The Folkton Drums
Something I have been working on the past several days besides ancient Greek architecture is the Folkton Drums.
Thanks once more to researcher Geoff Bath for putting another interesting subject on our radar. Geoff informed us that the Folkton Drums are the subject of a final chapter of his latest book, and I am delighted to think this may mean we can expect this latest work of his relatively soon.
I have been looking at the designs on these artifacts and it occurs to me that we may be seeing multiple graphic ways of representing the 2:1 rectangle and its internal geometry, the Vesica Piscis, which in the post before last, I have pointed out yet again serves to coordinate a number of ancient units of length measure.
Are those fish scales on the possibly Vesica Piscis-derived diamond in the detail at bottom left? These possible Vesica Piscis seem as if they may remarkably geared toward ichthyomorphic (having shapes characteristic of fish) expressions for something of their purported antiquity.
The Folkton Drums have been making the news the last several years because of the efforts of Mike Parker Pearson, Andrews Chamberlain and Anne Teather, who have proposed that the drums were used to measure out measuring cords in Long Feet, a unit that Pearson and Chamberlain have championed in spite of some remarkable implications.
One is that their proposed unit value of 1.056 ft = 1/5000th of a 5280 mile exactly. One wonders if Peason and Chamberlain are aware of this, and that because of it, their campaign for the Long Foot also represents something of a campaign suggesting that the 5280 mile and the Imperial Foot are older than Stonehenge.
I have no disagreement with that basic premise, but then again I’m on the further outskirts of “fringe research” whereas they are ordinarily very respectable orthodox archaeologists and academicians and I’m still rather surprised to find them dabbling in ancient metrologies that imply everything we think we know about the origins of the foot and the mile may be little more than sheer fabrication.
I am also tempted by all this to wonder if their eagerness to adopt such a heretical cause may imply that their generally dismissal of Thom’s Megalithic Yard may be somewhat in haste.
Meanwhile, back on “the fringe”, researchers such as Jim Wakefield and DavidK have known for some time that the Long Foot of 1.056 can be equated with the Indus Foot of 1.1, the European Rod, and etc (5280 / 1.1 = 4800).
I use a slightly different value for the Indus Foot, mainly 1.100874623 ft, which equates the Indus Foot to the Megalithic Foot rather than to Imperial, because this is one of the curious things that the design of Stonehenge seems to urge us to consider, along with no less than two additional Megalithic Yard values which are also based on the Megalithic Foot, as I’m sure I’ve written about before often when discussing Stonehenge.
I’ve personally never been comfortable with the idea of a mile of 5280 feet exactly being anything more than an Imperial-based reference unit reserved for unit conversions such as the number of miles in earth’s circumference; some may find the number appealing because it’s easily divisible by 11 as was just demonstrated, but it’s still not easily divisible by 7, 13, 17, 19, or a host of other while whole numbers popular with other researchers.
Either way, we may be able to push the origins of Imperial measures quite a ways back than usually given credit for.
At any rate, if I indulge Pearson and Chamberlain with the notion of the Long Foot and make the short side of 1/4 of 1:2 rectangle to be 1 Long Foot = 1.056 feet, the diagonal (sqrt 5 to the short side) looks like the Ubaid Cubit, rated by its academic proponents at about .72 cm.
As far as I’m concerned, the Ubaid Cubit is still only an experimental unit, and one for which I have yet to find any definitive or primary value, and one of the most promising examples of its possible use is the division of the Great Pyramid perimeter at the base into 1280 Ubaid Cubits, at the same time this base perimeter has already been reckoned by a growing number of sources including John Michell (in View Over Atlantis), Hugh Franklin, and myself as consisting of Inverse Megalithic Feet.
However, the subject has come up before as I tried desperately to plot the origins and nature of the problematic 5280 foot mile; at least once before it’s been lost in the shuffle, but since the Ubaid Cubit is rated at 72 cm, making it a value in Metric, and the Long Foot can be qualified as Imperial, this exercise highlights an apparent sqrt 5 relationship between Imperial and Metric that can be difficult to dismiss as sheer coincidence.
Perhaps it’s time to begin treating the subject more as if it isn’t coincidence.
“Out There”: The Outer Sarcen Circle Diameter Unit and the Egyptian Mystery Unit
I continue to struggle to try to give historical names to several by now well established metrological units or simple multiples or dividends thereof. These probably aren’t new ideas on my part either, but they do come to light again in the proceedings.
