For the second round of Short Reports, we seem to have some diverse topics that, in a timely fashion, may have some interconnection.
The Mysterious Eclipse Year
Even for as much as we are learning about the Eclipse Year and how it may be represented and recorded through measure and proportion, it continues to hold some mysterious qualities. One of these is that although the indication of the legitimacy of the “Best Eclipse Year Value” (346.5939351 days, representing the “textbook” value of 346.62 days) now appears to be growing by leaps and bounds, mathematical and metrological probes continue to fail to qualify this value as a quantity that can be made from any ancient unit of measure recognized herein directly (i.e, by means of a whole numbered ratio)
Were it not for this, we would have had a tidy dozen ancient metrological unit families, and might even have associated them with the 12 houses of the Zodiac if it made them any easier to remember, but there appears to still be a yet unidentified and unnamed family of ancient units of length measure which is still at large.
The Missing Piece
I am reminded of this album by one of my favorite musical groups and the conspicuous absence of the missing puzzle piece seen on the cover.
Recently, I have attempted to conceptualize our core group of ancient metrological units as a “Swiss Army knife” – each unit is distinctive and has certain properties and functions that may make it most suitable for a certain task, but all are related and “joined at the hip” as it were – they are all part of the same thing.
Shown again above is the recent description of the remarkable fashion in which our core bundle of ancient units of length measures may be related to each other in as many as four different ways. That is as many as four different ways in which the unity and integrity of this phenomenally well-chosen unit bundle is able to describe the precise size and “shape” of any unit which may be missing. Such a remarkably well integrated collection of ancient units scarcely seems like anything that can be reasonably considered to be the product of any accident.
Both the methods at lower left, and particularly the method at upper left, are among those able to corroborate the existence of the ancient “Egyptian Mystery Unit” (“EMU”), and to describe it mathematically. That is very much the actual story of how the “EMU” (also known as “LSR”) of 1.676727943 has managed to gain legitimacy in my eyes in spite of considerable reluctance on my part to truly accept it as an ancient unit because we still cannot seem to put a historical name to it.
The Pi or 2 Pi relationships particularly identify this exact value as a unit unto itself.
Just as with a jigsaw puzzle, if we are missing an ancient unit from our vocabulary, we have a good chance of being alerted to it because its absence may be made conspicuous by it neighboring pieces that are in place, because of these networks of unit relationships.
The Cubit of the Nilometer
Mercurial at GHMB recently brought up a fascinating Egyptological topic, and one that I’ve admittedly neglected, that of the “Nilometer Cubit”, in a discussion with fellow champion of the Remen, Jim Alison, wherein Jim and others are taking a closer look at some of the geographical relationships described by ancient authors and trying to put to right what may be some long-standing interpretive errors on the part of scholars, at least some of which may obscure the true level of ancient accomplishment that may be present.
Of particular interest may be some of the material from Letronne quoted by Mercurial which I hope to discuss in detail later in this post.
Essentially a “Nilometer” is a river depth gauge used along the Nile River that is used to predict the river’s behavior for the year, and the outcome. The Nile frequently rises enough to deposit rich fertile material conducive to agriculture onto adjacent land, but it may also fail to do so, and it may also sometimes rise to a level that may have destructive consequences.
Thus levels that are too low, or too high, foretell difficulties. It is said that therefore the year’s tax rates were based on Nilometer readings. Sometimes Nilometers may have come under the jurisdiction of Temples, as is said of two Nilometers of the Temple of Isis at Philae.
I first encountered the subject many years ago in my metrological studies, but to date had stumbled over so few helpful source materials that I had thus far assumed that these devices were much rarer than they may really be. Algernon Berriman in Historical Metrology includes a Nilometer Cubit in his list of ancient measures and devotes most of a page to the subject, but his readers seem to be left to their own devices to follow his references to even find out which Nilometer he is talking about.
Berriman’s source on the Nilometer and Nilometer Cubit (one wonders if his Samian Foot might possibly be the Megalithic Foot or HSMF)
The Nilometer Cubit that was described by several other sources at my disposal seems very different. I have clear recollection of these encounters of a Nilometer Cubit said to be approximately 1.74 feet in length, because this figure is reaching into the range of the reciprocal of the Radian (1 / (Radian 57.29577951) = 1.745329252 / 10) and it is precisely this fact which launched my very first extended metrological experiments, that were first undertaken purely for the sake of trying to determine if there was evidence of the ancients having used the value of Pi in Imperial Feet as a metrological unit, because of the intimate relationship between the Radian and 2 Pi.
