I’n a little hesitant to broach this subject for fear of ruffling a few feathers again, but I think it might be appropriate because it may touch on one of the more controversial features of Stonehenge.
William Stukeley proposed a unit of measurement in use at Stonehenge of purportedly of about “530 mm” or “52.83 cm” = ~20.8 inch. I am speaking in vague terms instead of historical ones because I may not have an appropriate reference work immediately at hand adn thus am relying on Internet quotes for the purposes of discussion, although Wikipedia’s discussion of “Cubits” makes reference to a discussion of the “Druid’s Cubit” by Burl.
Burl, Aubrey (2004). “A. D. Passmore and the Stone Circles of North Wiltshire”. Wiltshire Archaeological and Natural History Magazine. 97: 197 Retrieved 9 April 2020.
Often enough, someone may come to the realization that 25 / 12 = 2.083333333 and assign this value in feet to a “Druid’s Cubit”.
I have a few struggles with this, not the least of which is not having presently at hand Stukeley’s measurements which inspired this observation. Offhand I would trust Stukeley even less than I trust Burl to provide accurate measures of a Megalithic Monument.
It’s true that if we keep throwing the major metrological key 12 at it, 2.083333333 will produce some important values in Imperial Feet, but if one is going to embrace ancient use of Imperial Units, it may not be a good place to start.
The next thing that may happen is that someone may try to divide it by 12 and declare that yet another Egyptian Royal Cubit has come forth this way.
Thus although to the best of my knowledge, researcher David Kenworthy has championed a Druidic Cubit of 2.083333333 ft, for more than one reason this would have to be another point of departure between David’s work and mine.
There’s rather a deep divide here – I hope none will be insulted by this since there are few if any metrological researchers whose work I don’t admire, and I’m sure all hard work in the field must pay off with some findings of genuine merit, but there are a lot of people whose work I look at just sort of scratch my head, or roll my eyes, but my general complaint is that it seems to be taking them umpteen version of the Pi ratio AND of the Royal Cubit for them to patch together their mathematical systems, and yet what results still seems to be just as tangled and complex as my own system of numbers for anyone who isn’t the author of it.
If there is any island of calm in the storm of numbers that I’m aware of, it’s picking ONE value for Pi, and doing your best to pick ONE – or at least one primary – version of the Royal Cubit.
From my perspective, these two are the closest thing to “sacred” possible, and they are not to be trifled with lightly – not just for the sake of keeping things from getting unnecessarily complicated, but because of some of the things these numbers represent.
In terms of astronomy, when it comes to the Royal Cubit, it is first and foremost the mathematical link between Solar Year and Lunar Year – quite possibly the first two calendars ever discovered by ancient humans, and that, along with both the geometry-oriented nature of both Pi and Morton’s Royal Cubit of 1.718873385 (54 / Pi / 10) ft, may be something else that is not to be trifled with lightly.
Another complain of mine about a putative Druidic Cubit with a value of 2.083333333 ft, is that this is none other than the reciprocal of 1 / 2.083333333 = 480 / 1000, and since 48 / 12 = 4, this is really the same thing as 12. There simply is no need to make a metrological unit commemorating something that is already a firmly established part of metrology.
For what it’s worth, this should establish once and for all that 2.083333333 ft is a value in Inverse Imperial Units, and there is virtually nothing in all the data I’ve collected to suggest that literal use of Imperial Units was any kind of frequent event at Stonehenge.
For many years I’ve been familiar with 2.083333333 = 480 / 1000, as well as another number that is similar. The reciprocal of Munck’s height for the Great Pyramid, 480.3471728 ft, is 1 / 480.3471728 = 2.081828596 / 10^n ft.
Thus the difference here is the customary difference between Imperial Units and the very similar (but not identical, and for good reason) Hashimi Cubit/Egyptian Royal Foot. We can equate the two if we like, but in doing so we may only serve to help obscure the possible origins of both of them.
A key question however when proposing any metrological unit value should probably be “How well does it work in situ?” – do we really get anything sensible if we measure Stonehenge with it? – but of course since the Hashimi Cubit has long since been an integral part of Stonehenge’s mathematics and metrology, that may be something of a rhetorical question – in theory, at least, a Druidic Foot 2.081828596 should work well at Stonehenge because a Hashimi Cubit of 1.067438159 ft works quite well at Stonehenge – but because of this, it may not tell us much that we don’t already know.
(By the way, an “Imperial Hashimi Cubit” of 1.066666666 ft is indeed embedded in my model Stonehenge, but we have to dig so deep for it that few could find it, which only goes to contraindicate the idea of this being a Hashimi Cubit of great importance). Most would have an easier time finding it dividing Thom’s outer 48 Megalithic Rods for the sarcen circle by the inner 45 Megalithic Rods, but that’s not necessarily where it’s hiding and there were demonstrably a great many things Thom did not know about ancient metrology, the same as with Petrie, including that it stands to reason for the Megalithic Yard (times 2.5 = Megalithic Rod) values used in the sarsen circle to be different for the exterior than for the interior, for very good reason.
The reason I being this up most of all is that I’ve noted that a number of researchers into ancient mathematics seem to honor John Neal’s interpretation of the Stonehenge sarsen circle having a mean value in Greek Feet. Neal’s figure of 101.376 ft here for 100 Greek Feet is very near to my own primary value for same, 101.3944669 ft Imperial.
The mean of the indicated figures is (104.27245 + 97.32096) / 2 = 100.796705 ft, rather than 101.376, but technically ~97.32096 should be the inner diameter of the Sarsen Circle rather than the Lintel Circle. Few would be happier than myself to see the Greek Foot of ~101.376 here since it is the Remen at the ratio 10/12, but that’s not what it appears to be.
DavidK and rodz seem to want to take this mean figure in the direction of ~100.8, while I take it in the direction of 100.6036766 based on the other established parameters of my model. My model also indicates that the outer Lintel Circle diameter should be 104.0913798 ft rather than 104.27245 ft.
I’m not suggesting that’s what it is (it’s actually an unusual approach to the Hashimi Cubit of Egyptian Royal Foot like that of the Megalithic Yard as used in the Great Pyramid’s base length), but for the record, 104.0913798 ft would be 50 Druidic Feet of 2.081828596 ft each.
What the Lintel Circle’s own width is may still be up for debate; perhaps too few have noticed how similar Neal’s figure of 347.57485 / 100 actually is to the 346.62 day Eclipse Year but 345.8499644 is also a significant figure in Hashimi Cubits / Egyptian Royal Feet – it’s in fact the base length of the Mycerinus Pyramid in the revised model.
I’d like to emphasize this in light of my recent post on “Exclusion” that not even throwing out as many whole numbers as has been done in this work has been enough to keep metrological confusion like the Sarsen/Lintel circle mean from trying to happen — too many whole number of unit figures in one unit still closely resemble whole number of units values in other units of measures.
Thus, from my perspective, the whole numbers you see omitted here…
Weren’t omitted simply to accommodate the true Pi ratio – perhaps above all else, they were omitted to accommodate the use of multiple metrologies.
–Luke Piwalker
Luke Piwalker 