Member Ginkgo on the GMBH recently inquired whether the Gobekli Tepi site could be the legendary site of Babel and after a few days of looking at the thread sitting there, it dredged up a memory of hearing a version of the Tower of Babel story that had mankind being divided into 12 tongues and 12 tribes.
Since my very best advice to anyone wanting to explore possible relationships between ancient metrological units is to divide (or multiply) them by the number 12 (as in the 12 inches in a foot) in order to help sort through the Babel (read: confusion) of ancient metrology, the story of Babel began to remind me of metrology, which naturally caught my attention.
According to Wikipedia, the number 72 is seemingly a lot more common as to the number of different languages involved, but same difference, 72 is a simple multiple of 12 (12 x 6 = 72), a number of which seem perfectly effective for examining metrological relationships, probably for being made out of the number 12.
That includes 36 or 360 (12 x 3 = 36), and 24/25 = .96 (12 x 8 = 96), and so forth.
So my hypothesis hasn’t sunk, but while visiting Wikipedia, I might have found something even more interesting.
I ran into a lot of interesting numbers in the Wikipedia article with interesting relationships to each other, that make me think the story of the Tower of Babel could be largely a vehicle for ancient number puzzles much more than having any aspirations toward being accurate history keeping.
I’ve attempted to solve what looks like a similar one in a terribly gruesome but probably rather ludicrous “historical” anecdote featured in Robert Shoch’s book, Voyages of the Pyramid Builders (pgs 106-107), but in the case of the Tower of Babel story I think some later sources might perhaps have been making their own interesting contributions to the number puzzles?
Some interesting stuff in The Book of Jubilees it looks like, and in later works as well. The question may remain for now just how late various authors might have still been making interesting contributions to the story’s math puzzles? Even as late as Giovanni Villani’s account dated 1300 AD?
I don’t know if I want to jump right into A.R. George’s discussion of metrological concerns, but apparently attempts have been made to identify the Tower of Babel with the Etemenanki
https://en.wikipedia.org/wiki/Etemenanki
And a suspiciously round figure of “91” meters appears concerning it in both Wikipedia and George’s text. In spite of the blunted looking figure in meters, perhaps this value may be recognizably linked to well known ancient metrologies via squares or rectangles.
Something that looks very much like it has already appeared in my tables of metrological experiments
91 m = 298.556 ft
in cubits, remens, and Meg Yards, and Palestine cubits approximately:
298.556 / 1.72 = 1.735790698 (sqrt 3 = 1.732050808)
298.556 / 1.2167 = 245.3817704 (not 2.452595355 = x / 2^n, is it??? keep looking?)
298.556 / 2.72 = 109.7632353 = ~109.6622711 = ~4 / Earth Year
298.556 / 2.107 = 141.6971998 ((sqrt 2) x 10^n = 141.4213562)
I’m not certain of the specifics, but 298.556, whatever it is, resembles a potential metrological unit that is related to the main Egyptian units. We can spot that back where the mystery figure is divided by 1.72 to get ~sqrt 3. That may not be implausible in spite of the implausibly round meter value?
Anyway, if I take some of the numbers that come from different sources and examine their relationships, however randomly (and I’m sure others can see even more in here than I do),
5433 / 72 = about sidelength Cheops pyramid (Munck)
2354 / 2 = 1177 see 1177.245771?
2354 / 700 = 168.1325571 x 2 = ~1 / 2.98 (= 1/2.973661852)
700 / 107 = ~2 / inner circumference Stonehenge sarcen circle (Munck)
2354 / 107 = 22 = ?? (1 / 4523.893421) = 22.1048532 / (10^n)
2354 / 1656 = 1.421497585 = ~ 452.3893421 x Pi
30/13 = ~base Great Pyramid in meters???
13 stades of (1.216733603 x 500) = 7908.76842 ft (7912.668258 mi = “polar radius”)
30 stades of (1.216733603 x 500) = 18251.00405 ft = (365.0200808 / 2) x 10^n
70 / 72 = .9722222222 see inner diameter Sarcen circle (Munck) .9733868822 x 100 ft
1656 = ~5 / 3018.110298 (3018.110298 = perimeter Great Pyramid, (Munck)
1656 x 365 = 604440 (18980 / 604440 = 3.140096618 = ~Pi); perimeter Great Pyramid unpaved 3022.41664 ft — 3022.41664 x 2 = 6044.83328
1645 x 365.25 = 6048054 = 168.015 x 360
5433 / 1656 = 3280.797101 / 10^n; my usual meter – feet converter uses 3.28084 ft for the meter.
107 / 43 = 24883.72099 / 10^n
Notes:
Venus Orbital Period 224.701 / Saturn Synodic Period 378.09 = 1.682636036
Some candidates:
377.8020786 / 224.8373803 = 1.680334818
378.4528198 / 224.8373803 = 1.683229093
377.8020786 = 1/2 Base Great Pyramid, unpaved
(The length of a stade can be variable so I am just using my usual one to see what happens here).
I’m rather surprised at the amount of lip service that might be paid to the Great Pyramid’s proportions therein, although I probably shouldn’t be.
What we may have in such number puzzles from ancient myth and folklore may be similar to what we may have in cases like ancient America’s “pecked crosses” – blunt numbers that are selected and grouped very carefully so that their ratios can closely approximate import numbers with surprising precision.
https://en.wikipedia.org/wiki/Teotihuacan
The same may also be true of certain ratios between between numbers of parts of ancient monuments. Munck may have been the first two use approximations with his own style of math in the way he interpreted the physical parts of the El Castillo pyramid at Chichen Itza (this formula was still found on the Internet when last I checked a few months ago):
https://old.world-mysteries.com/chichen_kukulcan.htm
You’ll note that he uses the formula
“9 terraces x 365 steps x 4 sides x 4 stairways = 52,560”
To approximate the valid value 52562.8916
I like to take similar liberties with El Castillo’s 91 steps per side, for 91.18906528 x 4 = 364.7562611, an approximation of the 365-day calendar year that we can also make from 3600 / (Pi^2)…
Even though we can also use 91 as-as for 9 terraces x 91 steps per side = 819, a significant if sometimes strange Mayan calendar number
In the past I’ve worked extensively with the idea of ancient myth as a vehicle for both folk wisdom and the sciences; perhaps in the further I will be working more with the idea of myth as a vehicle for mathematics.
BTW, yes you read that right back there. I’m still not done ruling out that part of the multifunctionality of the Great Pyramid’s base length could have been as a tribute to the length of Saturns’s Synodic Period. Something to keep an eye on.
–Luke Piwalker
Luke Piwalker 