This past week, the one between Christmas and New Year's, I was
one of the few people not taking vacation from work. It was an eerie
feeling being nearly alone in the huge building, and brought to mind
the Aztec concept of "hollow days". Like humans in many eras, even
in our recent past with the Y2K fears of 2000, the Aztecs attached
special significance to neat, round numbers. Because they couldn't
come up with a system of regular months that added up to 365, to match
the actual year, they created 18 20-day months, followed by 5 leftover
days, known as the hollow days. These were considered very bad luck.
I think my favorite description of this superstition comes from
Gary Jennings's great historical novel, "Aztec". It reads, in part,
"...to do anything was regarded as rash-- patently fruitless and
possibly hazardous. The days were not really days; they were only a
necessary gap between the year's last month ... and the next year's
first month ...; they did not exist as days. Hence we tried to keep
our own existence as imperceptible as possible. That was the time of
year when the gods lazed and drowsed... So, during the five hollow
days, all work stopped. All activities ceased, barring the most
essential and unavoidable tasks."
Another mathematical oddity of the Aztec calendar was that there
were really two completely independent calendars. In addition to the
solar one that gave the hollow days at the end of the year, there was
also the ritual calendar, or "day count". This calendar contained 260
days, but was not divided into months in the conventional sense.
Instead, there were two interlocked cycles: a 13-day numerical cycle,
and a 20-day cycle of named signs. So for example, the year might
start at 1 Crocodile, then the next day would be 2 Wind, and so on up
to 13 Reed. But on the fourteenth day, while the number would roll
around back to 1, the named signs would continue to cycle-- so
following 13 Reed, the next day would be 1 Jaguar. Later on 7 flower
the day signs would run out, so the following day would be 8
Every 52 solar years or 73 ritual years, the solar and ritual
calendar would sync up, so this period was given special significance,
often translated as the Aztec century. I'm not sure I'd want to be
around for that end-of-century celebration though: they would mark
the occasion by choosing a sacrifical victim, opening his chest, and
starting a new fire there, which would be used to kindle all the major
altars of the empire. Apparently if this ritual was not carried out,
the gods might choose to dissolve time and end the world.
And this has been your math mutation for today.