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58. Reflections on David Genevier's Paper: Ragisma, and the numbers 6 and 7

Updated: Feb 23


The Great Mosque of Kairouan, in Tunisia, photo by Rubén Ramos Blanco, Wikimedia Commons

According to David Genevier the dimensions of the Great Mosque of Kairouan, as it is now, are 76 x 126 metres. 76 metres are just slightly over 12² x 16 Persian / Assyrian feet of 0.329142857 metres, or, with a conversion rate of 39.375, 12.96 inches, which is 6⁴ / 100 inches. Curiously, the Persian / Assyrian foot itself is 12 ² x 16 / 7 metres. A foot of 12.96 inches is exactly the Roman foot x 10/9, with a value of 11.664 inches. The width of the Kairouan rectangle could be understood as 12² x 16 x 2304 / 70 000 metres, or 12² x 16 x 12² x 16 / 70 000 metres, or simply 6⁴ x 4⁶ / 70 000 metres. When taken as 9072 inches, the base side of the Great Pyramid can be interpreted as 700 Persian / Assyrian feet.

However, it is the earliest Mosque at Kairouan which David Genevier analyses more deeply. The width he gives as 20 Q = 76.8 m, and the length as 27 Q = 103.68 m, the Q standing for qasab, Q = 12 Arab foot (AF) = 3.84 m

And these dimensions of the first Mosque are the dimensions of the first Dura Europos Synagogue x 14/3.


The first Mosque's width becomes the Great Pyramid base side x 12² x 16 / 7 000, to within 99.78 %.

Since the first Mosque's ratio between width and length is approximately 19 x 31.5, it might make sense to interpret the dimensions accordingly. The width of 76 metres is 19 x 4, and the length, of 126 metres, is 31.5 x 4, which might suggest a unit of 40 centimetres in use, or perhaps the shusi of 0.01666667 metres, which works out as 0.65625 inches. A 40 centimetre unit is interesting in that the Egyptian royal cubit of 0.523809 metres or 20.625 inches is 20 cm multiplied by Phi², approximated to 55/21, and the 0.52363636 metre Egyptian royal cubit is 20 cm multiplied by Phi² approximated to 144/55, and since Phi is an important number in ancient metrology, it follows that 20 cm must be an important base unit.


Indeed, the shusi can be understood as one 60th part of a metre, and a 20 cm unit is equivalent to 12 shusi. So the first Mosque's dimensions can be interpreted as 24 x 19 shusi and 24 x 31.5 shusi.


The dimensions of the synagogue of Dura-Europos seem to indicate similar measures. The dimensions are 103.68 x 76.80 metres, which can be interpreted as 40 centimetres multiplied by 259.2 for the length and multiplied by 192 for the width. 259.2 is 6⁴ /10 and 198 is 6 x 32. 76.80 metres are 100 varas of Aragon. The vara of Aragon, of 0.768 metres 30.24 inches, is connected to Phi squared, or at least with two approximations of it, in that it is 144/55 x 55/21 x 7 x 16 / 1000 metres.


Mauss defines the 0.768 metre vara of Aragon as 7/6 of the royal Assyrian cubit of 0.658285 metres, as 7/5 of the cubit of Amman of 0.548571 metres, as 3 feet of 0.256 metres, or 3 "petits djarib linéaires", as 6/5 of the cubit of Zyad of 0.64 metres (sometimes simply referred to as the Persian cubit, for example by Queipo), as 4/3 of the "coudée de l'arroseur", the waterer's cubit, of 0.576 metres, and as 8/5 of the hand cubit, "coudee de la main", of 0.48 metres. This Aragonese vara is therefore part of a system which has roots in the Persian and Assyrian empires.


The numbers that stand out are the many multiples of 6, and 4, and the number 7. Curiously the pattern of dividing a unit into either 6 or 7 parts, as occurs with the Persian and Egyptian royal cubits, is repeated here, albeit on a bigger scale: the royal Assyrian cubit is 4.608 / 7 metres. The Aragonese vara is simply 4.608 / 6 metres. A length of 4.608 metres is 12² x 32 metres, which suggests a duodecimal metric system. The vara of Aragon x 5/6 is the cubit of Zyad, and the same vara x 3 / 4 is the coudée de l'arroseur, and multiplied by 10/16 is the coudée de la main.

192 metres is length which lends itself well to the vara of Aragon, given by Mauss as 4 x 0.192 = 0.768 metres, being made up of 4 feet of 0.192 m. 1 qabdah of 0.288 metres is 3/2 of one of these feet, and the coudée de la main juste is given 1.728 metres by Mauss, which is 12³ / 100 metres, and 90 feet of 0.192 m, made up of 6 qabdah, or 24 digits of 0.072 metres. Joh Neal refers to a unit of 0.72 metres (so ten such digits) in his paper The Murder of Hippasus, which he terms the Ubaid cubit, and which he links to a "temple of Mesopotamian Uruk".

