UNITS OF LENGTH
The discovery of the group of statues of Gudea together with some other impressive objects caused a stir in the general public; Jules Ferry, a major political figure of the Third Republic who at the moment was Ministre de l’Instruction Publique et des Beaux-Arts, addressed the French Parliament on the excavations of Lagash; a department of oriental antiquities was established at the Louvre Museum; Oppert as a Sumerologist and as a metrologist was beside himself and announced to the Académie des Inscriptions: “It is the most precious discovery made in Mesopotamia since the discovery of Niniveh and Babylon. “ Indeed it was a red letter day for scholarship, but it happened that the evidence provided by the rule of the statues was not employed to increase knowledge, but to diminish it. There were those who concluded that there had been found a simple type of evidence which would allow to establish the length of the cubit without resorting to any intellectual operation; but those who do not want to use their mind and worship facts cannot perceive even the most elementary facts correctly. As it will appear below those who did not want to use the eye of the mind were not even able to make proper use of their physical eyes. Oppert examined the statues as soon as they became available at the Louvre in May 1881 and delivered a report to the International Congress of Orientalists held in Berlin in December. At that moment the existence of the Sumerian language was under attack, and hence the statues were of great significance, since they were part of a group of objects with purely Sumerian inscriptions. Oppert concentrated his attention on the inscription of Statue H, since it was easier to read because it contains a list of measures, and achieved the first entirely successful interpretation of a Sumerian text for which there was no Akkadian parallel text. He dealt with the measuring rule of the same statue and presented the most detailed report ever published about the divisional lines; but he must have examined the statue when it was not yet cleaned of incrustations, since he did not see some of the divisional lines that clearly appear on the photograph published in the report of the excavation. He drew the correct conclusion that the rule had a length of half a cubit but, not seeing all the markings, concluded that the entire length of the rule, 271 mm., should count. However, while declaring that the rule had “extremely significant implications for metrology,” he was careful not to interpret the evidence mechanically. He tried to link the rule with the length of the cubit he thought had been used in buildings of Nineveh, a cubit of 548.5 mm. He also tried to connect the length of the half cubit of the rule with the measures of volume mentioned in the inscription on the statue. About the same time Aurès asked the scholar of ancient and medieval metrology Héron de Villefosse, who was a curator at the Louvre, to examine the rules and the tablets on which they lie. On the basis of this report it was possible to determine a number of specific facts. The main one is that the rule extends at the two ends beyond the graduated part; also today often the straightedge is longer than the graduated part. When one excludes the two ends and counts only the graduated part, one finds that the rule is divided into 15 fingers, and hence is one half of the normal Mesopotamian cubit of 30 fingers. Old school metrologists agreed on this point: in 1889 Lehmann-Haupt wrote that the 15 fingers have a length of 249.2 or 249.3 mm. (cubit of 498.4 or 498.6), but warned that he had not examined the rule itself and had calculated from an heliographic reproduction; in 1903 Fritz Hommel stated that the 15 fingers have an average width of 16.6 mm. (cubit of 498 mm.). I have examined the rule at the Louvre a few years ago with the help of a pocket decimeter. It is difficult to calculate directly the total length since the edge of the rule is not straight. The fingers differ from each other by about one millimeter. The rule is roofshaped, as many modern rules are, and there are divisional lines on the two faces that are not in line with each other. If one measures the total length of the graduated part on the face that seems more important, one can arrive at a figure that agrees with the length of 249.7 mm. one could expect on theoretical grounds; but the extreme divisional lines on the other face are about one millimeter closer. It is clear that the sculptor did not intend to give a precise standard, but to suggest something the nature of which I shall consider below. It appears that having cut rather roughly a blank rule on the statues, one placed next to it a measuring rule and copied the divisional lines, but in copying them one did not worry about being a millimeter off the line. If one were to prepare a detailed report on the divisional lines exact to the tenth of a millimeter, as the one attempted by Oppert, one could by inference reconstruct the dimensions of the rule from which the markings were copied. It is certain that the rule was remarkably close to the theoretical length. Since we know from the study of Roman and Egyptian measuring rules that concrete lengths can be quite discrepant from theoretical ones, from the rule of Gudea that does not deviate from its theoretical length of 249.7 mm. more than a millimeter we could tentatively infer that the Sumerians were particularly nice in such matters. After the first examinations of the statues by metrologists,
Léon Heuzey who had been appointed to the new position of Curator
of Oriental Antiquities at the Louvre, took a proprietary attitude towards
his charges and reserved to himself the task of providing a report on
the rule. In other times he would have delegated the task to an expert
