One possible reason I still can’t seem to make absolute sense of the Greek Temples that Marcello Raineri uses for his examples (see preceding post) could be because I am overlooking some ancient Greek unit of measure or other. With this in mind, I took a look at Wikipedia’s page on ancient Greek measures. However, all that it really tries to tell me me is that ancient Greece was even better at splitting hairs and then naming each individual hair than ancient Egypt.
There are a plethora (pardon) of various unit names, all neatly derived from dactyloi (digits) the same way we have seen units derived from the Egyptian digit, and ideally there isn’t any difference between the Greek and Egyptian digit in the first place.
However, just like Wikipedia’s page on ancient Egyptian measures that are shows unit values skewed upward (remen = 1.22+ ft), apparently in part because of Clagett, the page on ancient Greek measures show unit values skewed slightly downward (Remen = ~1.213 ft) from our norm of about 1.216-1.217 ft, or the Short Remen of about 1.215 ft.
There are several Remen-like figures known of about 1.213 and 1.214, but there probably isn’t much known point in actually taking them to be Remens besides making things more complicated than they already are.
I was about to say that the thing to do would be to throw out all the skewed values in the Wikipdia tables and start all over with a Greek Foot of 12.16733603 inches, but there are several curious things about the tables as they currently stand.
One is that some of the figures are somewhat suggestive of some more mysterious values from Raineri’s paper, and another is that one of the values is suggestive of the Palestinian Cubit.
Here, a pygon = 15.17 inches; 1 Palestinian Cubit x 72/10 = 15.17067703 ft.
Since these units are all so tightly integrated, rather than throw it out we could treat Wikipedia’s page as “More Than You Ever Wanted To Know About the Palestinian Cubit”, including its relationship to some interesting figures like ~1.213.
The Wikipedia table isn’t actually the first hint that the ancient Greeks could have been using a Megalithic Yard value that is closer to the Sidereal Month rather than the established values, which appear to represent the Draconic Month, and that may be significant as well (13.65 in x 2 = 27.3), and if ever learned recently, we already knew that 2.107038476 x 360^2 = 27.30721865 x 10^n (Sidereal Month = 27.321661554 d).
The thing is, such a homogenous system as we glean from Wikipedia for Greek Measurement has little intrinsic purpose in any established terms concerning data storage and retrieval. If they’re all going to be fractions or multiples of the Greek Foot, there isn’t much point. The ancient Egyptian measures seem to show great diversity for the sake of data storage and retrieval and it’s still very difficult to imagine the ancient Greeks not following suit. How the ancient Greeks would have or could have missed out on the integrated bundle of diverse units that we see on display in Megalithic, Mayan or Egyptian architecture is very difficult to imagine indeed.
Why the Greeks and Roman would take archetypal Egyptian measures and alter them would have to be equally mysterious. Rather we might assume they not only inherited remarkably similar measures (dactyloi = digit, Roman Foot = Egyptian foot, etc), but the very same measures.
So, I still don’t know what the Wikipedia data of on Greek units actually represents except “More Than You Ever Wanted To Know About the Palestinian Cubit”, but of course that should include some basic information on why the so-called “Palestinian” Cubit is so Egyptian in the first place. We’ve seen this previously, which gives us some idea why the Palestinian Cubit and Megalithic Yard are both as Egyptian as anything else, and informs us of the nature of the Hashimi Cubit and why it’s important to ancient Egyptian metrology (the last diagram in the panel also explains how the Egyptian Mystery Unit of 1.676727943 ft relates to the Hashimi Cubit).
There is still more to the story of why I am including such units in the ancient Egyptian metrological vocabulary, such as
So how is it that the ancient Greeks should not have an equally diverse vocabulary of metrological units at their disposal when the Greek Foot is 10/12 to the Remen (12 Greek Feet = 10 Remens), but instead ended up with names for all sorts of fractions of the Greek Foot and nothing else? It’s difficult to think of any modern rational person wanting anything to do with any modern equivalent – again, if I said why don’t we call 2 inches a frapplesnoot and 4 inches a dinkledwiff and etc etc etc, you’re probably think I’d lost it completely and I wouldn’t blame you. You’d want no part of it, am I right?
