I’m not exactly the greatest scholar of orthodox Mayan mathematics, to put it mildly. Instead, I’ve focused my attention on simple calendar cycle values on how well they may be represented and coordinate by the mathematics I work with (“Munck’s” math).
Lately, I’ve been trying to change that just a little bit and have been looking more closely at Mayan math from surviving codices. So far, what I get seems to be a curious mix of the unknown, and a surprising collection of number generated as fractions of simple numbers that bear suspicious resemblance to numbers I’ve been working with for at least several years now.
In fact, we’ve already seen at least a few examples of that, formulas that may help explain and justify some of the departures from the norm that have been seen in my work, including some of the numbers from Rio Bec.
In more orthodox literature on Mayan mathematics (some of which I’m finding elusive or prohibitively priced), we see the trend toward generating and identifying numbers which have notable quantities of calendar cycles as their factors. (Not being all that familiar with the literature, I’, not entirely certain whose discoveries are whose).
To give an example, this article, Xultun Number A and the 819-Day Count by Barbara MacLeod and Hutch Kinsman, describes some of these large multiple of calendar numbers, including one from Floyd Lounsbury
At the 1974 Segunda Mesa Redonda de Palenque, Floyd Lounsbury presented a meticulous analysis of the pre-era initial date of the Tablet of the Cross at Palenque. This paper is well worth reading and is available on Mesoweb:
http://www.mesoweb.com/pari/publications/RT03/Rationale.html
Per Lounsbury’s work, the Palenque interval is 1,359,540 days, or [4 x 819 x 415]. While it is not an even multiple of the 18,980-day Calendar Round, it is [5229 x 260] and [1734 x 780] and [3735 x 364]. It demonstrates the application to dynastic mythological narrative of large multiples of [4 x 819] by Maya scribes in deep-time calculations.
Someday I would like to know just how many whole numbers were in the Mayan mathematical vocabulary, and what they did about formulas that don’t quite result in whole numbers. (So far, the Eclipse Cycle by any reckoning is not a whole number).
Yesterday, I discovered several such numbers, including one that I constructed from two rather experimental calendar numbers, 676 and 315, and subsequently discovered that it has a number of significant factors
676 x 315 = 212940 = 364 x 585 = 780 x 273 = 819 x 260 = etc
I also discovered another experimental number as 676 x 378 = 255528. This number also turns out to have a surprising number of significant factors.
255528 = 312 x 819 = 780 x 3276 = 364 x 702 = etc
Here is another example of finding equations that may lend justification to many of the approximations I use – if we divide 255528 by 399, rather than 640, we get 640.4210526, which is 6.404628973 (1 / 100th Mycerinus pyramid perimeter / height ratio, for starters) to an accuracy of .9999346649.
Before I go any further, I attempted to use Google to search for prior references. 212940 appears in the work of Kaldarhan Aliseituly Kambar
Nomads – their mysterious mentality, their calendar and much more that you did not know before
IT’S TIME TO CHANGE THE VIEWS ON THE MAYAN CALENDAR
“6) 819 days × 260 years = 212940 days ÷ 585 years = 364 days;
7) 819 days × 260 years = 212940 days ÷ 780 years = 273 days.
To be honest, I don’t even know how past and modern Mayan researchers studied an 819-day account or calendar when it was not at all difficult to calculate such a simple equality“.
I was not able to find any priors on 255528, but we may wish to note that 255528 / 1.2 = 212940.
Perhaps it remains possible for those of us without formal education in the matter (to think it only took me half an hour of geniune directed effort to independently discover 212940) to walk into the subject fresh and make new discoveries in Mayan mathematics.
Since most of the work I’ve seen thus far seems as if to gloss over the Jupiter Synodic Period of 398.88, or we might presume, 399 to common calendars
780 x 399 = 311220, whose factors include 13, 14, 19, 39, 364, 225, 117, 260, 585, 273, 819, and others.
It can also be reduced via 4725 / 10^n to 6586.666666, which is the Saros Cycle corresponding to an Eclipse Year of 346.6666666, which has often been seen in the experiments thus far.
6586.666666 / 19 = 346.6666666
David Kenworthy uses this figure for the Eclipse Year in his books and should probably be considered an authority on it (and although I have much difficulty making peace with some of the improbably fractions that I think he uses, even in hard his E-books would be twenty times the bargain as the works of Robin or Richard Hearth, or for that matter John Michell himself, I’ll give David that much due).
311220 also reduces via 29.53 to 311220 / 29.53 = (2 / 18976.92950) x 10^n, another example of the possible justification of unusual numbers (18976.67842 is the current experimental E value for the Half Venus Cycle, and figures like this have also been tentatively justified because sqrt 360000000 = 18973.866596), and another point that again raises the question about Mayan protocols for equations that almost work out, and for important quantities which are not whole numbers.
Here is a notable Mayan version of “Not close enough to accept, too close to ignore”: 676 x 54 = 36504. Would they have discarded that, or might they have begun to accept that whole numbers don’t work for everything?
I seem to be having difficulty locating priors for it, but 13104 probably should have been fairly obvious. (Some researchers may wish to take this as earth circumference in feet / 10^n)
13104 = 780 x 168 = 252 x 52 = 234 x 56 = 16 x 819 = 364 x 36 = 728 x 18 = 378 x 346.666666 = 48 x 273 = 117 x 112 = 336 x 39 = 315 x 416 = etc.
18980 / 13104 = 1.448412698 might lend justification to the number of Royal Cubits in equatorial circumference at a ratio of Royal Cubits to miles of 5280 ft. The standard figure I use is 24901.19742 / 1.718873385 = 1.448692943 x 10^n. Such numbers have recently been a peripheral part of a GHMB discussion.
Perhaps most surprisingly 13104 accepts a Venus Synodic Period of 585 days as a factor, via an apparent alternate Venus Orbital Period of 224 rather than 225 days — 224 x 585 = 13104 x 10 — but may also accept 225 as a factor — 13104 / 225 = 5284 / 100.
Here again I am not readily finding any priors although it is mentioned once in Kambar’s work Nomads…, but 5284 may be a significant calendar number in its own right (Factors of 5284: 1, 2, 4, 7, 8, 13, 14, 16, 26, 28, 32, 52, 56, 64, 91, 104, 112, 182, 208, 224, 364, 416, 448, 728, 832, 1456, 2912, 5824).
It seems very exciting to wonder what new discoveries may lie ahead.
–Luke Piwalker
Luke Piwalker 