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Mayan Math and Floyd Lounsbury
Posted:
Jan 16, 2012 9:31 AM
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A project has commenced focusing upon
http://www.python.org/workshops/1998-11/proceedings/papers/laningham/laningham.html
"2.3 Conversion of Calendar Round Coordinates into Their Mathematical Equivalents
In Mayan calendrical mathematics as practiced by Mayanists today, the names of the veintena days and the names of the haab months are to be converted to their numeric equivalents; ``'Ahaw'' is, mathematically, 0; the day name occupying position 1 is ``'Imix.'' A complete list of veintena day names is available on my website. The trecena, ``8,'' is directly usable as a number. The haab components are just as simple; ``13'' is just 13, while ``Sots'' is the fourth month of the vague year. ``Pohp'' is month 0, so Sots is, numerically, 3. A complete list of the haab month names is also available on my website.
Conversion of our sample Calendar Round into its mathematical equivalent, then, gives us (in Pythonic terms) (8, 0, 13, 3). In the downloadable code, the function parsecrt() will convert any reasonable Calendar Round string into a 4-tuple; the parsecr() function takes the process further, and converts the 4-tuple into a position in the Calendar Round.
2.4 Finding the Position in the Tzolk'in
Given the tzolk'in coordinates (8, 0) from section 2.3, we can determine the numerical position they refer to. What we're doing here is recovering a positional number from two remainders obtained by dividing by two moduli; Knuth (1998) has a full discussion. Floyd Lounsbury (n.d.) provided several widely used formulae for working with the Mayan calendar; all the formulae here in section 2 are Python translations of these.
def p260l(tr, v):
return((40*((tr - 1)-(v - 1)))+(v - 1))%260
For the example (8, 0):
tz = ((40 · ((tr - 1)-(v - 1))) + (v - 1))%260
tz = ((40 · ((8 - 1)-(0 - 1))) + (0 - 1))%260
tz = 59
Thus, converting ``8 'Ahaw'' to its mathematical equivalent gives us 59, our position in the tzolk'in.
2.5 Finding the Position in the Haab
With the haab coordinates (13, 3) obtained in section 2.3, we can likewise determine the position in the haab, but with a simpler formula (again taken from Lounsbury, n.d.):
def phaabl(hd, hm):
return (hm*20)+hd
For the example (13, 3):
h = (hm · 20) + hd
h = (3 · 20) + 13
h = 73
2.6 Finding the Position in the Calendar Round
There are two steps in this process, the first of which involves finding the minimum number of 365-day units that separate the day we are interested in (8 'Ahaw 13 Sots) and the day that begins the Calendar Round: this is the number of whole haabs (nH). Finding nH requires the coordinates we deterimined in the previous two steps, the position in the tzolk'in (tz) and the position in the haab (h): (59, 73).
def nHl(tz, h):
return (tz - h)%52
For the example (59, 73):
nH = (tz - h) % 52
nH = (59 - 73) % 52
nH = 38
The second step requires only two of the answers from the previous steps, the number of whole haabs and the position in the haab:
def pCRl(tz, h):
nH = nHl(tz, h)
return (365*nH)+h
For the example (38, 73):
cr = (365 · nH) + h
cr = (365 · 38) + 73
cr = 13943
Thus, the day ``8 'Ahaw 13 Sots'' is equivalent to position 13943 in the 18980-day Calendar Round. It is also quite important to realize that the Calendar Round is locked to the Long Count in a particular way. Day 0 of the Long Count, ``0.0.0.0.0,'' is set to day ``4 'Ahaw 8 Kumk'u'' of the Calendar Round, which is position 7283. As each day goes by both the Long Count and the Calendar Round advance by one."
One goal of the project is to freshly report Mayan math as written by Mayans... a much misunderstood topic.
Help is hereby requested. Please feel free to post your views.
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