To be honest, recent work has already uncovered so much that is new, it may take some time for all of it to really sink in. I’m really only still starting to learn why the ancient Maya combined some of the numbers in their altars that they did.
In my most recent notes there is a description of a presumably circular altar at Ucanal in Guatemala, from Vol 2 of Sylvanus Morley’s The Inscriptions of Peten, page 196. The altar is associated with Stela 3
As described by Morley,
D 1.68 = 5.511811024 C = 1.731586591 R = 2.755905512 T .53 m = 1.738845144 D/T = 3.169811321 C/T = 1 / 1.0004191620
Some might wish to interpret that as meaning the thickness was simply equal to the radius, but we may wish to check if something more subtle might have been at work.
The radius of course looks rather like the Anomalistic Month of ~27.55 days; the optimum value for the Anomalistic Month is currently thought to be (27.19256444 x 10) / (Pi^2) = 27.55182815 days. That might well have happened here, both because it’s not far from 27.55182815 to the Best Eclipse Year, however surprising. 27.55182815 x 4 Pi = 12 / Best Eclipse Year.
17.311322418 x Pi^n produces a brief, humble series. 17.311322418 is the short version of the Solar Calendar Year / Palestinian Cubit. It’s 2 / 1.1553132490 = Tzolkin 259.75757575 / Venus Orbital Period 224.8373808, and we can built it out of Megalithic Yard and Megalithic Foot: (2.720174976 / 1.177245771) / 2 = 1.155313123.
On the whole, though, the calendar stones may be more mathematically interconnected than it might appear at first sight. The scheme suggested here for the original proportions of this Ucanal “altar” might be something of a departure from the Sun Stone and Yaxchilan designs, and yet perhaps not necessarily a great departure.
It has been suggested for some time by my work that the number (30 / (Pi^2)) may have been highly conducive to the workings of more advanced Mayan calendar systems which may have been documented through architectural or artifact design itself rather than in more conventional ways such as texts or inscriptions, even though the significance of the structural equations themselves may be supported by the associated inscriptions.
Sadly, in this case, at least from Morley’s description, we might have difficulty finding out whether what the measurements show us match what the inscriptions show us, but this still seems a worthy study because the data implying a direct expression of the Anomalistic Month of ~27.55 days may be without precedent.
If nothing else, it may be a good reminder that a variety of Megalithic Yards are proposed to exist on account of this work, and that this may ultimately reflect the ancient desire to represent or record a number of Lunar Cycle values that are equally similar yet diverse, i.e., Anomalistic Month, Sidereal or Tropical Month, and Draconic Month, because again, we can readily construct the elusive and capricious figure of (27.19256444 x 10) / (Pi^2) = 27.55182815 from the “Incidental Megalithic Yard” of 2.719256444 ft.
Besides 1.0823232323 and (30 / (Pi^2)) = 3.039635509, one of the other numbers that is trying to become emblematic of ancient American calendar stones is the diameter of the Sun Stone itself, circumference 11.77245771 ft / Pi = diameter 3.747289670
Perhaps not that surprisingly, we find that 3.039635509 and 3.747289670 does seem to be interactive with a proposed value for the Ucanal “altar” of Radius 27.55182815 / 10 ft, and there is apparently exponential value present as well.
At all the way 27.55182815 / (3.747289670^5), we are still looking at valid data in the form of the seldom mentioned number 3.728757071, which was Carl Munck’s “Grid Point” for Marcahuasi, Peru’s “Monument to Humanity”, which fact will bear witness to the number having at least a modicum of both resonance and relevance. At the very least, 3.728757071 will form a significant series with 1.177245771 (which makes it directly accessible from the Great Pyramid’s missing apex section statistics), and it will essentially form the makings of the Best Eclipse Year if exposed to the powerful data mining tool, sqrt 60 – rather directly:
3.728757071 x sqrt 60 = Best Eclipse Year / 12
We can also squeeze this number out of the Great Pyramid using Munck’s base perimeter and our second favorite Phi approximation, 1.6188239140.
It may not be the most useful number, but it is something, and I do suspect it has still unappreciated significance to ancient American calendar systems, one example being that it can link the A version of the Calendar Round directly to the reciprocal of 12 times the perimeter of the Aztec Sun Stone, which is seen in Egypt as Royal Cubit / Remen = 1.2 Megalithic Feet, whereas Royal Cubit x Remen = Sacred Cubit and diagonal to Royal Cubit and Remen = Palestinian Cubit.
3.728757071 and (30 / (Pi^2)) = 3.039635509 interact in a way that affords exponential use of 3.039635509 to form a series that includes important numbers like (Pi / 3) and the reciprocal of Pi.
The way that 27.55182815 and (30 / (Pi^2)) = 3.039635509 interact is probably even more interesting. Among the numbers that are recovered that way are what is presumed to be one of several valid thickness figures for the Aztec Sun Stone that seem to result from the rough-hewn bottom of the artifact not giving a consistent thickness value, apparently giving different thicknesses from different sources even though their circumference values are essentially consistent to within approximately a few tenths of an inch.
10.823232323, which is quickly trying to become emblematic of these altars, actually works with 27.55182815 to at least the second power. The circumference would be 17.311322418 ft which is 6 / Best Eclipse Year.
