In the previous post, we took a first look at the 30th Egyptian Dynasty coffer of Wereshnefer, courtesy of photographs and data from the Metropolitian Museum, including pixel measurements I took of one the photos of the coffer lid in hopes of being able to extrapolate further data from the width and height provided.
Coffer of Wereshnefer, courtesy of the Metropolitan Museum, as seen in the previous post. “Dimensions: Box: L. 292 × W. at foot end 155 cm (9 ft. 6 15/16 in. × 61 in.); Lid: L. 292 × W. at foot end 155 × H. at foot end 81 cm (9 ft. 6 15/16 in. × 61 in. × 31 7/8 in.); Total H.: 211 cm (83 1/16 in.)”
In the previous post, we saw what may be our first mathematical and metrological discovery, apparently involving the Hashimi Cubit (a form of the Egyptian Royal Foot).
“Something I found especially interesting so far is that for Wereshnefer’s coffer, the total height is given as 211 cm while the height at the foot end is given as 81 cm. It should be then given the data that the total height of just the coffer should be 211 – 81 = 130 cm.
211 cm = 6.922572178 ft, 81 cm = 2.657480315 ft, 130 cm = 4.265091864 ft
Does 6.922572178 remind anyone else just a bit of the Metonic Cycle of 6939.688?
81 cm = 2.657480315 ft; 10.67438159 / 4 = 2.668595398 ft = 81.3388 cm; 130 cm = 4.265091864 ft; 1.067438159 x 4 = 4.269752636 ft = 130.142 cm.
4.269752636 + 2.668595398 = 6.938348034 = 6939.688 / 1000 = 6.939688 to an accuracy of .9998.”
The coffer lid may nor may not have some slight, deliberate irregularities in its design; for now we will assume either the final design or the initial design were regular and symmetrical, just as we might with a pyramid or other structures, and begin by treating it accordingly.
Measures of the coffer lid extrapolated from the photograph and data from the Metropolitan Museum.
To be honest, I’m not 100% sure of the assessment of the total height that was seen in the previous post. On the one hand, it seems very much in accordance with observations that have followed, but the emerging picture may be one of a particularly ambitious collection of astronomical references though measurement that may make it more difficult to feel certain about a particular parameter.
Even with as little of the data for the coffer overall as the projections actually contain, some very interesting things may become apparent.
The very first thing I should report is that from the raw data, we get the ratio 2.657480315 / 2.185537025 = 1.215939279, looking very much like yet another typical case of finding the value of the Remen in Imperial Feet, as a ratio (proportion) rather than as a measurement. Ratios withstand metrology; it will be proportioned this way regardless of any particular units of measurement that are applied.
The next thing I want to point out is 1.635925241. My first guess is that this may be 1.631553867, which would be the value of the Megalithic Foot that I work with in “modern” feet, cubed — 1.177245771^3 = 1.631553867.
It’s fairly rare that we see this remarkable number and I think that’s because it makes a poor multiple or divisor. In that sense we would prefer to use 1.177245771^1 so we get all the data out, whereas cubing the figure first is going to miss 2/3 of it. 1.177245771^3 = 1.631553867 is less a useful multiplier or divisor and more like “fodder” for more useful multipliers and divisors like (Pi / 3) or what have you (1.631553867 is a root for a truly amazing (Pi / 3) series), as I learned early on working at Tikal though the available data.
So far, experience suggests we might only see 1.631553867 wherein there is a specific point to emphasize about its role connecting particular important figures, or where it’s serving as fodder, or both.
This brings up what might be an important point, because one thing the 2.185537025 that seems to appear three times in the diagram might represent other than the Talmudist Cubit it so much resembles, is a decimal fraction of the square root of the height of the Great Pyramid as measured from the base.
sqrt 481.0335483 ft = 21.93245423
This is one of many reasons that particular interpretation of the Great Pyramid’s height was decided upon, that it can be conveniently represented though its square root in a valid fashion.
If the correct measure for the raw extrapolated value of “2.185537025 ft” is 2.193245423 ft, then the total measure across the three parts of the beveled top is presumably 2.193245423 x 3 = 6.579736268, which may not only be a valid and intended representation of the Saros Cycle of 6585.3211 days / 10^n, but it may also be something that can call data forth from the “fodder”.
My sets of approximations for the Saros Cycle are still experimental, but the projections already show me that if we take 6579.736294 as the “A” value, the improved accuracy version 6584.495251 will be the “B” value, and these may indeed be the best nominations for the A and B values, which generally tend to be the most important versions.
Thus it may be quite possible that we see something like this, with these two major Lunar Cycles, the Saros Cycle and Metonic Cycle, readily displayed side by side.
I’ll repeat this diagram here in hopes it helps keep people from having to keep scrolling back up to it, because there are some more things to point out. We may wish to note that for the diagram above showing the possible modeling of two Lunar cycles, this could be only where the Lunar references begin, rather than where they end.