Although these experiments caused new metrological discoveries to begin to flow, ultimately I wasn’t in the market for a new Cubit and the subjects of both a “Pi Unit” per se, and of a “Nilometer Cubit” eventually fell by the wayside.
In the case of the Nilometer Cubit mentioned by Berriman, I was fairly contented that what we see there is probably the irrepressible so-called Squared Munck Megalithic Yard and that there was little need to pursue such a Nilometer Cubit if I was already working with it under a different name. (Apparently, Berriman is referring to the Roda Nilometer, Roda being a name that appears to be particularly prone to variant spellings).
It’s only because of Mercurial’s remarkable finds amid Letronne’s text and the renewed interest in the Nilometer that it has inspired, that I’m becoming aware that there are a number of examples of the Nilometer and sources on the subject that I had previously overlooked (the texts may not have been available on-line at the time, which was more than 15 years ago).
Ludwig Borchardt, for example, is credited with a work devoted to the subject, Nilmesser und Nilstandsmarken (Nile Gauges and Nile Level Markers) (pdf link) of which I was previously unaware. This worthwhile blog page on Nilometers mentions one at Thmuis which is referenced back to an online National Geographic article.
Table from Borchardt. The 2nd through 4th columns from left to right describe “vertical borders of the scales”, “length of the scales” and “vertical distances between the scales”.
There seems to be no standard definition of a “Nilometer Cubit” given here and probably just the opposite. In the long run I am going to want to know more about this, including that I am going to want to see the scales for myself, but for now let’s see some of what this data might tell us so let’s take a quick look at the “lengths of the scales” given here.
0.541 m = 1.774834383 ft which would seem to be the Nilometer Cubit of the Roda Nilometer as per Berriman or one just like it, (Berriman, page 74: Nilometer Cubit = 17.71 inches!) across a scale of 1:12 somehow; 0.545 m = 1.788057743 ft.
1.788057743 may not be the easiest figure to instantly identify; it might represent either 3 / EMU = 3 / 1.676727943 = 1.789199025 or it might represent Hashimi Cubit x EMU = 1.067438159 x 1.676727943 = 1.789803389, in the same way that we form the Sacred Cubit as Remen 1.216733603 ft x Royal Cubit 1.718873385 ft = Sacred Cubit 2.091411007 ft (not necessarily a rational-looking metrological gesture, but an eminently rational mathematical gesture that is reflected in genuine archaeological data). “1.788057743” might even turn out to be something else yet again than either of these.
0.520 m = 1.706036745. This is quite interesting because this is essentially a value of 1.6 Hashimi Cubits (1.6 x 1.067438159 = 1.707901054) that is accumulating something of a history of being mistaken for the Royal Cubit. Perhaps compounding the confusion at times is the fact that 16 Hashimi Cubits is the precise circumference value of a circle with a diameter of 1 modified Megalithic Yard, which is actually a variant Megalithic Yard constructed out of Megalithic Feet and presented to us by Stonehenge’s sarsen circle.
1.037 m = 3.402230971 which outwardly resembles two of the Karnak Cubit described by Berriman from Breasted’s account. By my accounting, the Karnak Cubit would be a fraction of the standard Megalithic Yard: 2.720174976 / 1.6 = 1.700109360 = 3.400218720 but this is not yet certain. Normally, any thing that looks like this but isn’t, will very likely turn out to be 2 / Megalithic Foot = 2 / 1.177245771 = 1.698880598 = 3.397761197 / 2.
1.532 m = 5.026246719 ft. This is an interesting figure because we could so easily take it to be 1.6 Pi = 5.026548246, which as the product of a whole number and Pi^1 would belong to the standard Ryal Cubit family, but yet 3 of the Egyptian Mystery Unit (EMU) = 3 x 1.676727943 = 5.030183829 ft.
