For a long time now, I’ve been familiar with a figure of 2.718208958, which I’ve thought of as a mathematical constant rather than a metrological unit although it is indeed close to Alexander Thom’s Megalithic Yard of about 2.72 feet – so close that it may be up to mathematics and not measurement to sort them out.
One reason I hesitate to call this figure a Megalithic Yard is because we already have some very nice and very functional values. Why try to fix what isn’t broken by adding another one?
Another reason is that I don’t know if anyone, starting with me, wants to learn a dozen different Megalithic Yard values, in order to try to understand what the ancient were up to with their monument design.
Yet this figure has certain earmarks of being a bona-fide metrological unit in its own right, and it’s recently displayed several important mathematical properties that further round out its set of qualifications.
For history’s sake I’d like to point out a similar number, Michael Morton’s “Ideal e” value of 2.718263095, proposed to be how Munck’s numbers might best represent the logarithmic constant e = 2.718281828.
https://en.wikipedia.org/wiki/Natural_logarithm
We can see how similar Morton’s figure is to the figure in question here, 2.718208958.
Richard Hoagland proposed that Munck’s Megalithic Yard of 2.719725671 ft, represented an ideal average between e = 2.718281828 and what Hoagland and Torun called e’ ((sqrt 3 / 2) x Pi) = 2.720699046, which is also Hugh Franklin’s value for the Megalithic Yard.
Some of the possible pointers toward 2.718208958 as a bona-fide metrological unit
- 3.2 / 1.177245771 = 2.718208958 – this potential Megalithic Yard then can be constructed out of Megalithic Feet, using my customary value of 1.177245771 (Munck’s “Alternate Pi”) to approximate the Harris-Stockdale Megalithic Foot value in feet.
- 2.718208958 ft x sqrt 3 = 4.708076021 ft = 4 x 1.177019005, very close to 4 x 1.177245771 = 4.708983084 ft
- 2.718208958 ft / sqrt 5 = 1.215620001, very close to the short Remen I work with, 1.215854204
A little further background on Megalithic Yards for those who might be just tuning in…
Munck’s Megalithic Yard of 2.719715671 has the curious mathematical property that it does not belong to its own set of numbers until it is squared (at which point it becomes a very powerful and very useful mathematical constant).
That’s why 2.720174976 was “invented”, because I wanted a way to work with a Megalithic Yard value that does belong to the set of numbers without having to be squared first, and I called 2.720174976 the “Alternate e’ Megalithic Yard” (AEMY) – my own functional version of Hoagland and Torun’s e’ value ((sqrt 3 / 2) x Pi) = 2.720699046.
Since 2.720174976 isn’t quite the square root of the Squared Munck Megalithic Yard (2.719715671^2) = 7.396853331, it takes another false square root of 7.396853331 to go along with 2.720174976, which is 7.396853331 / 2.720174976 = 2.719256444, the “Incidental” Megalithic Yard (IMY), to generate 7.396853331 from 2.720174976.
This is one of the earliest false square root pairs from these numbers to be recognized. The system of numbers can use false square root pairs to circumvent numbers that don’t belong to the system.
The past year or so, the resemblance between the Megalithic Yard and another important mathematical constant, namely 1/10 of the the lunar Draconic Month of 27.212220, became more haunting than ever. I’ve known for a long time that Munck’s numbers can generate a strikingly similar figure
Generic Area of a Circle 10313.24031 (square arc-degrees) / ((16 x 1.216733603)^2) = 27.1223218
What I did not know until more recently is how well that 27.1223218 can actually work if we use it to replace AEMY 2.720174976 or IMY 2.719256444 in some of Stonehenge’s stunning equations.
Thus 2.71223218 has become the “DMY” – Draconic Megalithic Yard – although any Megalithic Yard in this general range might have represented 1/10th of the Draconic Month.
IF there is a general rule in effect that all valid Megalithic Yard values should be part of a false square root pair that multiplies to form (2.719715671^2) = 7.396853331, then the counterpart to the Draconic Megalithic Yard would be
- 7.396853331 / 2.71223218 = 2.718208958
Thus 2.718208958 would belong to a pair with another version of the Megalithic Yard that has already been “approved” by me because of how accurately it represents the Draconic Month, and because Stonehenge seems to recognize and accept it. I’m still of the belief that a designer of ancient architecture has to choose their numbers VERY carefully for that to happen.
This must seem almost insanely complex, but it’s exactly how someone who knew their numbers might opt to try to navigate between members of a cluster of important numbers right in this range including e, e’, and the Draconic Month, and how they might have to do so.
Probably the loudest and proudest vote of confidence for 2.718208958 as a bona-fide ancient metrological unit comes from paying a bit of attention to the work of Geoff Bath – both his observance of dimeteral vs circumferential units, and of the Pied du Roi or Hashimi Cubit (currently under further investigation as probably being the same unit as the Egyptian Royal Foot) – because
- 2.718208958 ft is the diametral unit to a circumferential unit of the ideal Pied du Roi value of 1.067438159 ft – that is, a regular circle with a diameter of 2.718208958 feet, will have a circumference of: diameter 2.718208958 x (2 Pi) = circumference 17.0790159 ft = 1.067438159 x 16 ft
- 2.718208958 may also be able to reconcile the work of Alexander Thom with the work of Flinders Petrie when it comes to Stonehenge.
Petrie suspected the inner diameter of the Stonehenge Sarcen Circle to be in Roman Feet, which seem to be derivatives of the Egyptian Remen (1 Roman Foot = .8 Remens).
Using 1.216733603 as the Remen to very slightly refine the values obtained independently by WMF Petrie and RJC Atkinson, 80 x 1.216733603 = 97.33868824 ft
Petrie (1877) 97.308 ft. – Atkinson (1956) 97.333 ft. – Mean 97.319 ft.
https://www.academia.edu/6478703/The_Acropolis_Width_and_Ancient_Geodesy
Professor Thom seems to have preferred to believe that the sarcen circle had an outer circumference of 48 Megalithic Rods = 120 Megalithic Yards of about 2.72, and an inner circumference of 45 Megalithic Rods = 112.5 Megalithic Yards of about 2.72.
112.5 x 2.72 = 306 ft circumference, circumference 306 / Pi = 97.40282617 ft.
BOTH Petrie and Thom may be correct if the inner circumference is 45 Megalithic Rods based on a Megalithic Yard of – you guessed it, 2.718208958.
2.718208958 x 112.5 = 305.7985078 = 97.33868824 ft x Pi.
Using the standard AEMY Megalithic Yard, 305.7985078 / 2.720174976 = 112.4186901 = 224.8373808 / 2. 224.8373808 is my best and most useful approximation of both Petrie’s neglected Stonehenge Unit in inches, and the Venus Orbital Period of about 224.701 days. 225 (2 x 112.5) is probably the second best value for the Venus Orbital Period.
This may then be another example of the proportions of Stonehenge being very carefully chosen to work with multiple version of the Megalithic Yard.
The strange part is that 2.718208958 is still not the most useful of numbers as far as I can tell. It will likely continue to do what it has done for years now, which is be overshadowed by more useful and more versatile versions of the Megalithic Yard like AEMY 2.720174976 and IMY 2.719256444…
Yet 2.718208958 still seems to have an important place in the scheme of things, and its own reasons for being. Even if it lacks what Michael Morton and I used to call resonance, it has credentials.
–Luke Piwalker
Luke Piwalker 