of metrics or would have become himself acquainted with metrology, but
in the new age of humanistic scholarship he could assume that no particular
knowledge was necessary. He had also the task of compiling the report
on the excavation of Lagash; obviously there are disagreements on the
standards of scholarship, since this report would exhibit The notion of a rule of sixteen fingers became a dogma with the new school of metrology. The new point of view on this specific question was expressed by Haupt. First of all he set the principle that the rule by itself could solve the problem of the length of the cubit: “The standard of Babylonian metrology is the graduate rule on the statues of Gudea.” But while making it the Mesopotamian equivalent of the Paris meter, he did not consider it necessary to evaluate it with accuracy. He claimed that the graduated part of the rule is a half cubit of 16 fingers of 16.6 mm. each, measuring 265.6. In order to reconcile this interpretation with the texts that mention the cubit as divided into 30 fingers, he declared that there was a cubit of 30 fingers (495 mm.) and also a “royal cubit” of 32 fingers (550 mm.) used in the construction of buildings. The last figures imply a finger of 16.5 mm., instead of 16.6 as indicated by the first datum, but no explanation is offered for the disagreement. Rev. Johns, who in 1902 wrote the manifesto of the new school, declares that the rule is composed of 16 fingers of 16.5 and 16.6 mm. In 1903 Rev. William Shaw-Caldecott wrote a special essay on the rule of Gudea with a drawing of it; this essay allegedly is based on an “original reading” of the rule, but the only specific datum is a quotation of Haupt’s figures. Later Unger, who came to be considered the new school expert on Mesopotamian units of length, explained the sixteen fingers of the rule of Gudea with the theory that the cubit had 30 fingers, but the Mesopotamians “inconsistently” derived from it a foot of 16 fingers. As to the length of this foot of sixteen fingers he gave different figures in different articles (at times quoting Heuzey and at times quoting Thureau-Dangin), but this was not a problem for him since in his opinion the length of the cubit was subject to fluctuations from one reign to another, and it could be as much as 518 mm. or as little as 495. This theory is the counterpart of Weissbach’s theory that the Mesopotamian mina was of fluctuating value. Weissbach was the only new school metrologist that did not consider the rule of Gudea fundamental; he took the position that the only reliable datum about the length of the cubit was provided by Greek authors. Thureau-Dangin, who could not decide himself between the old school and the new school, in 1909 reported that by a new examination of the rule he had found that the sixteen fingers have a length of 264.5 mm. and hence correspond to a cubit of 30 fingers with a value of 496 mm. But the length of 496 mm. for the Mesopotamian cubit was arrived at by Lehmann-Haupt by making a compromise between a shorter length he thought indicated by the weights and the length of 498 mm. he considered indicated by the rule of Gudea. Thureau-Dangin saw what he wanted to see and according to his temper tried to please everybody. The so-called sixteenth finger is bevelled and hence in calculating its length one can start at any point one chooses. Particularly regrettable is the careless intepretation
of the rule of Gudea offered by Father Deimel, since he is usually a careful
scholar who has creditably interpreted the metrics of the tablets of Shuruppak
(I have mentioned them among the earliest examples of writing), and since
the summary of Sumerian metrology included in the first edition of his
Father Deimel declares that the rule of Gudea was not constructed “with the scrupulous acriby of the Paris meter” and that it gives only an approximate value. In truth there is a great space between the alternative of the precision of the Paris meter and that of the slipshod test of Father Deimel. He concludes that the length of the cubit fluctuated according to the epoch and to the place, so that one can find in Mesopotamia a cubit of 518 and one of 495 mm. (These figures were accepted by Unger). He asserts as a general principle that all “natural” units of length fluctuate, and the proof of it would be the comparison of the English foot (304.797 mm.) with the Paris foot (324.839), the Lyons foot (341.760) and the Bordeaux foot (356.740). To this line of argument one can only answer that indeed Father Deimel would not change even a chapter, not to mention the entire structure, of his Sumerian grammar on the basis of an incorrect apograph of a Sumerian tablet, and would not draw conclusions about the organization of the Sumerian language by comparing it with a language such as Chinese, if he does not have any knowledge of this language. I have shown that the Lyons foot is a slightly increased version of the natural barley foot, the typical foot of Mesopotamia. The English foot and the Bordeaux foot are the normal and the septenary form of a foot derived from the so-called Babylonian-Egyptian great cubit, which is 32/30 of the barley cubit and is mentioned in cuneiform documents. The Paris foot is first found in Athens. These facts prove the contrary of what Father Deimel claims; they prove the extreme stability of lineal units. Nobody would blame Father Deimel for not being familiar with these data, just as I feel free to profess ignorance of many aspects of Sumerian grammar; but he should not show contempt for the metrologists who have dedicated time and love to the investigation of their problems. However, Father Deimel’s fault is extenuated by the general irresponsibility of the followers of the new school.