Everybody ready? All together now, “WHY DON’T WE JUST CALL IT 2 INCHES AND 4 INCHES?!?!?” 🙂
Yet what Wikipedia shows is the ancient Greek metrology doing this very same thing, over and over and over.
At this hour then, not only does the nature of Ranieri’s temples still remain somewhat in limbo, but so does the very nature of ancient Greek metrology itself, or at least as according to any orthodox view..
In a way, we were warned – if we follow the metrology in John Michell’s Dimensions of Paradise, there’s a point where the Greek measures seem want to take an uncertain turn, which has never really been explained, but which may obviously relate to a need for diversified measurements for data storage and retrieval purposes.
I believe score is now at Greeks 2, Piwalker 0 in spite of several nice plays from the side with the Wookie in their cheering section.
While that issue simmers on the back burner, I decided to take a prompt from a recent GHMB discussion of the the Saqqara Serapeum to investigate further. I don’t really know much about the Serapeum, mainly because it doesn’t have a pyramid placed over it, and pyramids are enough to demand one’s attention (there also seems to be something of a a shortage of maps showing the Serapeum in relation to Saqqara and its pyramids that helps make it easy to keep overlooking the Serapeum).
There’s an air of weird mystery about the Serapeum, rumors of bovine worship and enormous coffers purported to be for cattle that are more extravagant than even the coffers of pharaohs and so forth. We know those things about the Serapeum of course, but I really haven’t delved into the available metrological data (or lack thereof) for it.
This page, among other noteworthy things, purports to have data on several of the coffers and quotes from both the Isida Project and from explorer Auguste Mariette to say,
“I have measurements for three coffers. One is from Linant-Bey given to Mariette who added it in an addendum in his publication.
The outer dimension of the coffer is 3.85 meters long, 2.32 meters high and 2.32 meters deep. The inner dimension is 3.17 meters long, 1.73 meters high and 1.46 meters deep. The lid is 3.85 meters long, 0.92 meters high and 2.32 deep. The combined weight he calculated is 62 tons.
The Isida Project gives dimensions for two coffers:
Coffer#2, which doesn’t have a lid: outer dimension are 3.8 m x 2.5 m x 2.4 m
Coffer#17: outer dimension: 3.8 m x 2.17 m x 2.3 m.”
There is part of the experiments with Greek metrology where the using standard Remen value of 1.216733603 ft, (Remen / 16) x 18 = 1.368825303, which is very interesting because Raineri’s data gives us “136.8764” ft as the width of Apollo’s Temple at Didyma, and also because 5 / 1.368825303 = 365.2767076. – thus another possible explanation for troubles with Greek metrology could have been the observance of a more accurate Solar Year than the standard Solar Calendar Year, even without giving up the 12.16733603 inch Greek Foot value.
It’s really just another variation on the hopefully familiar theme, 133333.3333 / 365.0200808 = 365.2767076. 133333.3333 is something of a “Solar Year Exchanger” because the natural square root of 133333.3333 (365.1483717) is so near to valid figures for the Solar Year.
We may also want to note what 1/16th of the standard Remen actually is.
1.216733603 / 16 = 7.604585019 / 10^n ((1.216733603 / 16) x 20 = 1.5201917004, which has been proposed to be the corresponding Greek Cubit to the Long Greek Foot.
12.16733603 inches / 12 = Greek Foot 1.013944669 ft; Greek Foot 1.013944669 x 1.5 = Greek Cubit (?) = 1.520917004 ft = .760458501 x 2.
In the Serapeum box figures attributed to Mariette, the figure of 2.32 m recurs (and 2.3 m appears in the data attributed to the Isida Project). We haven’t seen much of 2.32 meters = 7.611548556 ft although it’s been tentatively spotted at Palenque in Mexico and in the Valley of Kings in Egypt, but it could experience some conflicts of interest with 3.6 Palestinian Cubits = 3.6 x 2.107038476 = 7.58338514 (2.312011179 m).
See where this is trying to head for, though, right or wrong?
Could it be that the data from Mariette isn’t reliable? Well, let’s look at our Exterior / Interior ratios a minute:
Again, “The outer dimension of the coffer is 3.85 meters long, 2.32 meters high and 2.32 meters deep. The inner dimension is 3.17 meters long, 1.73 meters high and 1.46 meters deep. The lid is 3.85 meters long, 0.92 meters high and 2.32 deep. The combined weight he calculated is 62 tons.”
