The Great Turtle
In high school, my best friend used to occasionally refer to the “Great Turtle” with a gleam in his eye. I never found out where he got this concept, but I always took it be something like a refinement of the idea of the “Flying Spaghetti Monster” – if you’re going to believe in something silly, it might as well be something that’s pleasant, or something you like, right?
At the time, I had no idea that there was such a thing in Native American mythology, and didn’t find out until years later.
Curiously, I still find myself looking at turtles in indigenous American mythology, and I’m still not sure exactly what they mean, but spending some time reviewing the iconography of some of the very sites and artifacts I’ve been studying mathematically, it occurs to me there may be much room for progress in Mayan studies, and I hope a little has been made with my latest attempt at a paper.
It’s probably a bit preachy, but then I’m a bit weary of being fed a steady diet of morbidity just for trying to learn about people’s roots (including my own), and Mayan history has probably been made out to be most morbid of all.
As detailed in the paper, the turtle symbol in ancient Mesoamerica seems to have to do with the earth, but possibly also with Saturn. It may be a hybrid symbol, and there may still be work to do understanding why that’s why it is, and exactly when, why and how it was used as one.
A similar situation exists with the moon and Venus; in the paper I have suggested that Xipe Totec (the “flayed” deity) may primarily a lunar goddess, so some consideration may have to be given to how this character may have acquired a connotation oriented to Venus.
Hopefully, asking questions like these is part of the process of gaining a more genuine and more satisfactory understanding of ancient symbolism, and the surprisingly extensive role that astronomy may actually play.
At any rate, I hope people will find the paper inspiring, or at least interesting. Just maybe it will be the start of something good.
Mayan Humble Pie?
I have a confession to make – there is something that still confounds me about ancient American sculpture, and it’s too important of a point to be in the dark about, but I have yet to be able to shed light on it.
While the circular altars I’ve been studying appear to usually be regular enough in shape for us to obtain meaningful measurements from, I still have no idea if the same is true for their accompanying stela.
It’s most strange how even though the stoneworkers in question easily had the skill to form more regularly-shaped stela, for some unknown reason they seem to have routinely declined.
What this means then in interpreting their measurements as possible astronomical data remains unknown.
Rarely if ever are the datasets inclusive enough that we could use them to try to answer that question, and even if they weren’t, exactly which measurements are we intended to use, and how?
It’s actually part of the reason I decided to do something more with my experience with symbolism and mythology and less with mathematics.
As it currently stands, the stela seem something of a humbling subject, because thus far if we are to learn anything from them, the usual tools – mathematics – may not avail us.
This even when many successful studies have been conducted of whether ancient architecture was designed with deliberate irregularities design that were seemingly intended to increase their data storage and retrieval capacity for handling astronomical data.
Stairway Denied?
One cannot do much looking around Copan without taking notice of the famed Hieroglyphic Stairway.
It’s something of a frustrating subject since it’s an intriguing study, but to date I have virtually zero architectural data on it, and no data collected describing any restorative efforts that might address the usual concern as to whether we are working with the original measurements as designed by the architects, or the measurements as they are following “consolidation”.
After the archaeological follies at both Chichen Itza and possibly El Tajin, I’m increasingly wary.
However, after finding some better photographs like the one included, I think I might have managed to get something out of Copan’s Hieroglyphic Stairway, since we can hopefully trust that at least the major architectural features are original.
Previously I have talked about Mayan stairways with “inclusions” – features placed right in the middle of stairways where one might even think they could be a hindrance – and how thus far (2 for 2) they seem to indicate the presence or applicability of square root functions, rather like the way Stonehenge’s unusual display of sarsens and lintels seems to do likewise.
It might sound crazy, but it’s been profoundly successful, and has seemingly promoted a greater understanding of many things.
The first person to my knowledge to suggest a refined value for any measure of a Tikal temple per se* is “Our Founder”, Carl P. Munck who, based on the data, proposed an exterior door width for Temple II of 1 “Squared Munck Megalithic Yard” or (2,71971567^2) = 7.396853331 ft.
Munck was no doubt proud to think of the Maya using his proposed Stonehenge unit, but there’s no vanity about it. In 20 years, not only have I been unable to overturn Munck’s finding, but I ended up going back to the data and building on it to have a more complete model, only to discover the amazing fact that while Temple II’s exterior door seems to honor Munck’s metrological unit, it’s height/width ratio seems to honor one of Munck’s particularly favorite numbers which he called “Alternate Pi”, 1.177245771.
Temple II rather inexplicably has a large block set in the middle, and even more curiously, in proximity to the upper temple itself. Using the best photograph I could find (from Edwin Shook), I attempted to use pixel measurements to complete an incomplete set of measures for it. The proximity to the temple provides for being able to make a guess from the photograph that it is the same length as the width of the door, and the pixel measures and calculations provided a height of approximately 5.7 feet.
Assigning this the value of 1/10 of 1 Radian in arc degrees, or 57.29577951 / 10, the Radian being an extremely important number from Munck’s basic vocabulary of constants, this provides a ratio of
7.396853331 / 5.729577951 = 1.290994449
Remarkably, this is the reciprocal of the square root of 60
1 / (sqrt 60) = 1.290994449 / 10
Sqrt 60 and its reciprocal happen to be the two most powerful mathematical probes ever discovered for working with these numbers. In recent years, we have seen them turn up again and again and again in ancient architecture, which is not surprising since like 1.177245771 and 1.622311470, they would be something that ancient architects would enthusiastically want to incorporate into virtually everything they design somehow.
The Pyramid of Niches at El Tajin also has “inclusions” in the middle of a stairway, there are five such inclusions each with 3 niches.
(3 x 5)^2 = 225; Venus Orbital Period canonically 225 days
Much more strikingly
(sqrt 5 / sqrt 3) = 1.290994449
The very same basic message communicated by the model of the block on the stairs at Tikal!
I couldn’t quite figure out the Copan stairway until I found a picture that gives a better view of the bottom. I’d counted six inclusions on the main stair and couldn’t figure out why they’d want to talk about the square root of 6.
The “sixth” on at the bottom is actually an apparently separate tripartate (three parts) construct. What we seen to really have here (can you see it coming a mile away?) is 5 inclusions of one and one inclusion of 3, no different at all in constitution than the Pyramid of Niches stairway with its 5 inclusion of 3 parts each, except that the same numbers have been arranged slightly differently, perhaps so that the inclusions might dominate the stairway less than takes place at the Pyramid of Niches.
That is now seemingly 3 of 3 of Mayan stairways with something set in the middle of them that not only seem to reaffirm the idea of this architectural gesture referring to square root functions, but 3 of 3 which are capable of specifically indicating what may well be be the most important square root there is this apparently ancient mathematical system.
–Luke Piwalker
Luke Piwalker 