Greetings!
A few more random items from my desktop…
The “Garsalian” State of the Tropical Month
I’ve been considering candidate values for representation of the Tropical Month the last several weeks. Cerrig at the Megalithic Portal has posted several threads with excellent details of several Megalithic sites which have me quite intrigued. Cerrig advocates for the importance of what he calls “Garsalian” geometry (there should also be a few YouTube videos about this), which I’m quite impressed with.
One of Cerrig’s diagrams showing geometry projected from Garsalian Triangles. I’ve callously decolorized it to provide contrast with the crude overlay of Hively and Horn’s diagram of the Newark Octagon in Ohio (green), which I’ve created to commemorate the possibility that the geometry that Cerrig is advocating could have been involved in the Octagon’s design.
Here we can see a description of a Garsalian triangle which if the base has a length of 1, has a hypotenuse of 1.366; here we can see Cerrig’s diagram showing his field measures of Cerrig Duon, giving a circular radius of 30.12 ft. The diameter of the circle would be 30.12 x 2 = 60.24 ft. Alexander Thom gave slightly different measures, with a diameter of about 59.8.
59.8 is course near to 59.9, and an x99 numerical motif at the beginning of a number may often indicate a reference to Jupiter’s ~399 day Synodic Period, so that is a tempting direction to consider, but the intriguing thing here is just from Cerrig’s data, 1.366 x 20 = 27.32 and 30.12^3 = 27325.29773, so that is another tempting direction to explore, the possibility that the Brecon Beacons are where we might go to get a Megalithic lesson in how to express the Tropical Month, which is not necessarily a teaching so easily obtained from Stonehenge, although we are still learning…
In order to feel better prepared to even tackle this problem in the first place, one of numerous parts of the Planetary and Lunar Cycles table I’ve been working on lately is the Tropical Year. I at least found a scheme that incorporates what I think is my favorite candidate from the Tropical Year, Palestian Cubit 2.107038476 ft x 360 x 360 = 27.30721864 x 10^n, and with a 360 Palestinian Cubit upper with for its platform, the Great Pyramid can easily express such a figure.
If anything, I may have more good candidates for the Tropical Year values than are actually useful, but it’s a gray area that calls for some thought, because the dynamics here and the relationship to the Sidereal Month may call for a particular degree of care.
So I am not sure what I know yet about the ways in which ancient astronomers and mathematicians might have rendered the Tropical Year, but I think I know much more than I did a month ago, and Cerrig’s excellent work may have provided us with some very important leads.
An Imposter Detained
Here’s something I hate to spring on people, but there is something of a segue here. It’s in the course of trying to work on some values like the Tropical Year which are still not accounted for that I got some hints that there may be a tangle somewhere (perhaps in more than one place) in the Planetary and Lunar Tables. I think the trouble starts when we go to respect the numerical value of the Hashimi Cubit in Imperial but end up with 2/3 our Saturn Synodic Periods coming out seemingly strange and rather dysfunctional.
There IS an imposter for the Hashimi Cubit value, and it’s a wily one, but I’m starting to wonder if it’s something we need to know to get the ancient calendars to align in harmony, so instead of running out of the room every time it appears on the calculator display, I decided to brave up and try to grab it by the back of the neck before it bit me.
We literally have its number now.
The notes from the moment of discovery – not the initial discovery, I’ve been seeing it now and then for some time now, but the moment of its capture and of the discovery of what it might actually be. At the moment, this is more or less everything I know about it.
So YES, it COULD be a value we need to know in addition to the Hashimi Cubit value, and I should be taking notes on formulas concerning it because I cannot even state the number offhand without a mnemonic formula.
Okay… It is THIS: 225 / PALESTINIAN CUBIT = This particular FALSE Hashimi Cubit value (there are more false Hashimi Cubits).
225 / 2.107038476 / 100 = 1.067849508 vs the standard Hashimi Cubit value of 1.067438159 ft
1.067849508 / 1.216733603 = Pi^6 Unit (Tikal Temple III Unit)
1.067849508 interacts with the Megalithic Foot to produce x/MF = 28125 / (Pi^3) Draconic Month Unit
Sacred Cubit / 1.067849508 = 15625 / (Pi^5); the (Pi^5) Unit is the AE Megalithic Yard.
So it will be interesting in the hopefully near future to see if there is an imposter to the throne, or if the King has an almost identical twin.
You Can Tune A Piano But You Can’t Tune Neptune… And You May Not Need To
Since I’ve been trying to do more work with the planetary tables lately, I finally decided that one glaring omission is that of Uranus and Neptune data, which in my opinion should be tentatively included so we can monitor the possibility of finding out whether, had the Maya known about Uranus and Neptune, the cycles of Uranus and Neptune would be harmonious with the Mayan Calendar.
When I started researching the Mayan Calendar, I found one site that bravely alluded to such a possibility, but I’ve never really seen anyone address this question, and that’s unfortunate because if the Maya WERE talking about Uranus and Neptune we’re going to need more data to round out the evidence for that because presumably we would have to match symbolism for Uranus and Neptune events to actual written Mayan dates.
Few may think to prioritize obtaining and distributing such data if we simply assume that the Maya somehow lacked knowledge of assistive optics, so such data may not be easily forthcoming and we may be at risk of being pulled into an unproductive vicious cycle where there is no evidence because there is no data, and no data because there is no evidence to show it would be relevant.
Relying on recent experience, I think the answer is most likely YES – Yes, the Maya may well have known about Uranus and Neptune, because they may have picked a rather brilliant calendar system that CAN incorporate and harmonize the cycles of BOTH of them. If we can’t file that under possible evidence that ancient astronomers possessed some quality assistive optical devices, we may have to file it under possible evidence of an ALMOST intelligent design to the Solar System.
