Sunday, March 26, 2006

More Mayan Musings ...

From: Elron Steele
Date: Fri Nov 25, 2005 10:18 am
Subject: more Mayan musings ...
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... The complexity of the calendar continues to fascinate me. It shows up in more than the cycles, though I can't really see ANY reason for this complexity. We have months and days, and the Mayans had similar concepts, uinal and kin (a kin is a day, a uinal 20 kin). The Haab calendar, used for civil observances, was fairly similar to our own, except with 18 months of 20 days each (and 5 extra days at the end to make 365). The days were numbered consequtively within a month like we do (1 Jan, 2 Jan, etc).

The Tolzkin was a twisted bit of calendar logic and record keeping though, lol. Essentially, they didn't have a concept of a month in the Tolzkin ... instead, they merged a 13 day week with a 20 day week, lol.

While our calendar uses a single week of seven days, the Mayan calendar used two different lengths of week:

  • a numbered week of 13 days, in which the days were numbered from 1 to 13
  • a named week of 20 days, in which the names of the days were:
0. Ahau 1. Imix 2. Ik 3. Akbal 4. Kan
5. Chicchan 6. Cimi 7. Manik 8. Lamat 9. Muluc
10. Oc 11. Chuen 12. Eb 13. Ben 14. Ix
15. Men 16. Cib 17. Caban 18. Etznab 19. Caunac

That's from the page I posted earlier, and gives the names for days of the 20 day week. Keeping track of the day here is bizzarely complex though. Here's a table that shows the 13/20 day sequence for about 60 days ... would seriously do my head in to have to keep track of this, lol ...

20-day 13-day
20-day 13-day
20-day 13-day
Ahau 1
Ahau 8
Ahau 2
Imix 2
Imix 9
Imix 3
Ik 3
Ik 10
Ik 4
Akbal 4
Akbal 11
Akbal 5
Kan 5
Kan 12
Kan 6
Chicchan 6
Chicchan 13
Chicchan 7
Cimi 7
Cimi 1
Cimi 8
Manik 8
Manik 2
Manik 9
Lamat 9
Lamat 3
Lamat 10
Muluc 10
Muluc 4
Muluc 11
Oc 11
Oc 5
Oc 12
Chuen 12
Chuen 6
Chuen 13
Eb 13
Eb 7
Eb 1
Ben 1
Ben 8
Ben 2
Ix 2
Ix 9
Ix 3
Men 3
Men 10
Men 4
Cib 4
Cib 11
Cib 5
Caban 5
Caban 12
Caban 6
Etznab 6
Etznab 13
Etznab 7
Caunac 7
Caunac 1
Caunac 8

Wow ... I sometimes have trouble reconciling a 7 day week with 28, 30, or 31 day months ... that would mess with my head, lol.

From: Elron Steele
Date: Fri Nov 25, 2005 10:28 am
Subject: Re: more Mayan musings ...
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There was one final point I wanted to make on this (final??? well, doubtful, lol). Part of the complexity (or apparent complexity) comes from our own biases I think. One of the "hidden" things about Mayan culture is that it appears they may have used a numeric system that was quite different from our own. Nearly every culture on the planet has counted using a base 10 system. The symbols we use are arabic and fairly recent in nature, but even Roman Numerals are base 10. It goes to some logical things about humans ... we have ten fingers, and so counting based on units of 10 makes good sense. Thats how nearly every human culture has thought of numbers ... in units of 10.

Apparently, Mayans didn't. From what we can see, it looks as though Mayans counted in a base 20 system, but they seemed to be comfortable with several different numbering bases, including 18 and 13. So a calender that has 18 months of 20 days may seem complex when we think of it in base 10 terms, but if we THOUGHT in base 20 and base 18 as a matter of course, it probably wouldn't seem nearly so complex.

But that raises another issue, IMO. Thinking in numbering systems other than base 10 is another fairly recent western invention. Certainly, the general public still finds anything but base 10 mystifying. In computer science, we need to lear about binary (base 2), octal (8) and hexideciamal (16) numbering systems and how to do math in them, and while there are lots of people who can do it today, VERY few people THINK in those bases in the way they think in base 10. And yet, it seems from the records, that 2500 years ago, average people were counting days and time, among other things, rountinely using base 20, base 18, base 13, and freely working with each system. Thats remarkable to me in a very profound way, IMO.


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