Dieulafoy, without knowing of Borchardt’s study, tried to relate the rule and the plan. But unfortunately he followed the interpretation of Heuzey not only in relation to the rule of sixteen fingers, but also in the peculiar notion (accepted also by Haupt) that the plan portrays a fortress, even though the inscriptions on the statues speak of the construction of a temple. Dieulafoy, assuming that the plan was that of a fortress, interpreted the advanced parts of the perimetral walls as towers; then he observed, correctly, that the distance of the towers in a fortification is determined by technical military factors and that in Mesopotamia fortification towers are about 30 m. apart. He concluded that the scale is 1:2304; this would give to the construction the immense length of more than half a kilometer, whereas the plan presents a building with a single courtyard. In my opinion the so-called towers are the usual buttresses of Mesopotamian walls. I would interpret the scale on metrological principles. The subdivisions correspond to the system of multiples of the cubit by which the first multiple is the double-cane of 12 cubits, which has a sexagesimal multiple of 720 cubits or 4 minutes of march. The finger corresponds to the double-cane and the maximum subdivisions of the finger, one twelfth and one eighteenth, represent the cubit and the half-cubit. It is reasonable to expect that a plan would have as minimum unit either the cubit or the half cubit. The half cubit of fifteen fingers represents 180 cubits or a minute of march, which is a standard unit of landsurveying, as it appears from the Smith Tablet. The maximum length of the building in the plan is 14 fingers, and the plan is so centered in relation to the rule that it leaves half a finger of rule at each end. The maximum width of the plan is 7 fingers. Hence the plan was based on a rectangle of 14 x 7; I shall show that the factor 7 is a normal occurrence in Mesopotamian buildings, as it is in the Egyptian ones. According to my interpretation of the scale, the maximum dimensions of the temple are 168 x 84 cubits; possibly the exact measures are 280 x 140 artabic feet. The spaces of the walls between buttresses appear to be 14 mm. on the plan and would indicate a distance of 5 cubits. Unfortunately the report of Heuzey about the excavations of Lagash does not allow to decide whether any of the buildings correspond to this plan. The plan was copied on the stone allowing the same imprecision of the lines we find in the rule; one should copy the plan and draw from it an architectual drawing with the exact proportion and uniformity of the parts. However, the plan is not as untechnical as Unger makes it, claiming that some parts are not drawn in horizontal section but in profile.
If the study of plans were to prove that one generally used scales of the type 1:180, 1:360, 1:720 etc., one could draw the conclusion that rules were currently subdivided as the one of Gudea. Not even Borchardt
as an Egyptologist has noted that that graduation of the rule of Gudea
has its counterpart in Egypt. The historian of science Sarton was struck
by the information he found in Lepsius that many Egyptian cubits present
sixteen fingers at one end subdivided into fractions of increasing denominator:
1, ½, 1/3, 1/15. He properly concluded that this peculiar subdivision
must correspond to a specific practice and asked for an explanation through
the pages of the magazine The two subdivisions
of the cubit correspond to two methods of calculating itinerary distances.