A digit of 0.072 metres suggests a connection to the Megalithic inch: if taken as 2.7216 feet, with a 39.375 inch conversion rate to metres, a Megalithic Yard works out as 0.82944 metres. There being 40 Megalithic inches in such a yard, the Megalithic inch is therefore equal to 0.020736 metres, so just over 2 cm, but importantly, a multiple of 12. One Megalithic inch is 12⁴/1 000 000 metres, and also 2 x 12² x 1 000 digits of 0.072 inches, and 9 x 3 / 1 000 varas of Aragon, of 0.768. The nameless unit of 4.608 metres, a seventh part of which is the royal Assyrian cubit, and a sixth part of which is the Aragonese vara, is itself 64 of these digits of 0.072 metres. It is also present as a 50th division of one base side of the Great Pyramid, if it is taken to be 9072 inches or 230.4 metres. 230.4 / 50 = 4.608. And because of the pi link between base side and height at the Great Pyramid, the height can be interpreted as 4.608 x 100 / π metres, which multiplied by √3 gives 10 000 inches, to within 3.3 inches. So that, hypothetically, we could consider this 4.608 metre unit as 100 π /√3 inches. This 4.608 metre unit then multiplied by √2 / 100π gives the Meglithic inch, if you accept a Megalithic Yard of 2.722557 feet.


A Roman / Egyptian digit of 0.0185185 m or 0.729166666 inches multiplied by 12³ and 0.054 would make up one coudée de la main juste of 1.728 metres. This 1.728 metre unit divided by 5.4 gives an Arab foot of 0.32 metres, and as David Genevier points out, the Arab foot goes in 720 times into the base side of the Great Pyramid. The ghalva is the unit that corresponds to the base side of the Great Pyramid.



David Kenworthy has found that the waterer's cubit, of 0.576 metres, being 0.576 x 39.375 = 22.68 inches, has a 0.9702 ratio to the 25 inch cubit.

This is his table of ratios:


David Kenworthy exlplains as follows:

"The Egyptian Royal cubit according to berriman is 20.625 imperial inches and this is 22/42 of the Egyptian meter, It has 54 digits and 60 shusi in it. It is most certainly and Egyptian construct. There are 40000000 of these meters in berriman's geodetic theory and he suggests the Greeks and Romans knew nothing of it but The Egyptians did.
It is 54 digits of 0.7291666... and produces a replication of the imperial measures in the metric for example 0.5184 x 7 = 3.6288 in meters and explains why 7 plays such a prominent role in understanding this system.
The ERC is 20 digits of 0.7291666... x 99/70 = 20.625. There is no doubt based on Berriman's analysis these measures are Egyptian and work with the 5 and one half sekhed of 14/11.
This meter I have also described as the 'Eye of Horus metre because Berriman classes it as 40 x 63/64."

In his analysis, David Genevier has defined the ratios bewteen several important units as follows:

In particular, David Genevier defines the ratio between the Arab foot and the Roman foot as 25/27 x 7/6, and rejects the simpler ratio of 27/25. This opens up the question of the ragisma ratio. 12.6 inches, or 0.32 metres, for the Arab foot multiplied by 25/27 = 11.6666 inches. But the Roman foot of 11.664 inches x 27/25 would give an Arab foot of 12.59712 inches. The Roman foot of 11.664 multiplied by 25/27 is 10.8, the unit "U", and this times 7/6 is 12.6 inches, the Arab foot. David Genevier also shows that the Viennese foot = 14/15 Arab Foot, and suggests that "the Arabic units can be considered as a key bridge between the measures of antiquity and the European measures of the Middle Ages." David Genevier has also written that in his view:

"To say that the Arabic measurements are 17.28 Digits is to affirm that according to the convention Arab Foot = 27/25 Roman Foot which is false, having demonstrated that Arab Foot = 25/27x7/6 which allows the following table:
Arabic Digits = 16x25/27x7/6 = 17,28395061728395 16x27/25 = 17,28 false AF = 12x21/20 = 12,6 II For the same reason : 1 m = 54xD digits D = 4375/4374"


This table comes from a discussion with David Genevier and David Kenworthy. One of the issues raised is the ragisma ratio of 4375/4374 and its role in defining the ratios between various units such as two forms of the digit, 0.729 and 0.729166667 inches, and the Roman foot, which is compose of 16 of these digits, and so has the same issue: should it be 11.664 or 11.666667 inches? the 0.729 inch digit is also 10/6 x 4374, and the 0.729166667 digit is 10/6 x 4375.

4375/4374 = 0.72916666667/0.729

4375 /4374 =16 x 7 x 10 000 / (12⁴ x 54 )

4374 /4375 = (27 / 35000) x 6⁴

= (54 / 70 000) x 6⁴

Berriman defines his constant k as either 1.296 or 1.296296296, and the difference between the two versions is the ragisma ratio.

Something that the ratios between digit, Roman foot, U, and Arab foot reveal is that this ragisma ratio is produced combining the numbers 7 and 6, or 7 and 12. For example, a metre of 39.375 inches is usually associated with a digit of 0.729166667 inches, not 0.729 inches, and yet, in the green section, you can see that starting with a digit of 0.729 inches, you can arrive at the 39.375 inch metre by multiplying by 16 x 7 x 1000 / 12⁴. There may be 54 digits of 0.72916666" in such a metre, but there are also 16 x 7 x 10000 / 12⁴ digits of 0.729 in this metre. The Aragon vara of 0.768 metres can be understood as 16 x 7 x Phi² x Phi² metres, or 16 x 7 x 144/55 x 55 / 21 metres.

