Jim Alison Wrote:
> Hi Stephen,
> Thanks for the kind words. I took another look at
> the Stecchini link and also the following one
> about the origin of the English foot, and as much
> as I like Stecchini, I remain troubled by his
> insistence that the primary Egyptian measures are
> exactly .3 m for the foot, .45 m for the cubit and
> .525 m for the royal cubit.
As well you probably should - any of us should probably be suspicious of data that looks too neatly rounded. The .525 m RC might be a slightly different case however.
(Personally I haven't gone near Stecchini much since I have seen him accused of virtually fabricating what were supposed to be quotes from classic Greek authors in regards to the Great Pyramid's content of geodetic data. If I have to go to the ends of the earth to get to the bottom of that, I probably never will, but I have been trying to round up my copies of the original Greek texts just in case).
> It makes me wonder if
> he was a little bit too metric. Also it makes me
> think his cubit is too long for early Egypt.
I almost want to say that maybe Stecchini was being too geometric, but that probably calls for some explanation too?
Well, to start with, if we look at what MC wrote
> Here is what Stecchini saw that
> made him think it was his modern meter of 39.39
> ins. that was being used.
If that's the figure Stecchini was using, I'm not sure it's a modern meter. We might usually see that kind of thing when someone is trying to make a meter out of the squared Radian
57.29577951^2 = (360 / (2 Pi))^2 = 3.282806350 x 1000; 3.282806350 x 12 = 39.39367620 inches
Likewise "his" (Lepsius'?) Cubit of 525 mm = 1.722440945 also seems rather resplendent of circular geometry
(1 / (360 / 2)) x (Pi^3) = 1.722570927 / 10
In spite of closely related geometric origins, 3.282806350 and 1.722570927 don't necessarily have the best relationship, and an RC of 1.718873385 of course also has geometric pedigree as (360^2) / 2 Pi =
20.62648062 x 100 and etc.
1.718873385 relates to a "meter" of 3.282806350, or at least to 1/1000 of the squared Radian of 3282.806350 in feet, via the elegantly simple and straightfoward (6 / Pi) rather than the more complicated relationship of 3.282806350 / 1.722570927 which is ((Radian^3) / (Pi^2) / 10^n.
It's things like that that make me wonder if that 525 mm rod couldn't have been a ceremonial one that pays due homage to a well pedigreed but possibly inferior Cubit of 1.722570927.
My model of the Great Pyramid can be very interesting to measure with a Cubit of 1.722570927, but in this model the GP appears to be designed on a Cubit of 1.718873385 with several important "checks" in place, so thus far 1.722570927 has achieved only very honorable mention.
On the other hand, it isn't necessarily easy to sort out 3.282806350 and its proper role in the scheme of things, which manages to end up making it possibly more difficult to sort out whether ~1.722570927 ft was too long to be an Egyptian cubit at any point.
Consider that one way of describing the relationship between Remen and Royal Cubit is as ~360 / (Royal Cubit^2) = Remen
With a Royal Cubit of 1.718873385, 360 / (1.718873385^2) = 1.218469680, which is sqrt 2 to a Cubit of
1.723176345, and to my reckoning at least, 1.218469680 may have actually been used in the Great Pyramid along with 1.216733603.
1.723176345 actually is 1.722570927 to greater accuracy than 22/7 is Pi, and 1.218469680 is 4 / 3.282806350...
(For those that like to look for interesting patterns, 1.218469680 is also .1234567901 x (Pi^2)).
So what does one decide to do with all this, and what did the ancients decide to do with all of it?
For whatever it's worth, I could never get 3.282806350 to be a good meter in practice, even after attempting to shave it down with the 1.000723277 ratio that's ubiquitous in my work. Certainly brings it closer to the contemporary meter, but it still may not make a good meter in actual practice, which is still an important test that any proposal has to face.
If that's what Stecchini did though was try to make a meter out of 3.282806350, I did the same thing myself for years.
BTW, I was reading the opening remarks of this thread again and reminded of an old problem I ran into with the Remen, which I hope you managed to get around in your paper, which goes something like
~Remen v x 27 = ~meter = ~4 / Remen w; Remen w x 300 = ~Solar (or calendar) year y; ~Solar (or calendar) year y x 360 = ~earth circumference in feet z / 10^n
Which may or may not be a good formula - it's gotten harder for me to tell lately ever since realizing that if I fine tune Michell's long values ever so slightly, most of his geodetic functions for them work quite well, except the resulting figure is a mean circumference value in his realm, in contrast to where the same value lands in my own models, and worse I was mainly relying on the authority of my Great Pyramid model to tell me it's "okay" to model the various circumference figures in feet for the earth using something other than the obvious ratios between the same figures in miles.
That may not be as well sorted out as I'd hoped it was so I hope that formula doesn't end up getting the better of any of us, speaking of Remens in geodetic roles. Maybe someone will figure out how to work that one if you haven't already in the course of writing your paper, or maybe DK will tell us to throw it out and rightfully so?
Apparently I'm still rather disoriented from finally getting it through my head that Michell's long unit values may relate to a mean geodetic value, lol.
Edited 1 time(s). Last edit at 21-Dec-19 16:02 by thinkitover.