There was a decimal and a sexagesimal method; both methods use the factor
3 in calculating the minute of march. By the sexagesimal method the minute
of march is calculated by the factor 180 = 3 x 60; by the other method
one forms a double minute or stadion of 600 feet in Greece and 300 cubits
in Egypt. It is a fact that in Egypt one prefers to calculate decimally
and that in Mesopotamia one prefers to calculate sexagesimally, but in
the ancient world one formed multiples by one method or the other according
to the foot or cubit taken as starting point, since one had to arrive
at an hour of march of about 5 to 6 km. The Roman system of landsurveying
uses sexagesimal units; the
It has been
also noted that the dream of Gudea has its counterpart in the vision of
Ezechiel who is given the dimensions of the Temple. I have explained in
the proper section how the outlining of an imaginary temple by Ezechiel
is connected with his reform of the Hebrew metric system, a reform which
like that of his contemporary Solon in Athens was the core of a legislation
for the protection of farmers against usury. But here it is relevant to
notice that in Ezechiel’s vision the plans were given by “a
man whose appearance was like bronze, holding in his hand a line of flax
and a measuring cane As a final remark I may be allowed to observe that I have tried to demonstrate how much information can be gathered by a pedestrian analysis of the statues of Gudea with the rule; but the prevailing view operates on a higher level and states, for instance, about the same statues that “In their angles and surfaces becomes visible the endlessly valid order by which the course of the stars regulates itself and all the regions act in harmony; man himself is bound by them to the eternal law.”
Herodotos
(I, 178) in speaking of the monuments of Babylon says: “The royal
cubit is longer by three fingers’ breadth than the common cubit.”
One called royal any measure larger than the ordinary one; this terminology
is found in Sumerian documents and lasts into the Middle Ages. Herodotos
calls “common” the cubit I call basic. Similarly, a gloss in
Loukianos ( In reconstructing the overall structure of the units of length I have shown that the longest foot is the foot of 18 basic fingers which is the edge of the cube containing a basic talents of barley, and that to this foot corresponds a barley cubit of 27 basic fingers. That the Mesopotamian foot was a unit of about 330 mm. had been already gathered by Oppert from the most common dimension of bricks. Particularly in the first millennium B.C., the brick of a barley foot is the standard one. But in mathematical texts the foot is never mentioned and all calculations are based on the cubit divided into 30 fingers. This cubit is called barley cubit, but its name occurs only when there is a possibility of ambiguity. I shall show that this term occurs in the Smith Tablet, because there is also used a “great cubit” equal to l½ barley cubits. In a Neo-Babylonian tablet in Philadelphia (CBS 8539) the cubit is defined as a barley cubit because the cubit is divided into 24 fingers and this could cause ambiguity:
I shall
deal with this tablet in relation to seeding rates and there it will be
confirmed that this is a standard Mesopotamian cubit. The Sumerian term
še, “grain,” is ambiguous, but usually refers to barley;
Neugebauer translates “seed-barley. “ As the basic cubit exists
in two versions, the natural and the trimmed, so the barley cubit of 27
basic fingers exists in two versions:
natural 506.250 mm. The most direct evidence of the trimmed cubit is the
rule of Gudea and the most direct evidence of the natural cubit is the
Tower of Babel
In 1913 under the direction of Robert Koldewey a survey was made of the Tower of Babel, which is the ziggurat Etemenanki in the Temple Esagila of Babylon. A tablet, written in the Seleucid age but copied from an older document, giving the detailed dimensions of this ziggurat, was seen and paraphrased in English by George Smith in 1876; then it was lost but was discovered again in the private possession of a lady who allowed Father Victor Scheil to print its text in 1913 and then donated it to the Louvre (AO 6555). But unfortunately the poorest use has been made of the data which should have allowed to solve all the main problems of Mesopotamian metrics. The Tower of Babel was excavated as a part of the longest and most complex campaign ever attempted in Mesopotamia. The excavation of Babylon started in 1898 and continued, without interruption for winter months, until the approach of the British Army