As I pour over the odd orthodox academic work on Mayan calendar numbers, some number or other often leaps out at me.
The other day I was looking at Venus and the Dresden Codex Eclipse Table (1995) by Frederick Martin and one caught my eye. It is in my notes that it is in the context of eclipses.
It is 11960.
One viable interpretation of this might be (11.77245771 / Pi^2) x 10^n although there might be another. This affords a very tidy ratio of 1 / (2 Pi) between this and the Calendar Round whereas the relationship between this Dresden number and the canonical calendar round is more on the order of a non-integral version of the reciprocal of 63, something I presume we will be told the Maya had either no use for or no comprehension of.
Interestingly, if I fire at this very speculative eclipse related number (11.77245771 / (Pi^2)) x 10^n = 11927.99350 the canonical 346.62 day Eclipse Year, the multiplied product looks like my nomination for the exact meaning of the “unifying value” from Harris and Stockdale’s work.
If I divide this number by 346.62, I get something that looks like the double (so called) Long Royal Cubit.
Trust but verify I think the expression goes?
11927.99350 x 346.5939351 = 4134.170225 x 10^n = 13159.47245 x Pi x 10^n, check….
11927.99350 / 346.5939351 = does NOT produce the double Long Royal Cubit, it produces 2 times a different figure, but the success of the first equation is sufficient to give this meaning.
In fact, the proposed “fine tuned” Harris-Stockdale unifying value enters the foray to find data from the equation up to at least the 4th power apparently.
1.192799350, like 3.7472896674, is a number we should be expecting to see more of, and I think we are finally beginning to, and of course finding either one essentially means finding the other since 3.7472896674 / Pi = 1.192799350.
Both are directly derived from the almighty 1.177245771 value and Pi or Pi^2.
The metrological unit at work there? It may come as a surprise, but it’s the Egyptian Mystery Unit of 1.676727943
2 / 1.192799350 = 1.676727943.
That’s what a prominent place in the scheme of things this still nameless ancient unit actually enjoys, it more or less sits at the right hand of both the Solar Calendar Year and the Calendar Round.
Not surprisingly 3.7472896674 as the diameter of the Aztec Sun Stone just begs for us to apply the Pi ratio and discover some of these things, because that’s all in the line of duty in determining the measures of circles.
This is only a suggestion for the intended interpretation of the crude value 11960, but unless some fatal flaw is discovered in due course, it might be what was intended by the original calendar designs.
In fact, the adapted version may be more harmonious with a number of cycles than is the canonical figure, and that is exactly what we are looking for is a fluid, universal system of numbers that does not experience the limitations described by academicians as taking place in Mayan calendar systems.
As previously stated, the Synodic Period variations seen in the Dresden Codex at least to us don’t represent a subdivision of the calendar that was spun off for the sake of simplicity; to us it is simply one more variation that is accommodated by our system, and as often may even help to explain the nature and utility of the system we are exploring.
For us, unlike the orthodox interpretation, they may not be an alternative that excludes the norm, and that may be part of both the beauty of our system, and why it is so important.
It’s when we consider the some of the gestures in the Dresden Codex contrasted against a clearer recognition of what a momentous mathematical achievement an all inclusive integrated calendar really is, that we realize the ancients may have avoided any innovations that would have disrupted the all inclusive nature of what they created.
That they proceeded anyway may suggest that either the Dresden gestures are inherently not as exclusive to that as archaeology may currently think, or that they were aware of some safety feature that may be very much like our own, and quite possibly the very same, all things considered.
I continue to wonder if our Eclipse Unit, one of the two latest additions to our 2 Pi series based on the putative Sacred Cubit, is none other than the Nilometer Cubit of Egypt, although I’m feeling uncertain of having adequate data to explore that question in situ.
Awhile back I asked the question about the mystery of the Nilometer Cubit and the mystery of the unidentified Egyptian sarcophagus measure could be one in the same mystery, but since the christening of the Eclipse Unit, I have not been able to establish this.
The sarcophagus measure remains a mystery because once again it seems to deflect inquiries in multiple directions like few things if any I have seen before, which is particularly strange because the same coffers often feature astonishingly simple and metrologically obvious proportions – I find it very difficult to argue against the idea that at least some of their proportions are indeed in very simple numbers of Royal Cubits.
Returning somewhat to the question of the eclipse related values 177 and 178 discussed in one of several preceding posts, I may not have exhausted my notes for observations about them.
We saw this before I strayed from the subject:
“364 / 355 = 1.025352113, which might be several things but at first sight it very much resembles the “Tikal Wonder Number” 1.025135530.”