One, is that the Stonehenge “Outer Sarcen Circle Diameter” value and its kindred like the height of the Great Pyramid from the base and the standard value used herein to approximate the Jupeter Orbital Period, which has been proposed to possibly derive from an oversized Assyrian Cubit that comes with its own rules opposite the usual when it comes to conversion into Remens, was actually featured in Teti’s pyramidion, whatever the true identity of the unit is.
Teti’s pyramidion, based on the available data, is a particularly good example of the metrological focus that may often be seen in the reported measures of pyramidia (pyramid capstones), with the data clearly indicating a rectangular base of 1 Royal Cubit long and 1 Remen wide.
It has been proposed that in this pyramidion, the standard Royal Cubit has been substituted for by the cubit-like value of 1.731717175 ft as a bridge between the Hashimi Cubit and standard Assyrian Cubit (1.731717171 / Hashimi Cubit 1.067438159 = Assyrian Cubit 1.622311470 = 1.5 Remens) where the standard Royal Cubit is not able to fulfill this function, even while the standard Royal Cubit value can be found in the base length of the very same artifact.
To me, it comes as a relief that we are less obligated than ever to try to pass off 1.731717175 as some sort of Royal Cubit once we learn what it really is. It appears that when the designers of Teti’s pyramidion were assembling a phenomenal collection of ancient metrological unit values in a single artifact, they didn’t overlook the “Outer Sarsen Diameter” unit.
At Stonehenge we see the mystery unit as diameter 51.5151515 ft – (circumference 120 Megalithic Yards of 2.720174976) / Pi = diameter 51.95151515 feet (and we have some recent revelations about the role of numbers like this in geometry thanks to fellow researchers); at the Great Pyramid we see it as the height from the base of 481.0325483 ft
I’ve been trying to make it point lately to mention more often that 51.95151515 / 481.0325483 = 108 / 10^n (the same relationship as between Hashimi Cubit and Egyptian Royal Foot); thus they are cut from the same unit, whatever it actually is.
481.0325483 / 1.731717175 = (1 / 360) / 10^n and 51.95151515 / 1.731717175 = 30.
Thus the value 1.731717175 ft not only isn’t a form of the Royal Cubit as far as I’m concerned, but it doesn’t have to be a Royal Cubit, especially since it’s already busy being a value in “Outer Sarsen Diameter” or “Great Pyramid Height” units.
Curiously, the next item is somehow in a similar vein and concerns the seemingly perennial quest for the historical identity of the “Egyptian Mystery Unit” or “LSR” of 1.676727943 ft. Proposals have been made that it may it be related to the Indus Foot (Jim Wakefield) or that it is a form of Sacred Cubit, but it was the failure of this unit value to slot into the John Neal-like array of unit values I was working on that just about tanked that scheme, and it may be the general awkwardness of the whole array that will manage to keep it tanked.
Previously, I’ve been called upon to give some thought to the possibility of several other Royal Cubit values, but the frequency with which they are mentioned (hardly ever) should already tell us that these “alternate cubits” are probably about as useful as the proverbial “screen door in a submarine”, in spite of some interesting pedigree.
One is 1.715917826 = ((1 / 1.6188249140) / 360) x 10^n; the other is 1.717631062.
What 1.717631062 is, or one way of expressing it, is the Morton Cubit / the most important very fine ratio 1.000723277: 1.718873385 / 1.000723277 = 1.717631062 – but this may not be a good direction to go in because the affinity of 1.718873385 for 1.000723277 generally seems to be in the upward direction (and “as a rule” it seems to be generally one or the other but not both with units modified by 1.000723277), with 1.718873385 x 1.000723277 = 1.720196697, which is a way for us to approximate and represent 1.216733603 x sqrt 2 = 1.720721163.
Readers may recall that this is because the relationship between ideal Royal Cubit and ideal Remen is not really sqrt 2, such that the true diagonal to a pyramid in Morton Royal Cubits is actually in short Remens standardized to (12 / Pi^2) feet each, and not the long Remen of 1.216733603. It would not be worth sacrificing either 1.718873385 or 1.216733603 to make it work out otherwise, not at all.