1.060 m = 3.477690289 ft and 1.061 (?) m = 3.480971129, both of which are remarkable for their resemblance to 1/100th of the Eclipse Year in days. This helps to kindle hope of perhaps not only learning more about our “Best Eclipse Year Value” (“BEYV”) but perhaps even more about its very nature and origins, but already it has also helped to inspire a fresh reconsideration of the width of the Stonehenge Lintel Circle, the way it hints at the possible legitimacy of the “BEYV” unison with the “Puzzle piece” concept.
A Necessary Detour to Mexico
I know why it didn’t bite me on the nose the first time around, which is just because it was so far back before more serious study of ancient calendar systems and cycles, but in spite of my misgivings of some of Hugh Harleston’s work, I’m still something of an admirer of his. As Michael Morton began to diversify his own metrological efforts somewhat, he eagerly took on the unenviable task of trying to fathom ancient American metrology, and seized upon Harleston’s idea of a “Standard Teotihuacan Unit” (“STU”) or “Hunab” as a possible lead.
To perfectly honest, the “Hunab” is one of the reasons I remain rather wary of Harleston’s work on the whole, because Harleston presented it as if it were an answer to all of ancient American metrology in itself) – more and more it is increasingly clear that trying to make anything ancient into a construct that uses only a single metrological unit in its design must be about the worst metrological folly possible for the modern metrologist (why do such varieties of ancient units even exist if not to be used?!?) – and although Morton came up with some rather compelling metrological possibilities, they never quite seemed to get off the ground, starting with the fact that they were based on a figure for the Hunab specified by Harleston in meters.
Essentially Michael took the figure of “1.059 meters” for the Hunab and identified it with “9 Alternate Pi” or as I would now call it, 9 Megalithic Feet: 1.177245771 x 9 = 1.059521194 x 10, but the great problem has been that the figure is still in meters, and to this very day no one knows what the primary value for the ancient meter is supposed to be. My most recent work with Greek architecture reinforces the the idea that there isn’t one, that the ancient meter is always going to be a problem child of ancient metrology that may always have an unstable, highly variable character to it and that may always be at odds with anyone’s idea what what an ancient unit of length measure unit should look like in action.
(I will say in Michael’s honor that I found one of the figures from his “Hunab meter” equivalency, 10.59521194, in the pyramid temples at Tikal, as modern feet rather than Hunabs).
To perhaps make matters worse at least several admirably open minded researchers who I have more than a little respect for may have fallen into the trap of thinking that the Hunab meter in feet – 1.059 m = 3.474409449 ft, represents the Double Egyptian Royal Cubit, which is that much more an insidious trap because they could turn out to be right.
I’m not one to talk, part of the problem may be that back when Morton and I tried to tackle the Hunab, neither one of us may have had any idea what an “Eclipse Year” was (I certainly didn’t) so I’m not in any position to be critical with this observation, but I’m going to say that the way we know that the trap has gotten hold of us is if we are thinking the Double Royal Cubit at the complete expense of a healthy curiosity whether we might be seeing the Eclipse Year of 346.62 / 100 = 3.4662 written as a metrological unit.
It seems like going on a limb a long way just to say all that, if I have no idea what metrological unit it might actually be, but with the modest menagerie of ancient metrological units based on Solar, Lunar, and plantary cycles what we have seen so far, we could easily predict that the next thing we might encounter is the value of the Eclipse Year enshrined as a metrological unit via the usual reference value of the “modern” foot.
I still don’t know if I think ancient Americans could have actually made it work, but then the more reasonable expectation may be something other than constant and continuous exclusive use of the unit.
I will have to give some credit where it is due to researcher David Kenworthy for being first to my knowledge to realize the likelihood of the Eclipse Year have been commemorated as a metrological unit, even if I’m not in agreement with his particular numerical values, or the idea of trying to make the Half Eclipse Year into a “Cubit”.
In fact, I’ve just shown up the page how the so-called “Karnak Cubit” may not be a Cubit at all but something as radically different as the Megalithic Yard, and I still feel a considerable sense of urgency toward trying to get across to anyone who can hear it, how the habitual Egyptological malpractice of slapping the name “Cubit” on any series of digits that starts off with a 1 followed by a 7 may be one of the main things that sustains the perennial folly of trying to make all of ancient Egypt into nothing but Royal Cubits even at the expense of a myriad of other historical units.