Depending on the form of the Solar Year we use and the proper syntax of the calendar structure, this might also be the classic reciprocal of the Egyptian-Roman Foot (.9 Remens), or 1/100 of the inner diameter of the Stonehenge sarsen circle, a call that wasn’t outlandish enough for even Petrie to avoid making it.
Indeed, Petrie’s work on Stonehenge seems to have held up just as well as his work in Egypt, and perhaps even better.
If we take their total as the Lunar Year (technically a Lunar Leap Year), 177 + 178 = 355 and test it against further established or canonical figures
Solar Leap Year 366 / Lunar Leap Year 355 = 1.030985915, so we can probably conserve here the .6 Royal Cubit value already being used as the ratio between ordinary Solar and Lunar Years (365 / 354 = 1.031073446 = ~.6 Royal Cubits = 1.031324031).
If we pit the figure of 355 against the canonical Jupiter Synodic Period, we get
399 / 355 = 1.123943662 = 224.7887324 / 200, a rather uncanny approximation of the standard VOP of 224.837808 especially considering it’s generated using only two crude numbers.
Hence we might get the impression that the curious focus on 177 and 178 may in part have been to facilitate harmony some between the lunar calculations and the cycles of Venus and Jupiter, and perhaps Saturn as well.
If we examine the relationship to Saturn’s Orbital Period, 10759 / 355 = 30.30804225, very similar to the (30 / (Pi^2)) = 30.39635509 figure that has been recurring in the context of calendar stones all the way back the very first study, the Aztec Sun Stone.
For the record, 30.39635509 is also the number of days in a month of our classic 364.7562611 days when evenly divided.
30.39635509 x 12 = 364.7562611
We may also wish to note that combining 355 with the standard Venus Synodic Period of 584 days canonically results in
584 / 355 = 5 / 3.039383562, quite a good approximation of 30.39635509 / 10 and vice versa.
On page S59 of Frederick Martin’s article, he states
“In the Dresden Eclipse Table as I have shown, the Maya brought the Moon’s synodic month (29.53059 days) together with the Moon’s nodical month (27.2122 days) in the creation of two intervals (177 and 148 days) which always separate linear sequences of the same kind of eclipse (lunar or solar)”
Note 177 / 148 = 1.195945946 in the context of 11960 and 1.192799350 above, but also that the ratio between 29.53059 / 27.21222 = 1.085195916.
It isn’t an arbitrary mathematical abstraction, it’s the very obvious and very legitimate question of how many Draconic Months are in a Synodic Month, the very same kind of thing that so many of these equations represent.
1.085195916 is more what I think Jupiter’s internal Orbital Period / Synodic Period ratio should look like, and one of the reasons I begin to think that I may have overlooked another register of Jupiter Synodic Period figures that may help to provide a ratio more harmonious with the Synodic / Draconic Ratio.
Curiously, if I use the best values for the Synodic and Draconic Months, the ratio is 1.084949702, and I do not know if the correct forms of Synodic and Draconic Months have been applied here.
Also curiously, this particular candidate looks like it wants to be part of a false square root pair representing almighty 1.177245771 — 1.084949702^2 = 1.177115856 — although I have no idea offhand if there is a reasonable approach readily available to work that out, or whether it is simply a coincidence that should be ignored.
Anyway, there are some thoughts on the Dresden Codex, a still mysterious major internal ratio of Jupiter, and more possible rationale for some of the otherwise sometimes odd-looking gestures that the Maya made with their calendar keeping.
More and more pieces of the puzzle seem to fall into place, but this still remains something of a work in progress. Hopefully we are managing to retrace the same steps as the ancients by wrestling with the same mathematical monsters they must have wrestled with to be able to achieve true harmony with their calendar systems.
A parting thought perhaps – if there were a truncated Calendar Round of about 18922, related to a 355 Lunar Leap Year, this is about
18922 / 355 = 53.30140845 = 106.6028169, which appears as if it is the Hashimi Cubit value once again of 106.7438159 / 100.
If we use a more conventional Calendar Round figure, 18980 / 355 = 106.9295775.
We have found a wonder number of 10.69734371 lurking near the limits of one of Tikal’s (Pi / 3) series, probably one of the most impressive (Pi / 3) series ever found – the one that contains 1.177245771 AND both of the two most powerful mathematical probes ever discovered.
Will all of that work out in real life? Let’s hope half of that works out in real life, it will be something no one should miss.
–Luke Piwalker
Luke Piwalker 