For the mean height of the bottom section of the lid, note that we have 1.021527894 for raw data, which is a bit uncanny, since the number 1.021521078 is one of the original “Mayan Wonder Numbers” from Tikal, which was later found to also be “hiding” (it wasn’t really hiding) in my model of the Great Pyramid. (Some of course may still be eager to try to make something more like 1.031324031 — .6 Royal Cubits — out of this measurement, but seeking maximum exactitude may eventually demand otherwise).
It gives us something to think about because I might have misread the metrology regarding the height – maybe they weren’t using the Hashimi Cubit quite so redundantly? – so we are reminded that this is still just a scouting mission, there’s no need to name or claim the territory just yet, we only need to be having a look around for now. At any rate, even if we take out one of the possible redundant uses of the Hashimi Cubit, we may still be able to get a total height that registers as a valid figure for the Metonic Cycle, thus preserving the model suggested in the small diagram.
The value of 5.085301837 is very much reminiscent of 1/2 of an important and increasingly familiar figure: (5.085701734 x 2) / 10 = 1.0171409347 = 360 / Lunar Year. This “backhanded” way of writing the Lunar Year, which is rather similar to the “backhanded” way of writing the Half Venus Cycle, with both of them having us diving 360 by “x”, seems to have been rather favored by the ancients, not only in Egypt but particularly in the ancient Americas.
Michael Morton may have the first claim on publishing 5.085701734; there may still be some informative equations of his on the Internet regarding this figure in association with a “geomathematical” interpretation of a “Baphomet” (i.e, it resembled a goat) monument of some kind, which Michael used to refer to as “Baphy”.
At any rate, I’m doing my best to try to stick to exploring the suggestion of 1.177245771^3 = 1.631553867 for now, partly because as I say on a regular basis that two of the numbers that ancient architects and designers seem to have been most eager to incorporate into virtually everything are 1.177245771 and 1.622311470. (The Pyramid of Niches in Mexico remains a memorable example of this, even out of a great many examples). Incorporating 1.177245771 via its cube 1.177245771^3 is one way of making sure its there somehow.
We may want to note that the ratio between the raw figures of 2.657480315 and 1.177245771^3 = 1.631553867 is 2.657480315 / 1.631553867 = 1.628803295 (raw data 2.657480315 / 1.635925241 = 1.624450952), could be the probably obligatory reference to 1.622311470 that we might be expecting.
This is one place where things may still be bit tricky; if we are looking at 1.177245771^3 = 1.631553867 and 1.622311470, 1.631553867 x 1.622311470 = 2.646888553 may be the true intended total height. This is the reciprocal of the standard Saturn Synodic Period of ~378.09 days: 1 / 2.646888553 = 377.8020797 / 10^n = 1/800th of the Great Pyramid’s base perimeter as measured from the base, but there is also the possibility of a reference to the Jupiter Orbital Period trying to crowd its way into the picture as well, and it remains to be seen what is the most harmonious interpretation of all this.
Specifically, the possible reference to Jupiter’s Orbital Period that may have been detected is Total Height of Lid 2.657480315 (ft) x Upper Height of Lid 1.631553867 (ft) = 4.335822284 = ~Jupiter Orbital Period 4332.59 / 1000.
Are there any notable justifications for the grouping together of some of these numbers as we might hope? That question is still being researched, however we might note that the possible display being suggested here includes an advisory that 1.666666666 / 1.631553867 = 1.021521078, which is actually a much better way to remember the “Mayan Wonder Number” 1.021521078 than I am currently using.
If the height across the top is really (sqrt 481.0335483 ft = 21.93245423) / 10, then 1.631553867 / 2.193245423 = 27.94546570 / 100. 27.94546570 ft is the projected height of the Great Pyramid’s missing section, so this combination ushers in some of the most important data found at the top of the Great Pyramid. Seen from this angle, it’s as if the designers of Egypt’s 30th Dynasty were still paying homage to the splendid mathematical achievement that the 4th Dynasty pyramid attributed to Cheops (Khufu). (This may well imply that 1.177245771^3 is also contained in the Great Pyramid).
The length of the coffer and/or lid is also proving to be somewhat enigmatic at first glance; 292 cm = 9.580052493, which isn’t that far from 9.606943459 ft = 9 Hashimi Cubits of 1.067438159 ft, but there may be a number of other possibilities as well, including
Saturn Synodic Period / ((2 Pi)^2) = 377.8020800 / ((2 Pi)^2) = 9.569838482 = 10.21521078 / 1.067438159.
Combining the Saturn Synodic Period with 1.177245771^3 can also generate the standard value for the polar circumference in miles via the square of 1.177245771^3.
There may also be some reference to another member of the same classic Tikal (Pi / 3) series that contains 1.021521078, namely 1.069734371. A striking thing about this truly incredible series is that we can create it from half of the standard Venus Orbital Period and (Pi / 3):
Venus Orbital Period 224.8373808 / 2 = 112.4186904; 112.4186904 / ((Pi / 3)^3) = (1 / 1.021521078) x 10^n; 112.4186904 / ((Pi / 3)^4) = (1 / 1.069734371) x 10^n.
