Hi all,
According to ancient cuneiform texts, the Mesopotamian/Babylonian shusi was contained 20 times in the foot, and 30 times in the cubit. Here is a 2020 Journal of Physics article that gives images and translations for the cuneiform texts, and also gives .333 m for the foot; .5 m for the cubit; and 1m for the step of two cubits:
[iopscience.iop.org]
According to Stecchini in the section of his website below on the structure of linear units: “The cubit considered standard in Mesopotamia is the barley cubit, composed of 27 basic fingers; in documents employing sexagesimal reckoning this unit is usually divided into 30 fingers.”
27 digits /30 shusi = 9/10
[saturniancosmology.org]
Regarding his barley foot, Stecchini says “Petrie calls it a Northern foot because it was used in the German provinces of the Roman Empire as pes Drusianus and because it continued to be used in north-western Europe in medieval times. Latin authors state that the pes Drusianus was 18 fingers of the Roman foot; from these statements Petrie calculates it as about 331.42 mm, but adds that ancient and medieval architectural remains indicate a foot of 332.74 mm, a figure that agrees with the value 332.94 mm I calculate for the trimmed (barley) foot.”
18 Roman/Egyptian digits for the Northern/barley foot, calculated in Mesopotamia as 20 shusi is:
18 digits /20 shusi = 9/10
In Stecchini’s charts on the same webpage, he gives .333 m for the Mesopotamian/barley foot, and .4995 m for the Mesopotamian/barley cubit.
According to Herodotus Book I Section 178: “Such is the size of the city of Babylon, and it had a magnificence greater than all other cities of which we have knowledge. First there runs round it a trench deep and broad and full of water; then a wall fifty royal cubits in thickness and two hundred cubits in height; now the royal cubit is larger by three fingers than the common cubit.”
If we take the common cubit as 24 fingers, then 3 more fingers gives 27 fingers for this Babylonian cubit, and given 30 shusi for the Babylonian cubit, 27 digits/30 shusi = 9/10.
[www.sacred-texts.com]
The earliest surviving statement of the size of the earth was the statement by Aristotle that “according to the mathematicians, the circumference is 400,000 stadia.” Since the metric system is based on the related multiple of 40,000,000 meters for the circumference, a stadia of 100 meters makes Aristotle’s statement accurate. Given 54 digits per meter, and 10 shusi = 9 digits, 60 shusi = one meter; one foot (20 shusi) = 1/3 meter; and one cubit (30 shusi) = 1/2 meter, so a stadia of 300 Mesopotamian feet is contained 400,000 times in the polar circumference, as is a stadia of 200 Mesopotamian cubits.
A royal Egyptian cubit of 20.625 inches, divided by 99/70 gives a remen of 14.58333..., divided by 20 gives a digit of .7291666..., times 9/10 gives a shusi of .65625 inches, times 20 gives a Sumerian foot of 13.125 inches, times 3/2 gives a Sumerian cubit of 19.6875, times 2 gives a meter of 39.375 inches.
I realize that the Sumerian foot, the Babylonian foot, the Mesopotamian foot, the Indus Valley foot and the Northern foot have all been rated as 13.2 inches, or 11/10 of an English foot, rather than my proposed 13.125 inches. Berriman gives 13.2 inches for the Sumerian foot based primarily on the graduated rule on the headless statue of Gudea. This rule is approximately 10.5 inches long, or shorter than one Sumerian foot, but according to Berriman “The scale on the rule has 16 nominally equal divisions, with a total length of 269 mm; the average length of a division, therefore, is 16.8 mm = .66 inches... In Decouvertes en Chaldee (1884-1912) de Sarzec and Heuzey included the full scale photograph from which I made these measurements of the 16 divisions of the rule:
17.5; 17.7; 16.5; 16.8; 16.0; 17.7; 16.6; 17.2 mm
16.5; 16.5; 16.5; 17.3; 16.2; 17.0; 16.5; 16.5 mm
Total length = 269 mm. Average division = 16.8 mm = .66 inches = Sumerian shusi.”
The ruled tablet on the statue of Gudea is regarded as the best evidence of the length of the Sumerian shusi and foot and cubit, but the intervals between the lines are not particularly equal, and based on the photograph, the lines are not particularly straight. From Berriman’s examination of the photograph, by far the most common interval between the lines is 16.5 mm, which he averaged up based on the total length and the more scattered longer lengths of some of the intervals.
Regarding the Indus Valley inch, Berriman says: “The Indus Valley inch is engraved on a broken piece of shell found at Mohenjo-daro; the find was made in 1931 during archaeological excavations carried out under the aegis of the Government of India. The fragment of shell measures 6.62 by .62 cm. (about 2.5 inches long) and shows nine parallel lines, .264 inches apart, cut with a fine saw. One of these lines is distinguished by a circle; another, five spaces distant from it, is marked by a large dot; it is the length of 1.32 inches between the circle and the dot that I call the Indus inch. These are published measurements based on a report by Sir Flinders Petrie; they make the Indus inch exactly equal to 2 Sumerian shusi.”
