Greetings, all… I hope all have been keeping safe and well.
A funny thing happened about six months ago apparently having to do with my becoming a victim of obsolescence and losing the ability to post this blog due to sudden lack of a supported browser. Ironic in a way; here I have a blog where I try to encourage the world to have some respect for our ancient ancestors and was silenced by a lack of respect for a 15 year old computer that had been limping along after having been the victims of a Windows update…
Anyway, I hope to be back posting here soon, and my apologies for suddenly vanishing without notice. In a way, it may be as well because I’ve devoted some months now to trying to unravel the symbolic astronomy language used in the surviving Mexican Codices and I had my work cut out for me there – but that might have been sort of a bait-and-switch for me to keep posting about those matters on a blog that started out devoted to ancient architectural mathematics, even if the subject of the mathematics does seem to be astronomy.
I have wrestled with some ancient architecture the past few months. Being rather excited about the new book by Peter Harris and Dr. Thomas Gough about the Megalithic Foot (most highly recommended), my enthusiasm for Megalithic monuments was stoked a bit and I ended up going back to try to scout out some of the finer details and mathematical infrastructure of Alexander Thom’s Flattened Megalithic Rings. I’ve also been a bit inspired by Peter’s skill at finding lunar cycle data in Megalithic sites using the Harris-Stockdale Megalithic Foot (HSMF) as the unit, and seem to have been finding a notable amount of lunar cycle data in my data projections for the Flattened Rings.
I also found out there may be more of the Golden Ratio, Phi, in them that was previously realized, and I do believe both the kind familiar to most, and the two main Phi-like numbers that feature in some major calendar cycle conversions. These deceptively simple geometry schemes really did deserve closer scrutiny, and still more scrutiny than I’ve been able to give them, although there have certainly been some notable highlights.
It was probably after I wasn’t able to blog anymore (I’ve been posting some things on a thread on the Megalithic Portal forum instead in the meantime, where Peter Harris also has an active thread about the HSMF) that I ended up looking at what I think must be a paper by Glen Dash that I had thought I’d read already because of its similarity to several others, and managed to deduce what I think seems a very satisfactory solution to the questions of whether it is the top or bottom width I been giving figures for from the projections, and what the minimum, maximum and mean widths (and diagonals) likely were.
At least the break may have been slightly refreshing; I managed to be encouraged by developments with the Flattened Rings and decided to tear into another set of unsolved mysteries, this time going back to the Giza pyramids. I worked out figures for the Mycerinus Pyramid some time ago, but was never able to tell if they were meant to be maximum, minimum, or mean figures, not to mention I’ve never produced a set of mean figures for the Great Pyramid or for Khafre’s pyramid that I’ve been comfortable enough with to “endorse”.
I’m still having trouble quite accepting this, but my current data projections make it look like for the mean values, each of these three big Giza pyramids have mean values that are skewed in an individual way. Mean values and their ratios to the minimum and maximum values that they come from, are typically skewed slightly because of the way the math in question works of the Stonehenge sarsen circle , which fortuitously increases the data storage and retrieval capacity of the monuments,
Of course, I’ve never had mean data for the exteriors of three adjacent monuments before, so it could be typical for all I know, but it still takes me some getting used to the idea that the mean values for the Big Three at Giza could be as skewed as some of them look.
Because the min, max, and means will be very similar for them, the ratios are going to be very fine and that is the other thing that make a little while to get used to – the projected individualized means generate a diverse spray of fine constants that it can be difficult to make sense of.
There may have been method to the madness of the ancient Egyptian architects, however. It’s quite possible that the variety of fine ratios projected from the data was intended to equip us with a variety of fine ratios we might need to better understand ancient calendar systems (the ratios between some of the planetary values can also be very fine ones, barely over 1:1), and it is striking how the almost preposterously “geodetic” Great Pyramid manages to get in a very rarely seen but very important constant, the ratio between Earth’s equatorial circumference and its polar circumference, another terribly geodetic gesture.
The curious data projections also seem to be making a good deal of sense astronomically speaking. It looks like that where Chephren (Khafre’s) pyramid was intended to “write a book” on the values for the Lunar Year, the Mycerinus’ design may have been intended to “write a book” on the values for the Eclipse Year – including that there is evidence that the design of the Mycerinus deliberately uses the multiplicity of maximum, minimum, and mean values to even address the similarity of the Eclipse Year to 1/10th of half the Metonic Cycle.
This work has of course been looking for evidence that the Metonic Cycle was actually discovered long before Meton is credited with it, as well as evidence of a possible greater antiquity for many mathematics and astronomy innovations that is popularly thought at present.
Something compelling about the data projections is the way that the Mycerinus Pyramid projections seem to be able to “unbundle” other important astronomy data when exposed to some of the more obvious things, requiring little if anything that is exotic to perform such an impressive feat, and the way the projections provide for the Great Pyramid to do the very same, with the mean length of a side finding the true best half Venus Cycle approximation via Pi and the ideal Anomalistic Month value via the Radian.
360 / 2 Pi = Radian being three of the most obvious statements of the Great Pyramid and its 2 Pi perimeter/height ratio and they seemed determined to have meaningful mathematical interactions with so many of the numbers we find through the measures and proportions of things at Giza.
I hope to have more – possibly lots more – to say about the Flattened Circles and the main Giza Pyramids soon. There are many other unsolved mysteries left to visit or revisit, including Egyptian’s Bent Pyramid, and one of the intriguing things about the current work on Giza is that the Mycerinus might just also be able to fill in one or more of numerous missing pieces in the Bent Pyramid’s original design scheme.
Also, of late I’ve designated two new numbers as “Wonder Numbers” according to some of the classic criteria that earned other numbers that title, as seen in previous posts to this blog. One of them has been under my nose the whole time and is a curious number that is part of the proceedings at Stonehenge and has been for quite awhile now; the other is a new one discovered after trying to place an unfamiliar number in the projections for the Thom Flattened Rings, and it finally being noticed that this number, slightly over 107, resembles the square root of 2 Radians.
A number slightly over 107 has also started to appear in certain astronomy calculations, so there’s quite a bit to think about there.
I might also mention that in recent weeks, some of the excellent fieldwork and geometry on several Megalithic sites in Wales posted to the Megalithic Portal by Cerrig have roused my curiosity, since something looking like the Tropical Month seems to recur in his data, and I’m still hopefully that the sites in question might indeed have something to teach us about ancient reckoning of the Tropical Month, because that is a subject I seem to have yet to find guidance on among the voluminous teachings of the Stonehenge design, or other Megalithic Sites.
All of that has also had me hard at work again on the master table of planetary cycle approximations and formulas. I like to think things have progressed there as well, but there are still a good number of tough choices to be made.
So, there will be many things to talk about in the subject area where this blog started out if I can get my act together. It will be good to be back!
Very best to all!
–Luke Piwalker
Luke Piwalker 