later than it actually is.

Knowing the limitations of your time piece can be valuable   It allows one to adjust accordingly.  That's how our own system of leap days came to pass.  They adjust for the limitations of our calendar which left to its own devices would get well out of whack.

A different method for adjusting would be to just keep track of how out of whack it had gotten and adjust one's behavior accordingly.  My watch doesn't really run fast or slow, it's just got the wrong time and so continues to have the wrong time at about the same degree of wrongness as the days go on.  I know it's wrong and it doesn't bother me much.  It might if I didn't know it was wrong.

If I wanted to, I seldom do, I could figure out exactly how far off my watch was and then, via adjustment, tell the correct time very accurately.

In some people's eyes that makes my watch a very accurate watch.  Technically it just has a level of precision and a mostly uniform inaccuracy.

I bring this up in a post with "Mayan Calendar" in the title because of, I suppose, a quote from Silverado: "Life is what you make it.  If it doesn't fit, make adjustments."

I adjust for the inaccuracy of my watch.  Calendars are forced to adjust for the inaccuracy of Calendars because the solar system never got the message that we'd like to have a calendar that consistently reflected the seasons year after year.

We make adjustments with leap days.  Add a day if the year is divisible by four, unless it's divisible by 100, unless it's also divisible by 400 in which case add the day after all.

They Maya people did something more akin to what I do with my watch.  The recognized the inaccuracy  they took it into account, they learned to live with it.  The result was that that their adjustment (which basically involves saying, "If we wait 1508 Haab' years that's the same as 1507 solar years and things line up again") gave them a better approximation of the solar year than ours by a nearly negligible amount.

Presenting that as them having an extremely accurate calendar is like me presenting my watch as extremely accurate because I happen to know how far off it is and can adjust for it.

Their calendar was not accurate.  It was wrong.  They did an impressive job of figuring out precisely how wrong it was and taking that into account, but the calendar itself was not accurate.  The Maya themselves were apparently able to be accurate in their use of it, because they were able to take its creeping inaccuracy into account.


  1. I wish most of my coworkers had such an easy time in dealing with precise wrongness.

    I find it useful, in a sort of "If X is wrong in this way, it indicates that; this other way indicates something else and further possibilities may exist" sort of way, but there's plenty of people out there who stop at "but it's wrong!" and don't interpret further, and it can be awfully difficult to communicate the nuances.

  2. I think Nate Silver and similar authors have done nice jobs of explaining how predictable wrongness can provide useful information.

    If polls from a certain firm are consistently skewed two points in one direction, shifting the results two points in the other direction should give you results that are (taking into account margin or error, confidence interval and all that) a pretty decent reflection of reality.

    If the polls from a certain firm are consistently wrong, but there's no rhyme or reason to the way in which they are wrong, you're probably not going to learn much from them.


    Obviously this applies to more than just polls. I can have a pretty good idea of what time it is by looking at my watch because it's always wrong in the same direction, and always wrong by the same amount. If it were always wrong but I could never be sure of the direction and/or amount then it would be useless in telling the time.

  3. When I was learning about science we called this systematic error (the scale always reads five grammes high) and random error (the scale reads somewhere within five grammes of the true value).

    Random errors can be coped with to some extent by taking lots of measurements (you weigh the same thing five times and take the average). Then you can use normal statistical techniques, generate a confidence interval, and so on.

    Systematic errors, you have to find out about and account for. No amount of repetition will help.