Exterior / Interior Length = 3.85 / 3.17 = 1.214511041
Exterior / Interior Width = 2.32 / 1.46 = 1.589041096
Exterior / Interior Height = 2.32 / 1.73 = 1.341040462
Which look a lot like 1.216733603 (typical for Egyptian work to see Remens and Royal Cubits as ratio), the reciprocal of almighty 2 Pi = 1.591549431, and probably (1.676727943 x 8) / 10 = 1.341382354 which we seem to see a fair amount of while working recently with the pyramids of the Faiyum region. This data from Mariette then might actually be trustworthy.
So I have no finished models for any of the Serapeum boxes as yet (and only the dataset from Mariette is relatively complete), but if we are fortunate, Saqqara, Palenque and the Valley of Kings may all be places we can go to learn more about numbers similar to some of those which may pertain to ancient Greek metrology, which is most often the point of bringing up distribution patterns of mathematical values – learning where we might go to find out more.
Certainly some skepticism is due whether the architects of Palenque were actually thinking of what numbers appear in the Valley of Kings (or vice-versa), but again both cultures appear to have been tapping the same pool of astronomy-related numbers for their architecture and any location where we find a particular number represents an opportunity for learning more about it.
While we are looking at the Serapeum boxes, there is at least one other thing that might be worth pointing out.
2.17 m = 7.119422575 = 14.23884514, which is remarkably close to 1.423799349, a Wonder Number that has emerged as seemingly prominent in the ancient architecture of the Faiyum Oasis. As we now know, this Wonder Number is intimately related to the Palestinian Cubit (and in turn to the Half Venus Cycle / Calendar Round). Thus another possible sign that although this number may be prominent in the Faiyum, it is probably not exclusive to the Faiyum, and the same with any other Faiyum Wonder Numbers.
Finally, in terms of “places we might go to learn more about a particular number”, perhaps a more careful comparative study of Greek architecture on my part might help? I’m still rounding up previous attempts to unravel the proportions of Greek architecture, and just happened across this one – apparently I did post at least one post based on Angelopolous’ data then: The Temple of Olympian Zeus
These figures from that page are particularly notable: The first looks like a clear case of 300 Harris-Stockdale Megalithic Feet (using 1.177245771 as HSMF, 300 x 1.177245771 = 353.1737313), and the second we may have seen echoed in Ranieri’s data where we obtained it for the Temple of Artemis at Sardis. It appears to be Equatorial Circumference in Miles / Royal Cubit in Feet: 24901.19743 / 1.718873385 = 1.448692943 x 10^n.
107.61 m = 353.0511811 ft
44.132 m = 144.7900262 ft
This number looks like another number from Raineri’s data
110.34 m = 362.0078740 ft
This is also from the Temple of Artemis at Sardis, where it is the calculated diagonal length, whereas in Angeloplous’ data it is the length of the Temple of Olympian Zeus.
This is really reminding me a lot of the way the Egyptians recycled important numbers in their pyramid building (we also have accounts of them re-incorporating actual pyramid material the same way).
With that vote of confidence, we can be probably be more certain what the diagonal of Artemis’ Sardis temple was supposed to be, which is outlined in the post on Zeus’ temples,
“110.34 m = 362.0078740 ft = probably 362.1732357 ft”
I recently found occasion to mention that this number belongs among the “Wonder Numbers”, even if it’s a little shy in front of 2 Pi, 1.622311470 or 1.177245771 – not the most wonderful Wonder Number then, but an important one nonetheless. Students or followers of Carl Munck may recognize the number as one of his introductions and the very same for 1.448692943. The two are related thus: 3.621732357 / 1.448692943 = 2.500000000.
Metrologically, 362.1732357 ft is 216 x Egyptian Mystery Unit (LSR) 1.676727943 ft.
In case anyone noticed the 110.34 figure in meters looking like Eclipse Year / Pi, that actually works to give the best value for the Eclipse Year if the meter here is (Radian^2 / 1000) ft = 3.282806350 ft.
It may be worthwhile then to explore whether 362.1732357 represents by way of analogy the correct recognition of a word on the Rosetta Stone.
–Luke Piwalker
Luke Piwalker 