There is a footnote to this paragraph to: Further Excavations at Mohenjo-daro by E.J.H Mackay, volume 1, pp 404-405. Mackay’s book is in the internet archive, and there is a longer discussion of the shell fragment and also a long quote from Petrie that gives various comparable feet that he estimates from 13.0 to 13.4 inches:
[archive.org]
Mackay also makes the point that the width of the lines on the shell fragment are .02 inches, which could bring into question the given spacing of the lines of .264 inches apart, accurate to 1/1000 of an inch. I do not really disagree with the idea that the Indus Valley inch is twice the length of the shusi, I am just not so sure about exactly 11/10 of the English inch. A few pages before the pages about the shell fragment, Mackay gives several pages of measurements of about 700 Indus Valley seals. Some are square, some are nearly square, and some are not. Several are given as 1.31 inches square and one is given as 1.31 by .65, or 2x1. Several are also given as 1.3 square and a couple are given as 1.32 square, but not as many as 1.31 or 1.3. Some others are bigger and some others are smaller.
Here is a 2020 article by Dr. M. R. Goyal that presents some of the evidence above and some other evidence in support of the 13.2 inch foot, relating this length to lightspeed. This webpage also has a picture of the Indus Valley shell fragment, although it is kind of blurry, which is probably to be expected, since it shown at about 10 times life size.
[www.indictoday.com]
There is a much more evidence about the length of the royal Egyptian cubit, the remen and the Egyptian digit, but disputes about these lengths exceed the difference between .66 vs .65625 inches for the shusi. I think the better geographic relation of .65625 inches, and the better relation with the standard digit, and the ancient references to 18 digits = 20 shusi, and 27 digits = 30 shusi, supports a rating of .65625 inches for the shusi.
Bonus rating: I mentioned in my remen article that a circle with a diameter of 9 digits has a circumference of one royal Egyptian cubit. Given the 9/10 relation between the shusi and the digit, this means that a diameter of 10 shusi also has a circumference of one royal Egyptian cubit, and a diameter of 10 shusi also has a circumference of 10 pi shusi, so:
One royal Egyptian cubit = 10 pi shusi, or
20 x 99/70 x 10/9 = 10 x 22/7.
Best,
Jim
According to ancient cuneiform texts, the Mesopotamian/Babylonian shusi was contained 20 times in the foot, and 30 times in the cubit. Here is a 2020 Journal of Physics article that gives images and translations for the cuneiform texts, and also gives .333 m for the foot; .5 m for the cubit; and 1m for the step of two cubits:
[iopscience.iop.org]
According to Stecchini in the section of his website below on the structure of linear units: “The cubit considered standard in Mesopotamia is the barley cubit, composed of 27 basic fingers; in documents employing sexagesimal reckoning this unit is usually divided into 30 fingers.”
27 digits /30 shusi = 9/10
[saturniancosmology.org]
Regarding his barley foot, Stecchini says “Petrie calls it a Northern foot because it was used in the German provinces of the Roman Empire as pes Drusianus and because it continued to be used in north-western Europe in medieval times. Latin authors state that the pes Drusianus was 18 fingers of the Roman foot; from these statements Petrie calculates it as about 331.42 mm, but adds that ancient and medieval architectural remains indicate a foot of 332.74 mm, a figure that agrees with the value 332.94 mm I calculate for the trimmed (barley) foot.”
18 Roman/Egyptian digits for the Northern/barley foot, calculated in Mesopotamia as 20 shusi is:
18 digits /20 shusi = 9/10
In Stecchini’s charts on the same webpage, he gives .333 m for the Mesopotamian/barley foot, and .4995 m for the Mesopotamian/barley cubit.
According to Herodotus Book I Section 178: “Such is the size of the city of Babylon, and it had a magnificence greater than all other cities of which we have knowledge. First there runs round it a trench deep and broad and full of water; then a wall fifty royal cubits in thickness and two hundred cubits in height; now the royal cubit is larger by three fingers than the common cubit.”
If we take the common cubit as 24 fingers, then 3 more fingers gives 27 fingers for this Babylonian cubit, and given 30 shusi for the Babylonian cubit, 27 digits/30 shusi = 9/10.
[www.sacred-texts.com]
The earliest surviving statement of the size of the earth was the statement by Aristotle that “according to the mathematicians, the circumference is 400,000 stadia.” Since the metric system is based on the related multiple of 40,000,000 meters for the circumference, a stadia of 100 meters makes Aristotle’s statement accurate. Given 54 digits per meter, and 10 shusi = 9 digits, 60 shusi = one meter; one foot (20 shusi) = 1/3 meter; and one cubit (30 shusi) = 1/2 meter, so a stadia of 300 Mesopotamian feet is contained 400,000 times in the polar circumference, as is a stadia of 200 Mesopotamian cubits.