17.311322418 x Pi^n produces a brief, humble series. 17.311322418 is the short version of the Solar Calendar Year / Palestinian Cubit. It’s 2 / 1.1553132490 = Tzolkin 259.75757575 / Venus Orbital Period 224.8373808, and we can built it out of Megalithic Yard and Megalithic Foot: (2.720174976 / 1.177245771) / 2 = 1.155313123.
1.1553132490 / 1.0823232323 = 1.067438159 and 1.067438159 / 1.0823232323 = 1 / long Greek Foot (in “modern” feet).
It is always noteworthy to find what may be 1.067438159. The number seems to have been highly favored, and for many reasons.
Let’s step back for a moment and touch base with the original data projections and see what else we might find.
D 1.68 = 5.511811024 C = 17.31586591 R = 2.755905512 T .53 m = 1.738845144 D/T = 3.169811321 C/T = 1 / 1.004191620, with D, C, and R
(diameter, circumference, and radius) possibly meaning D 5.510365631 ft, C 17.31132418 ft, R = 2.755182815 ft.
1.738845144 might be where they are trying to let the Metonic Cycle into the picture along with the Eclipse Year, or it could one of several other important numbers just above that range. For the diameter/thickness (D/T) ratio projection of 3.169811321, I’m reminded of 3.176266261, which I’ve been saying for some time seems to be an important number in ancient astronomical math, that I’ve reported seemingly finding at both Tikal and in its immediate vicinity.
Numbers in the range of 1.0004191620 very often turn out to be 1.006036766. It hardly seems by chance that the mean diameter of the Stonehenge sarcen circle projects as 100.6036766 ft.
This would make the thickness of the stone to be circumference 17.311322418 ft x ( 1 / 1.006036766) = 1.741582860 ft, which would be one of the two most expected figures for the exact meaning of 1.74 ft or greater (the other one is 1 / Radian 57.29577951 = 1.745329252 / 10^n). It is twice the height calculated for the outer door of Tikal Temple II, divided by 10:
width 7.396853331 (one Squared Munck Megalithic Yard) ft x (ht/width ratio 1.177245771) = height 8.707914303 = 17.41582861 / 2.
A possible problem with this might be that the product of the diameter and the thickness might then become a nonsensical figure? – not that we have been able to establish protocols that the diameter or radius or circumference times the thickness is always supposed to give a meaningful result, but perhaps other possible scenarios deserve equal attention.
Even more strangely, putting the reciprocal of the Radian into that scenario may also produce ostensibly nonsensical figures, it appears.
However the combination of 3.176266261 with 17.31132418 might also prove to be something that the designer actually wished to communicate? I think it’s best seen if we switch around larger and smaller here: 3.176266261 / 17.31132418 = 18.34791047 / 10^n. 18.34791047 / 2 = 9.173955233, which has already becomes something of an apparent trend in Mayan altar proportions, with some justification for that already having been given.
There is another number (at least one) in the 1.74 range, and I very recently wrote a post in “lament” for it even though it may in fact be beginning to stage a revival.
That is the number we get if we apply 3.176266261 as the projected ratio, and if we do so, then the circumference/thickness ratio becomes one of the next most likely fine ratios implied after 1.006036766 for the meaning of C/T = 1 / 1.0004191620, which if we are not too preoccupied with exactitude, is 1.002151140.
Note that this gesture ushers in the Synodic Period of Jupiter to accompany the indications of Jupiter and Saturn that may already be present.
What may have just happened is that once again, 3.176266261 may have exhibited its usefulness as a number significant to calendar functions, and in doing so, may have facilitated access of further data pertaining to both the Jupiter Synodic Period, and the Metonic Cycle (because that is in the context of the post about the Chephren pyramid’s “Grid Point”).
If this inquiry has managed to consistently follow consistent logic then, the raw data
D 1.68 = 5.511811024 C = 17.31586591 R = 2.755905512 T .53 m = 1.738845144 D/T = 3.169811321 C/T = 1 / 1.004191620
Would refer to refined figures of
D 5.510365631 ft, C 17.31132418 ft, R = 2.755182815 ft T = 1.734856330 ft
D/T = 3.176266262 C/T = 1 / 1.002151140 = Saturn Synodic Period 399.1413901 days / 400.
While it would be imprudent to insist this in any way because of my knowing so little in general here, it may well be possible that if there were correspondence between the measures, and the decorations and conventional chronology, that like the altars at Tikal, this stela / altar pair may have commemorated the ending of a cycle coinciding with the end of the dual retrograde of Jupiter and Saturn.
Exactly why there would be strong overtones of the Anomalistic Month and the Metonic Cycle as well as the Eclipse Year, I probably couldn’t say – was the Metonic Cycle the large cycle here, or one of them? – but suffice it that
a) the basics of an actual working model for the stone have been identified
b) that we seems to see looks rather skillful and not that unfamiliar all things considered
c) the ability to recover even that much astronomical data from the stone’s design seems to reinforce the premise that it is indeed a calendar stone even if a somewhat unusual one.
Note that as I continue to try to further advance the idea that a theme of bondage or captivity in the altar scenes may refer euphemistically to the standstill or retrograde of celestial bodies, that the drawing of altar 3 at the link toggles via a slider to also show a photograph (if you click on the drawing), wherein the theme of bondage can clearly be seen, as in this detail from the image which seems to show a seated figure with arms behind back and ropes around arms.
Luke Piwalker 