I thought I’d stare a bit more at my expanded tables of ancient American “altar” data and see if any more helpful patterns appeared to coalesce.
I may have spotted one, but it may bring up something of a strange and sad tale.
There is a number we hear from very little these days, which is unfortunate, because it’s an amazing number. It was Carl Munck’s “Grid Point” for the Great Pyramid in his “geomathematical” coordinate system, with the full coordinates being Grid Latitude 67858.40132 / Grid Longitude 11.77245771 = Grid Point 5764.166072.
I more or less still remember that number even when I’ve barely put it into a calculator in 12 years, I referred back to it so often. Every new find, every new number, was referred back to the purported “Grid Coordinates” of Giza’s major pyramids.
For the record, the number is still alive and well at Giza. How so? Well for starters,
5764.166072 x 2 = 1.152833215 x 10 – the Egyptian Royal Foot in “modern” feet (which are apparently the ancient reference unit of measurement that gives such amazing values to other ancient units of length).
Remen in inches times (2 Pi) squared = 1.216733603 x 12 x (2 Pi)^2 = 5764.166072
For whatever it may or may not imply (some may associate the number 5760 with calendar systems already), we can construct it as 5760 x 1.000723277.
5764.166072 may be safely preserved by the Great Pyramid, in any number of ways.
As a token of proof, the most obvious way to do it might be to simply convert Munck’s height for the Great Pyramid, part of his non-“geomathematical” work that we are still striving to conserve, in inches
Munck Height Great Pyramid 480.3471728 ft x 12 = 5764.166072 inches.
There’s something that doesn’t get mentioned often enough, that’s probably a first for this blog.
What’s sad is that we may have been barking up the wrong tree totally with the “geomathematical” considerations, and what’s strange is still how little of this number I see in actual practice, even for just having identified it as such a simple variation on the Egyptian Royal Foot.
I actually brought it up neither to lament nor to reminisce, but because it managed to turn up in a train of thought about the Mayan calendar stones that I think is rather interesting.
It’s the one where the math we use around here doesn’t necessarily share a protocol with the “common” calendar math when it comes to the relationship between Eclipse Year, Jupiter Orbital Period, and Metonic Cycle, not that there was necessarily a common tactic that worked.
The gist of it is that Metonic Cycle / 2 = ~Eclipse Year x 10 and Eclipse Year / 8 = ~Jupiter Orbital Period / 10^n, but the math I am using seems to be able to distinguish the ideal Eclipse Year from the ideal Metonic Cycle instead of lumping them together along a 2^n chain like that.
Thus far the ideal Metonic Cycle seems to be the cube of the reciprocal of 2 Remens x 10^n: (1 / (1.216733603 x 2))^3 x 10^n = 6939.425316.
That’s where we get the distinction between Eclipse Year and Metonic, since
6939.425316 / 2 = 346.9712658
Which isn’t registering as an Eclipse Year since there are better things we can use, and doesn’t seem to divide via 2^n into a Jupiter Orbital Period figure that is useful to us either.
At any rate, this discussion manages to dredge up the subject of the Chephren Pyramid’s “Grid Point” of 5764.166072, simply because
40 / 6.939425316 = 5.764166072
Thus in the course of the inquiry we learn a new thing – that 8 / Egyptian Royal Foot = 6.939425316 = 1/1000th of what may well be the ideal figure for the Metonic Cycle.
One other thing that might be worth mentioning here, 30 / 5.764166072 = 5.204568990, which is also of relevance to calendars because that is likely one of the premiere approximations of the number 52, as in 52 weeks in a year or 52 years in a Calendar Round, etc.
We should probably be allowed to feel entitled to take liberties with that if only because it isn’t precise in the first place. There aren’t really “52” weeks in a year, 52 weeks x 7 days = 364 days, not 365.
5.204568990 is half of 10.40913798, which we can easily obtain from Pi / Munck’s Perimeter for the Great Pyramid (i.e., measured from proposed pavement level): Pi / GP Perimeter 3018.110298 = 1.040913798 / 10^n.
1.040913798 was influential in working out how the ancients would have preferred to represent the Equatorial Circumference in Miles, and how the consensus symbolic Precession Cycle value of 25920 (years) can be involved
25920 / 1.040913798 = 24901.19742 miles (textbook figure for the Equatorial Circumference in miles = ~24901.55 miles).
Not to be outdone, 5.764166072 x 43200 = 24901.19742
That’s the actual story of the number. Munck and Morton should get all of the credit for that, but as it happened, Munck envisioned the equation, Michael Morton perfected it, and I solved it and then eventually explained why we probably had the right solution. By the time I knew this number had a valid cube root of 24 Remens, I knew we really had something.
As of the most recent effort on the Stonehenge lintel circle, my model gives the maximum circumference as 104.0913798 feet, which has been discussed in various posts referring to Stonehenge (it didn’t get there just because it’s an interesting number found in the Great Pyramid, it’s dictated by a much more detailed list of considerations).
The other reason I wanted to bring all this up in the first place is because of something else back where we started.
A subject in question is one the Jimbal Altars (J.1) from Guatemala (data source: Tikal Reports 33). The diameter is rated as Diam 1.06 m = 3.477690289 ft, so we get to ask, does this mean the ideal Eclipse Year value 346.5939351 / 10^n, or does it mean half of the seemingly ideal Metonic Cycle 3469.712661 = 6939.25316 / 2?
Interestingly, as a diameter, 3.465939351 may prove to be associated with a somewhat awkward circumference value, while as a diameter, 3.469712661 would be associated with a circumference of diameter 3.469712661 x Pi = circumference 10.90042380, which I find very interesting because in the preceding post, it was discussed how the reciprocal of this number provides the necessary linkage between the Saturn Synodic Period and what may well be multiple Lunar Cycles
“Saturn Synodic Period 377.8016633 / 9.173955233 = 411.8198244 thus far the preferred form of the Full Moon Cycle of “411.78443029” days, and
Saturn Synodic Period 377.8016633 x 9.173955233 = 346.5935546 thus far the preferred form of the Eclipse Year of ~346.62 days”
1 / 9.173955233 = 10.90042380
So what have been happening is that they were choosing scenarios that actually accommodate both the Eclipse Year and half the Metonic Cycle even when they have technically become distinctive things. A lack of an applicable 2^n series to tie together the Eclipse Year, Jupiter Orbital Period and Half Metonic Cycle really doesn’t so far seem to have been an obstacle to them, and if there is therefore such a trend of finding 9.173955233 in altars, then the Jimbal altar under discussion may have a circumference of 10.90042380 as another example of the same.
Analysis of the calendar stones is still a science in its infancy, so I’m still rather proud of any “baby steps” that might be taking place with it.
–Luke Piwalker
Luke Piwalker 