in 1917 forced the withdrawal of the German staff; this staff was by far the largest ever gathered for such an enterprise. When the Germans decided to enter the field of Mesopotamian exploration they had neglected, they outdid themselves and chose the city of Babylon which already amazed the Greeks by the acres and acres of its monuments. It was also decided that an effort should be made in the direction of architectural archeology for which Mesopotamian archeology was inferior to Egypt and Greece, and still is. But the direction of the enterprise was entrusted to Koldewey, who was a devotee of pseudo-sciences. He regulated his life by demanding numerogical superstitions, studied astronomy but was in fact an astrologer, and considered himself a lay scholar of medicine, but was an adept of quack medical theories. He was chosen because, particularly at the turn of the century, one thought that ancient Mesopotamia was the kingdom of such scientific views; it was considered to the credit of Koldewey that he considered himself a yogi—although he should rather be called a fakir, judging by the admiring reports of some archeologists about his mystical feats of endurance. The kind of archeology he represented is best summed up by the following declaration of aims by the Koldewey Society for history of architecture: “We could try to specify our purpose in the following way: what has been achieved at the material pole and may have been grasped as emotional and even in some measure as psychological, should also be energetically searched into at the spiritual pole, being thereby complemented. “ The city of Babylon with several huge constructions of regular shape, for some of which cuneiform and Greek texts give the dimensions, should have been the ideal ground for metrological investigations about linear units. Furthermore, one could have tested the theories of Aurès and Dieulafoy about the units used in constructions, but in this last respect nothing was attempted. Koldewey was fanatical about measurements, and insisted with reason that “measuring, measuring, and measuring” is the task of the archeologist, but his approach was purely compulsive; he regularly recorded temperatures and minutes of time, bringing into the field a collection of odd timepieces. Even though this campaign produced the most voluminous and expensive archeological report ever printed for Mesopotamia, there is nothing in it that a metrologist can evaluate directly, except for the dimensions of the Tower of Babel. (In order to avoid misunderstandings I must state that this does not apply to the recently published report by Alfred Mallwitz about the theater constructed in Greek times; this one proves that proper concern with measurements makes for a superior archeological report.) Walter Andrae who was the most devoted collaborator of Koldewey, even though he tried to apply methodically Newton’s method in his report about the Temple of Ishtar, produced only pages of worthless numerology. Andrae’s work is deeply colored by his theosophic beliefs. As an example of what was missed I may note that, whereas
Oppert had repeatedly dealt with the occurrence of near-squares in Mesopotamian
architecture, the excavators did not notice that the most important building,
the Temple Esagila, was certainly calculated as a near-square, even though
they note incidentally that the building is Not all scholars approved of Koldewey’s ideas; the
The Tower of Babel was measured and it was ascertained that its basis has the following dimensions (in meters):
The report states that the testing of the South side is less reliable, since it was obtained by measuring from the two extreme points, whereas for the other three sides it was possible to measure each section of the wall and the buttresses. I am not entirely convinced by the argument, since the elements of a wall broken by buttresses are bound not to be in a perfectly rectilinear line and hence give a slightly longer measurement. According to the theoretical length of the cubit, one would expect a length of 91.125 m., whereas the three best preserved walls average 91.54, though I would consider the dimensions of the South Wall as the most reliable. In any case, it is to the credit of Koldewey’s technique of excavation that one may be concerned with such fine details. Inside the ruins of this ziqqurat there were found the remainders of an older one, constructed with unbaked bricks and having the following dimensions;.
For the
sake of clarity, I shall cut through about twenty different commentaries
on these data and present my conclusions.