This may prove to be a very reckless suggestion, but with both 1.618829140 and 1.622311470 x 1.000723277 = 1.623484851 (possible root unit of the “Outer Sarsen Diameter” value: 1.623484851 x 32 = 51.9515151) emerging as possible variants of the Assyrian Cubit of 1.622311470 ft that may come with their own rules about not trying to convert them to Remens as we would the the standard Assyrian Cubit, perhaps it’s possible that 1.676727943 qualifies as a variant derivative of the standard Royal Cubit (rather than a derivative of a variant Royal Cubit) that comes with its own unusual rules about not back converting it into Royal Cubits?
I apologize for that rather convoluted looking proposal but hopefully my metrology still isn’t half as strange or complicated as John Neal’s. The lack of historical identification of 1.676727943 really has gone on for far too long not to turn every stone possible in search of the answer.
For what it’s worth, the equivalent to 288 / 1.717631062 = 1.676727943 x 10^n using Morton’s Cubit would be 288 / 1.718873385 = 1.675516082. It’s curious that we don’t see this number once in a while – not because I am always turning it into 1.676727943, but rather it just doesn’t seem to fit anywhere while 1.676727943 fits in many places and has many important roles – because it’s really not more exotic than (Pi / 3) x 16 = 16.75516082.
Given that ornaments from Chichen Itza frequently show division of a circle into 16ths, and we can readily fathom the relationships between the number 16 and the Venus Orbital Period, I’m really somewhat surprised that I cannot seem to remember emerging from any proceedings there.
This is even more strange because where we would use 1.676717943 with Pi to generate the A version of the Calendar Round: Pi x 1.676727943 = (1 / 18983.99126) x 10^n, we could use 1.675516082 analogously to generate the B version of the Calendar Round: Pi x 1.675516082 = (1 / 18997.72195).
What is more – I was about to say that 1.675516082 with Pi^n probably generates an unwanted junk series, but the fact is that 1.675516082 with Pi^n generates a useful and familiar, if very modest, series which includes 51.9515151.
It may really be only semantics anyway, but one reason I’m still very hesitant to accept any of this is because even if there is some variance in the equations, there are so many pointers to 1.676727943 metrologically that I still would expect it to have a novel identity of its own, if it cannot achieve equivalency with any already established major unit.
The Stonehenge “Oval With Corners” Unit Still At Large
There is another metrological mystery still afoot, which is the fundamental metrological unit of the Stonehenge Bluestone “Oval With Corners”.
After years of thinking it was going to turn out to be probably (1 / 12) x 10^n = 138.8888888 or maybe 1.177245771^2 x 10^n = 138.59070605, the value settled on as the likely value of the Stonehenge Bluestone “Oval With Corners”, 138.6375741 ft, came as a last minute surprise.
It’s a number that may have some strange properties but by now it has hopefully been rather well tested. It’s important because it’s a simple multiple of the ideal Eclipse Year value, and it quickly accumulated pedigree when under study with multiple metrological pointers to it – readers might happen to recall that the ideal Eclipse Year value can also be fashioned from the Megalithic Yard and Megalithic Foot, therefore so can the “Oval With Corners Number” 138.6375741
(Megalithic Yard 2.720174976 / Megalithic Foot 1.177245771) x 15 = ideal Eclipse Year 346.59939339 / 10).
It’s still a tricky figure, though, because since it didn’t turn out to be 1.177245771^2, it’s ended up as the freakish contraption 1.177245771 x 1.177643424. The trick here is of course to not divide it by 1.177245771 if that’s going to generate nonsense, but to multiply it by 1.177245771, repeatedly, which generates a nice little series that goes at least as high as 138.6375741 x (1.177245771^6) = ideal (“Best”) Lunar Month / 8.
Perhaps it’s a bit odd because it has (1.067438159^2) x 1.216733603 in its pedigree – another combination of fundamental Stonehenge metrological units we can build it from, but the incorporation of a square like that is unusual.
(138.6375741 also has some other aliases related to important components of Stonehenge; for example (51.95151515 / 1.177245771) x Pi = 138.6375741).
Again though, the “Oval With Corners Numbers” does have some unusual mathematical properties; for instances it tries to trick us into thinking it’s 1/49 of the Nodal Cycle or ten times 1/495 of the Saros Cycle, both 49 and 495 being numbers we know do not actually belong to our vocabulary.
It’s simply a very novel number that has become associated with a very unusual Megalithic construct. It’s status as 4 x ideal Eclipse Year is reason enough to put up with it.
So even for as far as we’ve come, we may still have a slightly incomplete picture of ancient metrology, but I like to think it isn’t for lack of trying.
Maybe someday?
–Luke Piwalker
Luke Piwalker 