Once again, I’m rather intrigued with the proportions of ancient doorways ever since Tikal. The first things I want to look at here then are the doors into the antechamber, both the one leading through the portcullises into the antechamber, and the door above it to the “abandoned upper passage”.
Thankfully we have a fair amount of data from Flinders Petrie describing some of the Mycerinus pyramid’s internal architecture, and I’ve begun re-examining some of it.
It seems as if we have another mystery on our hands.
Once again, we may be seeing the signs of a diversity of different metrologies in use – 117.7 inches, for example, is certainly suggestive of a measurement in Megalithic Feet of 1.177245771 “modern British” feet, and the upper door width is rather suggestive of a measurement in Remens or Assyrian Cubits (4/3 Remen = Assyrian Cubit).
46 inches between the two doors vertically is suggestive of 3.881314681 although it remains to be seen whether this value actually fits into a larger scheme, and what metrology 3.881314681 might represent. Applying the number 12 as a probe, we quickly discover that at 3.881314681 x (12^3) = 6.706911769 x 10^n = 4 x 1.676737951 x 10^n, we see the possibility that this may have been measured out in an integral value of the 1.676747943 unit that may still be seeking a proper name.
As we know, I’ve proposed 38.81314681 as the length of Tikal temple I, and I’ve reported it also appearing in the data for Chichen Itza’s El Castillo calendar pyramid.
This data has yet to be subjected to a rigorous metrological or ratio analysis, but I wanted to share some of what I have so far because I find it more or less amazing that according to Petrie’s data, the lower door to the Mycerinus pyramid chamber seems to share a height / width ratio with the corresponding door from the Chephren pyramid, i.e., the Royal Cubit in modern feet as a ratio, and more amazingly, builds this same ratio out of different numbers.
One can only wonder what would have happened if Petrie had been just a little more curious about the architectural proportioning used inside these greater Giza pyramids, just as we can only wonder what would have happened if he had been just a little more curious about the role of his Stonehenge Unit in the actual measures of Stonehenge.
There may also be metrological similarities between the height Mycerinus pyramid antechamber and the King’s Chamber of Cheops’ pyramid, with a mean height of 19.21388691 feet proposed for the King’s Chamber, and a possible height of 192.1388691 inches suggested here for the height of the Mycerinus antechamber.
For those curious, the suggested 1.394274995 height / width ratio for the upper antechamber height is 1/4 of 1/1000 of Munck’s “Giza Vector” number 5577.096019 (the square root of 31104000). In turn, 1.394274995 is the square root of 1944 / 1000. As a metrological unit value, thus far the only identification of such square roots has been the Thom Mid Clythe Quantum of apparently sqrt 60 feet, of which 1.394274995 may be considered a derivative (or vise-versa)
I am quite excited to see some of these results, because I think it rather dramatically underscores what I have been saying for some time now, which is that we are frequently seeing metrological unit values as ratios, strongly implying that the ancients were well aware of these unit values in “modern” feet.
However it still poses a lingering mathematical puzzle, as does the door to “Belzoni’s Chamber” in the Chephren pyramid. At first sight, we seem to see blatant reiterations of the Royal Cubit, but at a closer look we may see something slightly different. The Mycerinus antechamber door seem very reminiscent of the Belzoni Chamber door in that respect, yet here even on a second look it remains suggestive of the formula “2 Royal Cubits of 1.718873385 times 1.718873385 = (1.718873385^2 x 2), but is that really what they meant to say?
Yet the door ratios for both as 1.718873385 seems very clear from the data – Petrie’s data gives for the lower door of the Mycerinus antechamber 71.1 / 41.4 = 1.717394394, very close to the 1.718873385 value. These propositions aren’t necessarily exclusive, because both proposals treat the architecture as symmetrical, but it may not have been perfectly symmetrical, which may allow for more than one right answer.
This seems to hold true for much of what we can see in Petrie’s data – there is a great deal indeed to suggest that the irregularities and assymmetry we often see may be deliberate, and for mathematical reasons.
It’s still perplexing nonetheless, though. At Giza, as with Tikal, we can hopefully assume that not only is ratio of height divided by width meaningful, but so too is the product of height times width, but with 2 Royal Cubits width and 2 squared Royal Cubit height, of course the product of width times height will contain the cube of the Royal Cubit value.
We can make comments like these about the exponential use of unit values as multipliers and divisors; here we might say that with the door height x door width having the cube of the unit value, that someone is cleverly describing the volume of something using the area of something else, a 2 dimensional representation or a 3 dimensional construct, but is that actually what the architects meant, and what might be the 3 dimensional construct so described?
Here, we seem to have the overall 1.718873885 ratio value corroborated for us by the ratio between the height/width ratio of the two doors so that hopefully we can feel fairly certain about that much at least. We can wonder then if the upper door was ever really intended to lead to a finished passage, or whether it was added primarily for the purpose of making an important expansion of the data provided by the lower door.
For now, we can ask the skeptics how it “just so happened” for these doors from two separate “Old Kingdom” pyramids to have the same height/width ratio without the ancient Egyptians known the values of their metrological units in “modern” feet. As ever, on closer inspection the data seems just too full of “amazing coincidences” to actually all be mere coincidences.
–Luke Piwalker
Luke Piwalker 