Well, I don’t really know if it’s a cubit or not. Nobody actually put me in charge of ancient metric standards, and that’s not something I want to be in charge of anyway. Had I been recruited by some ancient agency in charge of metric standards, I presume my job would be try to keep the number of possible variations Cubits, Remens, and what-nots approved for actual use down to a minimum…
Which is the same thing one can accomplish just be being hesitant to “endorse” any values that don’t have some obvious and compelling standard such as the geometric origins of precise values for Cubits, Remens, and etc.
I know lots of possible Royal Cubit values, including that sqrt 3 is ostensibly similar enough to the consensus Royal Cubit value (1.732050808 and ~1.718+ respectively, or 1.718873358 if we apply a precise geometric standard).
However, I can tell the difference between these two numbers, and I’d like to at least give the benefit of a doubt to ancient mathematicians that they were able to do the same at at least as easily, and quite possibly more so for having actual careers in mathematics.
I’ve nominated a few possible Royal Cubits in my time – 1.722570927, 1.721325932, 1.712234567, 1.720116607 (and perhaps 1.731717175, which might be better off considered as an ancient version of sqrt 3), but I’m still not sure if any ancient persons considered them to be Cubits any more than I do, I’m still not sure that any register as the fundamental metrological unit of any ancient architecture, although 1.720116607 might have been used conditionally with Chephren’s pyramid and its subsidiary.
I often attempt to indulge the many who insist the Great Pyramid is “280 x 440” cubits, although it isn’t as far as I can tell. In my models, 438.9663491 Royal Cubits is the correct figure for the Great Pyramid after placing of final pavement, and 439.5926811 Royal Cubits, and keep in mind with that last figure I am being as conservative as I possibly can with consensus data.
I’ve also considered some larger values. The Meg Yard x a 2 Pi pyramid’s overt version of Phi is about 440 (literally, 2.72 x 1.618033989 = 440.105245 and my school of though might make of this 2.721074976 x 1.618829140 = 440.3498517, but given the fixed parameters of the model, this would produce Cubits of 1.713472874 and 1.715917826, which are several things I really don’t know enough about to have any business whatsoever going around calling them cubits.
I should note that the Megalithic Yard may be the true unit of the Great Pyramid’s baseline as it exists without the hypothetical missing pavement, rather than the Royal Cubit, and nothing odd about that since the Megalithic Yard would have been a very obvious unit to the ancient Egyptian through direct geometric relationship to some of their major units such as the Royal Cubit and the Remen.
Anyway, as with “Not A Remen” which could be a Remen for all I know (and I need to get back to Moyer’s “Happiness Interrupted” page about these matters), there’s a figure I’ve run into once too often and I don’t know what to do to help keep it from falling through the cracks but slap the dumbest name imaginable on it so it has a working title.
As a matter of fact, we just saw it – “Not A Cubit” is what I’m calling 1.715917826. It’s very hard for me to take it seriously as Royal Cubit or any metrological value, but as with all of my nominations for possible Royal Cubits, it’s something I have to take very seriously as a mathematical constant.
“Not A Cubit” 1.715917826 has a very interesting pedigree – it’s (1 / 1.618829140) / 360, so we would assume right there that it’s something important and useful, but it yet it may be something that defies general utility, making its true purpose something that remains to be seen.
I’ve found a use for “Not A Cubit” – linking the secondary figure for Earth’s equatorial circumference in miles to what I presume to be the (or one of the) intended value
24903.44232 / 1.715917826 = 145.1319051
Which may help to reinforce the idea of 1.715917826 being fairly secular in nature, and having specific but very limited functional value.
On the other hand, once we realize that 1.715917826 may generally reside near the bottom rather than the top of certain important series, that view could still quickly change.
1.715917826 x (360^1) = 1 / 1.618849140
1.715917826 x (360^2) = 5 / 224.8373808
1.715917826 x (360^3) = 8.005786209
1.715917826 x (360^4) = 2882.083035
1.715917826 x (360^5) = 10375.49893
That’s not a bad series! Those are all nice numbers.
1.715917826 may be a poor responder to 2 Pi (?) but 2 Pi is able to bring forth 168.0334823 from this “Not A Cubit”, which may be important.
As long as a Leap Year figure for these calendar systems hasn’t been figured out yet, it could be important that 2 Pi / 1.715917826 = 366.1705247
Who knows? Again it’s just a largely unexplored number that’s come up once too often and has thereby aroused curiosity.
This just a general advisory – be aware that “Not A Cubit” could be in your neighborhood, approach it with caution, don’t fire until you see the whites of its eyes, etc.
–Luke Piwalker
Luke Piwalker 