In my more recent posts to various places (here and GHMB), I’ve been emphasizing both the difference between geodetic modelling and geodetic measurement, and of course between various values for earth circumference – polar, equatorial, and mean.
I may end up eating these words, but I’m skeptical that units of measurement are going to be found that can fulfill these functions without there being one variation on a unit for each function (and some of the ones required might be so different from each other as to generate uncertainty that they are the same unit).
In fact, I’m still new enough at this that I probably shouldn’t be attempting to lecture on the subject, but a few of these units I’ve been working with for a long time. It turns out that apparently I’m rather geared toward equatorial circumference – and why not? (24 x 1.216733603)^3 = 24901.19742 / 10^n rather amazing), but because of that focus there’s probably still a lot I don’t know, and some that I can still barely guess.
For a long time, I’ve worked with a value called the Pole aka the Rod, after being introduced to by Henry Lincoln’s “Key to the Sacred Pattern” – perhaps a number of people know that story now. Lincoln gave the unit as 198 inches, which I identified with 198.1574328, which turns out 24901.19742 / (4 / Pi).
As I said, I seemed to be somewhat geared toward toward the equatorial, but as I see it the Great Pyramid and other ancient architecture are also.
Some time awhile back I noticed that 198.1574328 / 1.5 = 132.1049552, which is near to the “132” inches in of the Indus Feet that Jim Wakefield had been writing about.
Others likely noticed some of the relevant things before I did, including the relationships between Indus Feet and other units (including a slightly oversized mile that I still don’t know to do with).
I think for me the light started to go on about here
http://grahamhancock.com/phorum/read.php?1,1121946,1124175#msg-1124175
Here’s where the light finally started to get brighter,
http://grahamhancock.com/phorum/read.php?1,1198957,1211562#msg-1211562
That was when I started heading back toward the question of what “Pi Jedi” are supposed to do about the fact that 33 is not as far as we know, in their number system, which takes us back to a figure introduced by Munck, 660524.7768 which he took to be a “grid coordinate” of Cahokia’s “Rattlesnake Mound”.
We can “shave” it down with the fine ratio 1.000723277 — 6.605247768 / 1.000723277 = 6.600473789, which brings us “Pi Jedi” closer to having 33, 66, 99, etc of our very own, but frankly 6.605247768 is generally a much more interesting number.
16.51311941 x 40 = 660.5247768 ft; 660.5247768 / 3 = 220.1748256 = (2.7201749764 x 1.618849140) / 2 = 1.100874628 x 2, 1.100874628 being the Indus Foot I work with, in feet = 1/5 Radius Silbury Hill
220.1748256 x 3 x 8 = 660.5247768 x 8 = 5284.195814 = 24901.19742 / (15 Pi or height Chephren Pyramid / 10); 5284.195814 x 24901.19742 = 131582803.2, almost the 131594725.4 ft figure I use for the Earth’s equatorial circumference in feet, recycled from Munck’s Cholula Pyramid “Grid Point”.
I should not here that I no longer have a lot of confidence in the value of 131594725.4 ft for the equatorial circumference – revisiting John Michell’s work has thrown my geodetic work in feet into something of a state of limbo, because my polar circumference in feet is essential Michell’s mean circumference in feet, and that still hasn’t gotten sorted out yet.
We can however likewise “shave” 198.1574328 and 132.1049552 down a little lower with the 1.000723277 fine ratio. Not only may this be a useful thing to do for some applications, but it’s hardly without precedent in my work.
A number of candidate values for metrological units are separated by a 1.000723277 ratio, which also helps to reinforce the idea of these metrological units having originated with the mathematics of calendars, given that 1.000723277 is also the ratio between the two main sets of calendar numbers I work with.
I’d begun exploring the question here but didn’t follow through well on it
http://grahamhancock.com/phorum/read.php?1,1198957,1212517#msg-1212517
At this hour, I still don’t know who I have to thank for this one, but David Kenworthy posted this
http://grahamhancock.com/phorum/read.php?1,1216169,1217085#msg-1217085
> Let’s sort out once and for all what the Royal
> cubit actually is
>
> The Royal cubit x 9.6 is the English Rod in feet
>
> 20.625 x 9.6 = 198 / 12 = 16.5
And there’s no getting around this being a major metrological missing link that’s been biting me on the nose for years. 96 is a multiple of 12, which makes into highly substantial metrological connective tissue, so to speak, being that one of the very first things I discovered when looking at Berriman’s work is that the number 12 is even better at relating ancient metrological units to each other than Berriman’s remarkable Remen fractions.