Why does the number 7 come up so much in metrology, and why so often combined with 6? Indeed, why is the ratio between the dimensions of the first Mosque of Kairouan and the first Dura Europos Synagogue 14/3? Seven is not part of a sexagesimal or duodecimal system. Yet it is in the divisions of the royal cubit. An English yard is 6.4 / 7 metres. A Persian / Assyrian cubit of 25.92 inches is 6 x 6x 6 x 6 x 2/100 inches, and in metres it's 4.608 / 7, or 12 x 12 x 32 /7, and the Great Pyramid base side x 2 / 700. another unit I've been looking at is an nameless unit that Flinders Petrie mentions in two books of his, Stonehenge and Inductive Metrology, of roughly 22.5 inches, "of Phoenican origen", which happens to be 4/7 metres, and a megalithic inch of 0.81648 inches multiplied by 1 000 000 / (3 x 7 x 12³). The middle section of Turin cubit rod of 0.525 metres measures 7/(36 x √2) metres. Is the use of sevens and sixes intended to reflect the cycles of the sun and the moon?

A lunar year of 12 months is roughly 5 x 70 days plus approximately 5 days, and a solar year is approximately 6 x 60 days plus five or so days.

It is possible that it is simply as a result of the use of sixes and sevens combined that the ragisma ratio appears between two versions of the same unit.


The history of where and when these units were used is intriguing. On the one hand there are reports of Charlemagne adopting Arab standards of measure, particularly of weight, despite the tensions between the Christian and Muslim worlds.

One historian writes:


For the origin of standards of weight in France we have to go back to the Arabs, as the basis of the ancient French system is reputed to be an Arab yusdruma, which was sent by Caliph Al Mamun (786-833) to Charlemagne. This yusdruma, or later Arab pound, was the monetary pound or livre esterlin of Charlemagne, and amounted to 5666 1/4 grains, or 367.128 grams. It was divided into 12 ounces, or 20 sols, of 12 deniers, of 2 obolwa of 12 grains, or 5760 grains in the aggregate, each grain weighing 0.063738 grams. (1)

However, the commonalities between units of measure from europe and rthe Middle Easdt goes back much further in time that charlemagne. Indeed, the same author writes:


The resemblance that exists between the Babylonian and Egyptian cubits could lead us to believe that they both had the same origin. It would be possible, if necessary, that the relations established between these two nations, after the conquest of Egypt by Cambyses, had introduced the use of the Egyptian royal cubit among the Babylonians. Be that as it may, the testimony of Herodotus is so positive, and of such authority, that we cannot doubt the existence of this cubit in the city of Babylon. The question is therefore not to prove that its value was 0m, 525, since we have already demonstrated it, but to know if this cubit was the only one in use among the Persians, or if there was none. was not some other older one to which the other parts of their metric system related. This is precisely what neither Herodotus nor any of the authors of antiquity tell us.

And further on:


According to this famous scholar, Golius, in his notes on the Astronomy of the Arab Alfargan, cites an author of the same nation who asserts that the cubit called hashemic, of thirty-two fingers, was also called royal, because that it originated from the ancient kings of Persia. Admitting this fact, to which we have nothing to oppose, and which we find on the contrary perfectly in accord with other testimonies which we will quote below, it follows that the ancient cubit of the Persians was 0, 640 , since we will demonstrate ( 387 ) that this value is exactly that of the hashemic cubit of the Arabs. It is still , according to Kelly, that which is used today throughout Persia . same as Newton calculated for Chaldea, although on data quite different from those of the Arabic author on whom we rely.(2)

The ancient Chaldean, Persian and Arabic units were fundamentally the same. Moreover there are clearly simple fractional relationships to the imperial units, to the metre, and to other units in use in Europe, from the Aragon vara to the Megalithic yard. It seems that going back to prehistorical times, units may have been multiples of 0.03 and 0.02 metres, from the Persian foot of 0.32 metres, the Persian cubit of 0.64 metres, the Megalithic inch of 12⁴/1 000 000 metres, and the English yard of 4³ / 7 metres, to name but a few. As for the role of a fraction such as 4374/4375, it could be that it is simply the by-product of the combination of a duodecimal system and the tendency to divide units into seven parts.


Notes


1. Queipo, V., 1859, Essais sur les Systemes métriques et monétaires des anciens peuples depuis les premiers temps historiques, Paris. p 269

https://play.google.com/books/reader?id=IDEVAAAAQAAJ&pg=GBS.PA268&hl=en

2. Ibid


Bibliography


Neal, John, Murder of Hippasus

(99+) Murder of Hippasus.docx | John Neal - Academia.edu


Queipo, V., 1859, Essais sur les Systemes métriques et monétaires des anciens peuples depuis les premiers temps historiques, Paris.

https://play.google.com/books/reader?id=IDEVAAAAQAAJ&pg=GBS.PA268&hl=en





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