These important considerations then may be casting an alternative vote that 292 cm = 9.580052493 ft may actually be intended to mean the reciprocal of (Pi / 3)
1 / (Pi / 3) = 9.549296586 / 10^n.
That is still a lot to think about.
I did mention that there may be more to the lunar references than just the possible occurrences of Saros Cycle written across the three parts of the beveled top and the Metonic Cycle written with the height, in addition to the possible reference to 360 / Lunar Year that may be represented by the width of the lid.
So far it seems unusual to readily pick up traces of the Apsidal Cycle; one notable place we found it is in Mexico at Oxkintok where they literally seem to have been specialists in this number – they don’t just mention it, they seem to have a lot to say about it there.
Already, however, possible traces of the Apsidal Cycle have been detected in the coffer of Wereshnefer. A possible reference to the Tropical Month has also been found. In asking someone might group these two numbers together as if emphatically, it appears as if a functional approximation linking the two might be (12 x (Pi^2)) x 10, the very same critical link used to connect the Venus Orbital Period to the Half Venus Cycle (aka Calendar Round).
In regard to the possible bundling of these Lunar numbers with the Saturn Synodic Period, Apsidal Cycle 3233 days / Saturn Orbital Period 378.09 days = 1.068859266 = ~1.069734371 x 8.
How this quite possibly under-appreciated number 1.069734371 first entered the discussion here, is comparing the Sothic Cycle to the Tropical Month: 1460 / 27.3 = 106.9537070 / 2.
Allow me to demonstrate what else the Apsidal Cycle may be doing in the discussion:
Possible Center Width of Coffer Lid 2.193245423 ft, cubed / Possible Upper Height of Coffer Lid = (2.193245423^3) / 1.177245771^3 = 6.466365938 = 3233.182969 / 500.
Suggested Width of Coffer Lid 5.085701734 ft, squared and divided by 4 = (5.085701734^2) / 4 = 6.466090532 = 3233.045266 / 500 = 1.177245771^3 / 1 Pole (unit of measurement = 1.5 Indus Feet)
The figure of 1.449882405 ft I probably haven’t much insight into yet. It’s quite similar to the value of the Earth’s circumference at a ratio of miles to Royal Cubits (24901.19742 / 1.718873385 = 1.448692943 x 10^n), but it’s still hard to be certain of that at all, although we also see potential geodetic modelling value where the value of the Pole in inches can be seen as being equal to the Equatorial Circumference in miles / 4 Pi.
At present, I am resting no faith whatsoever in such speculations on my part, but in a attempt to explain why Thoth might be associated with both the Moon and with Saturn, and perhaps the Apis bull as well, I posted the following images to GHMB based on comments that were make by R.H. Wilkinson, in response to one of engbren‘s scholarly threads about whether Saturn was an influence in the design of the pyramids.
I am including it here as part of this discussion because
a) The cycles of both Saturn and the Moon may be represented boldly in the mathematics of Wereshnefer’s coffer
b) Wereshnefer’s coffer is said to come from Saqqara
c) Saqqara is also the location of the Serpaeum where the idea of the Apis bull “cult” predimonates
c) the Serapeum contains coffers (the “Serapeum boxes“) which have similarly beveled tops
I will leave it at that for now because again, there is much to consider, but even with an incomplete dataset for Wereshnefer’s coffer, it very clearly has great potential to be at least as royal mathematically as it is aesthetically.
Postscript (Next day): There may be a few other possibilities that we might not want to miss out on. Whether or not the scheme of Wereshnefer’s cooffer can accommodate it, technically
Saros Cycle 6585.3211 / ((1.177245771^3)^2) = 8 / (3233.820167 / 10^n) = ~8 / (Apsidal Cycle / 10^n)
Interestingly – but perhaps misleadingly? – the data gives us the length of the artifact as 292 cm = 9.580052493; sqrt (1 / 9.580052493) = 3230.84449 / 1000, and sqrt (1 / (9.580052493 / 10)) = 1.0215682738.
Perhaps as at Stonehenge, here the reach of the ancient designers eventually began to exceed their grasp?
We may also wish to note that with the suggested possible width of the artifact of, 5.085701734 ft, 5.085701734 x (360 / 2) = 366.1705248, possiblya valid Leap Year figure, and the reciprocal is 27.30968039 / 10^n; 27.30968039 could still prove to be a viable approximation of the Sidereal Month.
Finally, something that truly should not have been omitted from the preceding post, which is that the ratio between Metonic Cycle and Nodal Cycle can be seen as 6939.688 / 6793 = 1.021593394.
To emphasize again a critical point, ratios like that are not mere mathematical abstractions. Questions like “How many Venus Orbital Periods are there in a Solar Year?” or “How many Nodal Cycles are there in a Metonic Cycle?” are not only very natural questions to ask about calendars, they are vital ones as well.
–Luke Piwalker
Luke Piwalker 