The older ziqqurat has the
surface of an The dimensions of the Tower of Babel are exactly those reported by Herodotos (I, 181) and Strabo (XVI, 1,5). that is, a stadion. In this case by stadion is meant a minute of march and not two, but this use of the term is not totally unusual, as t was already remarked by metrologists of the time of the French Revolution. At this point I have to move from the realm of facts
to the emotional world of scholars. Oppert had criticized Koldewey’s
plan of excavation on the basis of Herodotos’ description of Babylon
(errors in Koldewey’s planning were noted In the first pages of his book on Babylon (the first
edition is of 1914), Koldewey demonstrates the absurdity of Herodotos
by noting that the latter claims that the walls of Babylon form a square
with a side of 120 stadia; the unreliability of ancient authors would
be further demonstrated by the fact that Ktesias (who apparently is the
source of Diodoros II, 7) reports a total perimeter of 360 stadia. Koldewey
assumes that in the ancient world there was only one type of stadion,
that of 600 Greco-Roman feet, and calculates Herodotos’ and Diodoros’
figures for the perimeter as 86 and 65 km; then he observes that the perimeter
of the inner walls of Babylon is about 8 km. These figures are repeated
in several recent books by Parrot. But it is quite clear from Herodotos’
texts that he meant the outer walls, which enclose an area divided at
the middle by the Euphrates, whereas the inner walls are on one bank of
the river. Two sides of the outer walls have been measured by Koldewey
and found to be about 18 km altogether. Since Herodotos’ stadion
in this case equals 180 barley cubits, a side of 120 stadia corresponds
to 9935 m. Diodoros reports the figure of 360 stadia, but adds that those
who wrote Alexander’s history, such as Kleitarchos, reported a figure
of 365; this detail, not mentioned by Koldewey or any other writer on
the subject, proves that among the Greeks there was concern with accuracy.
Curtius Rufus ( V, I, 27), who draws from Kleitarchos, also reports the
figure of 365 stadia. This must be also a stadia equal to a minute of
march, but calculated by the Mesopotamian foot. A stadion of 300 trimmed
barley feet is 99.9 m., and one of 300 natural feet is 101.25 Presumably
the difference between the datum of 360 and 365 stadia corresponds to
the relation between trimmed and natural units which is exactly 72:73.
Hence. the reported length is 9112.5 for each side of the walls. Curtius
Rufus reports that in the age of Alexander only a part of the city, with
a circuit of 90 stadia was inhabited; he is obviously referring to the
inner walls, which by this reckoning would have a circuit of 8991 m. The
length of the actual walls has been measured as 8150 m, but if one measures
at the margin of the moat one obtains a larger figure. Esarhaddon in mentioning
his reconstruction of the inner walls, ascribes to each side a length
of 30 In 1915, in the volume in honor of Eduard Sachau, Delitzsch
wrote an article about Herodotos’ testimony in which he repeats Koldewey’s
arguments; but to prove even more forcefully that “no weight must
be given” to Herodotos’ words, he assumed that the only stadion
was that composed of 600 artabic feet and arrived at a figure of 90 km.
for the perimeter. In the same vein Leon Legrain, in publishing the texts
of Nabonidus mentioning a circuit of 14,400 cubits for the inner walls,
accepted for the Mesopotamian cubit the incorrect length of 556 mm., thereby
claiming that Nabonidus’ datum was exact; then he indulged in the
usual remarks about Herodotos, repeating verbatim the statements of Koldewey.
The climax in this trend is achieved by Otto Emil Ravn who has dedicated
a volume to The length of ancient stadia had been intensely studied in the period between Newton and the French Revolution, when the exact measurement of the circumference of the earth was a lively problem; by the end of the eighteenth century all the ancient texts then available had been explained. But in reality there never was a serious problem in interpreting references to stadia, since they can be easily checked against actual data; the only period in which there were misgivings about the length of the several types of stadion was in the time of Columbus, because there had been recently rediscovered the geography of Ptolemy which, for philosophical reasons, gives distorted geographical distances in the direction East-West. The effort to make sense out of Ptolemy led to the discovery of America, but contemporary humanists do not need to strain their mental faculties, since it is easier to assume that the ancients lived in a realm of nonsense. A further proof of Herodotos’ exactitude is his statement that the walls of Babylon have a width of 50 cubits; it has been found that the outer walls consist of an inner line with a thickness of 7 m. and an outer line with a thickness of 7.8 m. with a space of 12 m. in between. Taking Herodotos’ figure to the letter, it indicates a width of 25.31 m. against a total of 26.8 reported by Koldewey. Returning to the realm of facts, there are two texts
in which kings who claim to have rebuilt the Tower of Babel mention that
it has a side of 180 cubits. King Esarhaddon quotes the dimension of 1