Few if any Egyptologists ever talk about pyramids measured in Spans or Fists or any of the other known units, just Cubits, Cubits, Cubits – all day, every day, and if they can’t get away with that, they’ll chop the Cubit into simple subdivisions, which is still the very same thing except when taken to such an extreme as the digit, the unit itself usually becomes smaller than the margin for error! These are the very sort of tools one needs to always be right even if they’re often wrong.
At any rate, the Eclipse Year-like values of 1.060 m and 1.061 m among Borchardt’s figures, once converted to so-called modern feet inevitably bring – and probably should – all of this to mind.
The Stonehenge Lintel Circle Reconsidered Again?
Since I was called upon to once again consider the possibility of the Eclipse Year having been commemorated with a metrological unit, it’s put me once again very close to the most recent work I’ve done on Stonehenge. Richard (Orpbit) Bartosz at the Megalithic Portal seems something of an advocate for the presence of the Eclipse Year at Stonehenge (as am I), and I feel almost apologetic that my model of the Lintel Circle atop the Sarsen Circle doesn’t quite permit the width of the Lintel Circle (rather roughly about 3.5 feet) to be a representation of the Eclipse Year with anywhere near the same accuracy seen in the Sarsen Circle’s design.
I recently resigned myself to a particular figure as the most likely because there are multiple metrological pointers to it (always a good sign, essentially), but even then accurately affording the Lintel Circle with a plausible figure required a way of calculating that is almost without precedent, which is obtaining maximum and minimum diameters by adding half the target figure to the mean value, rather than simply subtracting the minimum from the maximum. One might hardly think so, but both of these perfectly legitimate ways of doing the math give slightly different answers, and the difference is a significant one.
Ultimately, only two days after posting the Megalithic Portal with a proposed width for the Lintel Circle of 3.483165721 ft, it appears to be time for the mercifully rare retraction of a proposal, or at least taking a step backward for with it for the moment and recognizing it more clearly as a possibly rather than a likelihood.
Because I’m still very unfamiliar with the method of obtaining minimum and maximum by adding half a target figure to a pre-established mean (if the Lintels are centered, they share a mean value with the Lintels, so the experimental mean here for the Lintels is already pre-determined by the mean of the Sarsens), what I did not realize until shaken up by two different Nilometer figures resembling the Eclipse Year is that the very same method of adding halves to mean figures may allow it to be mathematically correct that the Lintel Width might be 1/100th of the Eclipse Year in days after all, and in terms of metrological pointers, more and more metrological pointers to the Best Eclipse Year Value seem to appear all the time.
Several weeks ago, the “Best Eclipse Year Value” was thought of as either a simple multiple of the ratio between standard Megalithic Yard and Megalithic Foot, or a simple fraction of the squared Hashimi Cubit times the Remen, and thus was its presence at Stonehenge justified in the “Bluestone Oval With Corners” according to my model. By now, at least four different metrological pointers to the “BEYV” in total have been found, and there may well be more.
While it’s something I’d very much like to do is put some of the Nilometer figures into the context of their immediately mathematical environments – in other words, I hope I can learn more about the measures of the buildings they are associated with, and how the Nilometer figures may fit in – for now I can only hope that the Nilometer measures might hold the key to a more definitive understanding of an an ancient “Eclipse Unit” – it might not be a Cubit, and it could be a Hunab, but the idea of an ancient “Eclipse Unit” of some kind that commemorates the value of the Eclipse Year, begins to make more sense with each passing hour.
Is There Hope for the Accounts of the Classic Authors?
Since this post has gone on much longer than I originally intended, I think I will save this item for a future post. This might give me the chance to see what’s at the end of that road before I point others down it with any sense of urgency. Many readers may already be able to guess just what might be at stake and anyone who’s been following the GHMB thread may already know, but I really don’t want to be getting anyone’s hopes up for nothing, particularly with something that might be of such importance.
Suffice it for now that Mercurial may have culled from Letronne’s possibly sometimes questionable text, something that could prove to be a literal Egyptological treasure.
After that, I may have to get back up on my soapbox because searching for Letronne’s first name seems to have landed me on a Wikipedia-like page concerning “pseudoscience” – I beg your pardon?!? – and I’m sure I can find a few words to say about that. First, though, how about we go on that treasure hunt? It sounds like way more fun, and if this isn’t fun, why am I doing it?
–Luke Piwalker
Luke Piwalker 