We can file it under actual intelligent design for those so inclined, but I do so much work trying to harmonize these cycles to a higher level of perfection that nature seemingly DIDN’T do for me, that I tend to be inclined toward non-intelligent (but probably mathematically meaningful) design.
At any rate, if things go well the next several weeks I can hopefully make a presentation of some of these latest amazing cosmic near-coincidences and what we might do about harmonizing them as perfectly as possible. I hope to learn a little more about the way planetary Orbital Period / Synodic Period ratios and the way they they might work other planetary values, because there’s where I think a substantial amount of the remarkable action has been when finding out these things about Uranus and Neptune for the first time.
I’m sorry it took so long to get to the question, they might be some of the easiest planetary cycle values I’ve ever figured out if I was lucky enough to figure any of them out, but you know the drill — the Maya didn’t have telescopes. Everyone knows that. Show me one. Aha! You can’t. Rinse lather repeat.
Quite the contrary, my studies of the Codices suggest to me people who could see Jupiter close-up enough to be aware of its coat of many colors, a realization that helped to precipitate a renewed interest in the question.
In the meantime, I’m not exactly certain where we can look for assistance if we want to move further ahead with the question. All I can think to tentatively suggest is perhaps the data from George F. Andrews on Oxtintok, which I once declared (possibly hyperbole) to be the “Maya capital of the lunar Apsidal Cycle”.
It’s true that I seemed to find considerable resonance between the measures at Oxkintok and the Apsidal Cycle and it’s also true that it’s one of the things that dragged me into thinking about the question of Uranus and Neptune again was the boost of confidence in the relevance of the question when I saw how readily values for both planets seemed to potentially harmonize with the Apsidal Cycle.
Can You Build Us A Table? (We Meant for the Kitchen)
I’ve been doing some work on other tables besides the grand Planetary and Lunar Cycles table that I’ve been trying lately to tidy up and fill in. My very latest at the moment is my newest post to my Megalithic Portal thread, in case the data is of interest in the meantime until I can do more with the table (still no listing at left for the Sacred Cubit — sacrilege!)
The effort included my first rather half-baked attempt to actually design some architecture (or at least create an initial design) in what I am experimentally taking to be the ancient traditional manner, which I undertook to try to illustrate how I think such reference tables might be of great assistance in both interpretation and design of astronomy-oriented ancient architecture. As I noted in the post, I don’t think I could have done it without them (nor do I think I could have half as well without them).
I also marvel at how quickly I was able to complete the exercise.
I hope some of these reference tables will be appearing here in the future, hopefully a few more omissions and typographical errors will be worked out by then.
I posted this recent table to the Portal awhile back. It remains state of the art for illustrating the two metrological series that can be represented as derivatives of the Imperial Foot and the Sacred Cubit via 2 Pi and a progression of circles where the circumference of one becomes the diameter of the next (even if this schemata would probably not reflect a chronically correct description of the origin of the Sacred Cubit; as Remen x Royal Cubit in Imperial, my Sacred Cubit was likely to come after both of those units, not before)
Included here for the first time are the NUMBER of units involved in the unit to unit conversions that define and organize these two metrological unit series, and the +pos(itive) and +neg(ative) indicators intend to tell us whether the normal “forward” (+pos) form of the unit is being referenced, or whether the “backward” inverse or reciprocal (-neg) form of a unit is being referred to. (For example, in my model of Stonehenge, the inner sarsen circle circumference is technically a figure in inverse Megalithic Feet).
Thanks to jonm at the MP for encouragement toward including such important details that I sometimes hesitate to include because I tend to wonder if people want to bother with them. I really DID want to create something that made it easier for readers to verify for themselves what I am saying about metrological unit relationships, so hopefully this actually will help in the here and now.
A Wrong Turn Diagonally or A Diagonal That Points The Way?
I’ve reconsidered the problem of the minimum Great Pyramid platform diagonal. I projected it at possibly being (57.29577951 x 2) / 106.9734371 = 107.1215080 / 10^n, but it may be that a different candidate belongs there. I was skeptical that the ancient Egyptians would have used a false Megalithic Yard here (even though we can create one at Stonehenge as a compromise with Thom by (mis)interpreting the inner sarsen circle circumference as 48 Megalithic Rods as literally as Thom may have.
The Great Pyramid platform diagonals seem to have a format of (2Pi)^2 x “X”, which could give to the upper diagonal a potential value of (2Pi)^2 x (false Megalithic Yard 3.2 / 1.177245771) = 107.3105884 ft, which apparently DOES pass accuracy standards compared to projections, and might even make a more sensible bookend for that side of the mean value.
Something that encouraged me to try to dig deeper into this and to slow down before I get too sure what’s going on here, is that during the experiments with Uranus and Neptune cycles, even while it’s going to be difficult to make (32 / Megalithic Foot 1.17724771) = 2.718208958 into either a Megalithic Yard or what the Megalithic Yard actually represents which is 1/10th of the approximated Draconic Month (and we already have three very good ones), the reciprocal of 2.718208958 COULD serve a valid approximation of Neptune’s ~367.49 d Synodic Period (1 / 2.718208958 = 367.8893034 / 10^n)
The other two proposed values for Neptune’s Synodic Period could be reciprocals of actual Megalithic Yards, which could in turn allow synchronization of Neptune Cycles with the lunar Draconic Month.
So these are some recent thoughts on the possible ways of ancient timekeeping and architectural recording of astronomy data and formulas. I hope that time will soon tell us more about these things.
–Luke Piwalker
Luke Piwalker 