This means that for purposes of geodetic modelling, we can use the Royal Cubit according a formula that is essentially:
Royal Cubit in inches x 96 = Pole/Rod; (Pole/Rod x 4 Pi) / 12 = earth circumference in miles / 10^n
This gives us for equatorial, mean, and polar respectively
24901.19742 / (4 Pi) / 96 / 12 = 1.720116605
24883.20000 / (4 Pi) / 96 / 12 = 1.718873358
24858.38047 / (4 Pi) / 96 / 12 = 1.717158910
The first two are very familiar, but I’m a bit amazed by that last one. I’ve spent years trying to avoid claiming it was a cubit, even while suggesting it may help accommodate the persistent notion that the Great Pyramid is supposed to be “440” cubits wide, which as a literal mathematical statement is rather absurd from my perspective, and if you’ve read any of my recent remarks about mathematics that incorporates numbers like 7 and 11 (11 x 40 = 440) may exclude the true Pi ratio, you can probably see why I think it’s absurd, it’s sort of my job to think that.
However, now suddenly faced with a very strong raison d’etre for a 1.717158910 ft cubit, which I know almost nothing about yet, I get to go back and see just how close “440” might actually be to the truth even if 440 per se isn’t and cannot be the truth in the system I work with.
Almost any fact I can come up with about 1.717158910 is going to be newsworthy.
An interesting thing, I hope, I think my chances of making the same discovery were dampened by the fact that to make the equation above more condensed,
circumference in miles / (4 Pi x 96 x 12) = Royal Cubit in feet
4 Pi x 96 x 12 = 14476.45895, and I’d already developed something of an infatuation with the wonder number 14486.92944 (14476.45895 x 1.000723277).
14486.92944 / (360^2) = 1.117818628 – there’s that number I just talked about that may be in both King and Queen’s chambers.
I’m probably going to be disappointed by some of the properties of 14476.45895, and yet as it turns out, it’s able to perform a vital geodetic service.
We could swap the two in the geodetic equation, but I’m not sure it would be quite the same, and 14476.45895 accommodates 1.720116605 while 14486.92944 doesn’t, and gives us instead the 1.715917823 that I just wrote a post about, insisting that it didn’t seem to be a cubit as far as I could tell.
I hope we’ll be hearing more about 1.717158910 soon, although I still haven’t even gotten back to that recent observation of a geodetic Remen that Stonehenge tried to teach me.
At any rate, while it doesn’t give me the answer I prefer, which would be 2.720174976 x 1.61882914 = 440.3498516, it may give me the next best thing, which is 440.3498516 / 1.000723277 = 440.0315868, which is 400 of my shorter experimental Indus Foot, and 440.0315868 is what I get if I measure my model of the Great Pyramid with a Royal Cubit of 1.717158910 ft
Alright, I should wind this up for now, but before I do, let’s turn on our resonance detectors and launch a couple of standard mathematical probes. 1.717158910 is still a strange number and we all deserve more reassurance that it deserves a place among established cubits.
Maybe it would be better to try to look at its parentage from the Great Pyramid equation first.
(440.0315868 / 4) / (1.622311470^3) = 1 / 388.13114682
Perhaps we’re not that far from the beaten path?
(440.0315868 / 4) / (1.622311470^4) = 1.588133130, which is still trying very hard to be designated as the major/minor axis ratio of one of Stonehenge’s ellipses. It’s half of 1.588133130 x 2 = 3.176266264 which I seemed to have found used at Tikal very early on in my studies of the data, and later as might be predicted, in the architecture of several of the sites that surround Tikal.
(440.0315868 / 4) / (1.622311470^5) = 1 / 1.021521079 – it’s my lucky day, that’s one of my favorite numbers found at Tikal, and later found prominently featured in the Great Pyramid (base perimeter of pyramidion in Royal Cubits)
(440.0315868 / 4) / (1.622311470^6) = 1 / 1.657225362
I might be getting a little bit out on a limb here now, but 1.657225362 / 8 = 20.71531703 = 1.726276419 x 12.
1.726276419 would be another geodetic modelling cubit if someone wanted the polar circumference to be 144 x (10^n) units, although I probably like the new proposal better
1.726276419 x 144 = 24858.38047 / (10^n)
It find this new “polar cubit” idea, strangeness and all, somehow even more plausible after just looking at more European measurements in the preceding post and finding the Royal Cubit seemingly alive and well in Europe until quite late in some of only the thinnest of disguises.
It’s almost ironic after saying so much about how I think the modern foot is a surviving unit used by ancient Egyptians, seeing some of the ancient units that seem to still survive in certain circles.
On the other hand, maybe the sheer strangeness of 1.717158910 really is too much to accept. It would mean a loss of accuracy on polar circumference in miles of about 5 miles – less that half as accurate according to error size than the current and well-tested 24858.38047 for ~24860 miles – but maybe 1.717631062 should be given more consideration as a potential “polar cubit” before making what may be a hasty decision.
On top of this lingering confusion, I guess I might still be in search of a true geodetic cubit. Maybe I should check back with Jim Alison about that, who’s done literally inspirational geodetic work with the Remen.
http://home.hiwaay.net/~jalison/blu5.PDF
I should probably check back with a lot of things soon, lol 🙂
–Luke Piwalker
Luke Piwalker 