Introduction to Maya Hieroglyphs - Wayeb

Kettunen & Helmke 2011
Appendices
APPENDIX E: NOTE ON THE CALENDAR
The Maya calendrical system is a rather complex arrangement with a number of overlapping systems. Usually the
dates recorded in the inscriptions cover major parts of the texts. Fundamentally, the Maya calendrical system is
twofold: it records linear time from a (mythological) zero point (13th of August 3114 BC) onwards (Long Count),
and cyclical time with (basically) two calendrical cycles (the Calendar Round, comprised of the Tzolk’in [260
days] and the Haab [365 days]).
MATHEMATICS 48
The Classic Maya mathematical system is a vigesimal (base twenty) positional system that was employed
throughout Mesoamerica during the Precolumbian times (instead of the common Western decimal [base ten]
system). In practice this means that the position shift is made at twenty rather than ten:
Vigesimal system:
Decimal system:
Position: Value: Numbers: Position: Value: Numbers:
20 0 1 0 – 19 10 0 1 0 – 9
20 1 20 20 – 399 10 1 10 10 – 99
20 2 400 400 – 7 999 10 2 100 100 – 999
20 3 8 000 8 000 – 159 999 10 3 1 000 1 000 – 9 999
20 4 160 000 160 000 – 3 199 999 10 4 10 000 10 000 – 99 999
20 5 3 200 000 3 200 000 – 63 999 999 10 5 100 000 100 000 – 999 999
etc. etc. etc. etc. etc. etc.
Table V: Vigesimal vs. decimal system
In Maya calendrical calculations, however, the Haab coefficient breaks the harmonic vigesimal rule being a
multiplication of 18 times 20 rather than 20 times 20. With this exception to the rule the Maya were
approximating the closest possible number of days to the solar year (as well being a figure divisible by 20),
thereby reaching a compromise of 360 days 49 .
Vigesimal system applied for calendrical calculations 50 :
Formula: Value (days): Numbers (days):
1 or 20 0 1 0 – 19
20 or 20 1 20 20 – 359
18 X 20 or 18 X 20 1 360 360 – 7 199
20 X 18 X 20 or 18 X 20 2 7 200 7 200 – 143 999
20 X 20 X 18 X 20 or 18 X 20 3 144 000 144 000 – 2 879 999
20 X 20 X 20 X 18 X 20 or 18 X 20 4 2 880 000 2 880 000 – 57 599 999
etc. etc. etc. etc.
Table VI: Applied vigesimal system for calendrical calculations
48
Examples of mathematical calculations will be provided during the workshop.
49
The Haab coefficient (360 days) in the Long Count calendar is not to be confused with the Haab calendar (365 days) in the Calendar Round (see
below).
50
It should be noted here that the coefficient examples in this table run beyond the standard number of coefficients found in most Long Count
dates (the first five are/were sufficient to record historical time).
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