A royal Egyptian cubit of 20.625 inches, divided by 99/70 gives a remen of 14.58333..., divided by 20 gives a digit of .7291666..., times 9/10 gives a shusi of .65625 inches, times 20 gives a Sumerian foot of 13.125 inches, times 3/2 gives a Sumerian cubit of 19.6875, times 2 gives a meter of 39.375 inches.
I realize that the Sumerian foot, the Babylonian foot, the Mesopotamian foot, the Indus Valley foot and the Northern foot have all been rated as 13.2 inches, or 11/10 of an English foot, rather than my proposed 13.125 inches. Berriman gives 13.2 inches for the Sumerian foot based primarily on the graduated rule on the headless statue of Gudea. This rule is approximately 10.5 inches long, or shorter than one Sumerian foot, but according to Berriman “The scale on the rule has 16 nominally equal divisions, with a total length of 269 mm; the average length of a division, therefore, is 16.8 mm = .66 inches... In Decouvertes en Chaldee (1884-1912) de Sarzec and Heuzey included the full scale photograph from which I made these measurements of the 16 divisions of the rule:
17.5; 17.7; 16.5; 16.8; 16.0; 17.7; 16.6; 17.2 mm
16.5; 16.5; 16.5; 17.3; 16.2; 17.0; 16.5; 16.5 mm
Total length = 269 mm. Average division = 16.8 mm = .66 inches = Sumerian shusi.”
The ruled tablet on the statue of Gudea is regarded as the best evidence of the length of the Sumerian shusi and foot and cubit, but the intervals between the lines are not particularly equal, and based on the photograph, the lines are not particularly straight. From Berriman’s examination of the photograph, by far the most common interval between the lines is 16.5 mm, which he averaged up based on the total length and the more scattered longer lengths of some of the intervals.
Regarding the Indus Valley inch, Berriman says: “The Indus Valley inch is engraved on a broken piece of shell found at Mohenjo-daro; the find was made in 1931 during archaeological excavations carried out under the aegis of the Government of India. The fragment of shell measures 6.62 by .62 cm. (about 2.5 inches long) and shows nine parallel lines, .264 inches apart, cut with a fine saw. One of these lines is distinguished by a circle; another, five spaces distant from it, is marked by a large dot; it is the length of 1.32 inches between the circle and the dot that I call the Indus inch. These are published measurements based on a report by Sir Flinders Petrie; they make the Indus inch exactly equal to 2 Sumerian shusi.”
There is a footnote to this paragraph to: Further Excavations at Mohenjo-daro by E.J.H Mackay, volume 1, pp 404-405. Mackay’s book is in the internet archive, and there is a longer discussion of the shell fragment and also a long quote from Petrie that gives various comparable feet that he estimates from 13.0 to 13.4 inches:
[archive.org]
Mackay also makes the point that the width of the lines on the shell fragment are .02 inches, which could bring into question the given spacing of the lines of .264 inches apart, accurate to 1/1000 of an inch. I do not really disagree with the idea that the Indus Valley inch is twice the length of the shusi, I am just not so sure about exactly 11/10 of the English inch. A few pages before the pages about the shell fragment, Mackay gives several pages of measurements of about 700 Indus Valley seals. Some are square, some are nearly square, and some are not. Several are given as 1.31 inches square and one is given as 1.31 by .65, or 2x1. Several are also given as 1.3 square and a couple are given as 1.32 square, but not as many as 1.31 or 1.3. Some others are bigger and some others are smaller.
Here is a 2020 article by Dr. M. R. Goyal that presents some of the evidence above and some other evidence in support of the 13.2 inch foot, relating this length to lightspeed. This webpage also has a picture of the Indus Valley shell fragment, although it is kind of blurry, which is probably to be expected, since it shown at about 10 times life size.
[www.indictoday.com]
There is a much more evidence about the length of the royal Egyptian cubit, the remen and the Egyptian digit, but disputes about these lengths exceed the difference between .66 vs .65625 inches for the shusi. I think the better geographic relation of .65625 inches, and the better relation with the standard digit, and the ancient references to 18 digits = 20 shusi, and 27 digits = 30 shusi, supports a rating of .65625 inches for the shusi.
Bonus rating: I mentioned in my remen article that a circle with a diameter of 9 digits has a circumference of one royal Egyptian cubit. Given the 9/10 relation between the shusi and the digit, this means that a diameter of 10 shusi also has a circumference of one royal Egyptian cubit, and a diameter of 10 shusi also has a circumference of 10 pi shusi, so:
One royal Egyptian cubit = 10 pi shusi, or
20 x 99/70 x 10/9 = 10 x 22/7.
Best,
Jim