Why did the Mayan Calendar cycle every 52 years?

[chacoguy]

I’m guessing Lunar; but I can’t make the math work out.

[yabob]

Least common multiple of 260 and 365. They used a 260 day basic calendrical cycle:

Tzolkʼin

Superimposing this pattern on a 365 day solar cycle gives you a 52 year period before the whole thing repeats.

[ftg]

Yeah, they were big on counting in multiples of 13 and 20. Another cycle was 5 sets of 13 Venus cycles (584 days), which is 104 years or 2*52 solar cycles.

If they could figure out a way to cram something into a cycle involving 13 and factors of 20, they would.

[Bremidon]

@ftg

Yeah, they were big on counting in multiples of 13 and 20. Another cycle was 5 sets of 13 Venus cycles (584 days), which is 104 years or 2*52 solar cycles.

If they could figure out a way to cram something into a cycle involving 13 and factors of 20, they would.

Ok, but why 13 and 20? I realize that the answer may simply be cultural with no easy access for any of us on the outside looking in, but I’m kind of hoping that there’s some fascinating story behind those two seemingly “pulled from a hat” numbers.

[yabob]

The 20 was likely because they used a base 20 number system. When inventing their number system, they apparently counted on their toes as well.

The 13 is possibly more mystical, or related to something non-astronomical.

Wiki’s version:

The original purpose of such a calendar, with no obvious relation to any astronomical or geophysical cycle, is not securely known, but there are several theories. One theory is that the calendar came from mathematical operations based on the numbers thirteen and twenty, which were important numbers to the Maya, (Thompson 1950: Maya Hieroglyphic Writing:Introduction). The number twenty was the basis of the Maya counting system, taken from the total number of human digits. (See Maya numerals). Thirteen symbolized the number of levels in the Upperworld where the gods lived, and is also cited by modern daykeepers as the number of “joints” in the human body (ankles, knees, hips, shoulders, elbows, wrists, and neck). The numbers multiplied together equal 260.

Barbara Tedlock, studied this system in the contemporary K’iche Maya community of the municipality of Momostenango in highland Guatemala. She underwent a formal apprenticeship in calendar divination with a local adept, and was initiated as a diviner in 1976. She says: “The Momostecan calendar embraces both the 260-day cycle and the 365-day solar year, with the four Classic Maya Year-bearers, or Mam, systematically linking the two. The 260-day cycle is conceived as linked firmly to worldly or earthly affairs, mirroring no astronomical period but rather the period of human gestation. Past ethnographic accounts of this cycle contain various conflicting opinions as to what its first day is, but a comparison of the present results and those of previous studies indicates that there is no fixed first day.”[8]

[Blakeyrat]

It’s worth mentioning they actually had 3 calendars, used for different purposes:

1. The Tzolk’in, 260-day ceremonial calendar already mentioned
2. The Haab’ 365-day (exactly-- no leap years) calendar for practical use, for example, determining when to plant or harvest
3. The Long Count which was just a count of days since a arbitrary epoch, similar to the Julian Day Number used by modern archaeologists.

The Haab’ and Long Count, working together, were just as accurate if not more so than any European calendar at the time. They were quite aware the Haab’ gradually lost days, and adjusted dates accordingly.

[Indistinguishable]

@yabob

Least common multiple of 260 and 365.

I don’t know anything about Mayan calendars, but pedantically, I’ll clarify that 52 isn’t the least common multiple of 260 and 365 (that would be 18980). Rather, 52 is the result of dividing this least common multiple by 365.

ETA: Although I suppose what you implicitly meant is “52 years is the least common multiple of 260 days and 365 days”, which is completely correct, and I was just stupidly confused. So nevermind this post.

[yabob]

@Indistinguishable

I don’t know anything about Mayan calendars, but pedantically, I’ll clarify that 52 isn’t the least common multiple of 260 and 365 (that would be 18980). Rather, 52 is the result of dividing this least common multiple by 365.

ETA: Although I suppose what you implicitly meant is “52 years is the least common multiple of 260 days and 365 days”, which is completely correct, and I was just stupidly confused. So nevermind this post.

Yeah, I left a middle step “for the reader”. I could have spent a few more words observing that 18980 days is 52 years (with no leap correction, as observed above).