From 1901 to 1903 Weissbach was the expert of Akkadian language attached to Koldewey’s expedition, and he left with a resentment that was still welling thirty-five years later when he wrote a brief postscript to his last book, dealing with the Tower of Babel and the Smith Tablet. This feud became to him gradually more important than that with Oppert and Lehmann-Haupt, to the extent that in the mentioned last book, published in the year of Lehmann-Haupt’s death, he included a sentence in which he recanted his main lifelong contention about metrology and accepted the position of old school. One wonders whether in his struggle with Koldewey’s supporters he had been willing as a last resort to lean on Oppert’s side, since Koldewey and his supporters referred to Oppert as “the Enemy. “ One can understand that Weissbach felt provoked by Koldewey; Meissner who preceded Weissbach at Babylon for one year, reveals his dislike of Koldewey; after Weissbach left, Koldewey was not able to find a capable substitute and had to rely on the distant help of Delitzsch, who had been mainly responsible for his selection as leader of the Babylon expedition. Delitzsch too finally engaged in an acid dispute with Koldewey about a deail in the reconstruction of the Ishtar Gate. Weissbach was a precise rational worker unless his vision was distorted by hatred, and even in this last case he used bad logic, which still is a form of logic, whereas Koldewey was a kind of Nostradamus, endowed with limitless and undefined learning and imagination, who gained people’s minds by arguments other than logical ones. Furthermore, Koldewey must have been particularly trying for an excellent linguist, as Weissbach was, since he did not know how to read cuneiform texts, but felt that his intuition was not appreciated by “philistine Assyriologists.” As a result of this conflict large bodies of tablets discovered by Koldewey are still unpublished today. What irritated Weissbach is not too important; he may have had perfectly legitimate reasons to regard Koldewey with scorn. Other members of the expedition were antagonized by more trivial decisions of Koldewey in the conduct of the campaign, such as his refusal to allow the playing of musical instruments by those who did not agree with his musical theories, or his refusal to allow visits by the familities on the ground that intelligent men do not waste time with women. But it was disastrous for scholarship that Weissbach built his scientific theories on the psychological need to oppose Koldewey. In 1904, promptly after he had left Koldewey’s staff,
Weissbach printed his manifesto in the booklet Koldewey for his part wanted to prove that he could obtain results without the help of Assyriologists; specifically he intended to prove that he could solve the problem of the length of the cubit by his own means. There was found a text mentioning the construction of a section of wall of a given length at the Ishtar Gate; the figure was clear but it was not at all clear to which wall it referred, since the Ishtar Gate was a complex structure and had been altered several times; Koldewey, nevertheless, thorught that he had traced the specific portion of wall to which the text referred and concluded that the Mesopotamian cubit had a value between 533 and 544 mm. For him this one uncertain datum, in conflict with all the evidence gathered in the preceding half century, could dispose of the matter. Later Koldewey excavated the Tower of Babel and could have vindicated the honor of having unearthed the most conclusive piece of architectural evidence in the field of metrology; but he had made up his mind and for him metrological research had come to a halt at the Ishtar Gate. In 1914, just when the first reports about the dimensions of the Tower of Babel were being received, Weissbach wrote his challenge on the question of linear measures both to Koldewey and to Lehmann-Haupt. He rejected Koldewey’s calculation, not on the ground of the unreliability of its technical details, but on the ground of a general condemnation of Newton’s method and of the use of architecture as evidence. Against Lehmann-Haupt he repeated the argument that there is no link between length and volume, since not one document indicates this link for Mesopotamia. He concluded that there was only one form of documentation that could legitimately be used to determine the length of the Mesopotamian cubit, the statement of Herodotos, supported by a gloss to Loukianos, that the Babylonian royal cubit has a length of 27 fingers. He interpreted Herodotos correctly, but he was just as absurd as Koldewey in claiming that one should limit oneself to this single piece of evidence. In this case Weissbach used an argument opposite to the
one he had used against Lehmann-Haupt on the question of weights; he had
maintained that Greek authors do not constitute a reliable source of information
about Mesopotamia and that only Mesopotamian sample weights can be trusted.
The contradiction of Weissbach was emphasized by Viedebannt who just at
that time had broken with his mentor, Lehmann-Haupt, and taken the side
of Weissbach. Viedebannt claimed that the challenge of the new school
to the old school was expressed by the slogan Weissbach calculated correctly that from a Greek cubit of 444 mm. one should derive a Mesopotamian cubit of almost 500 mm., but did not realize that when Herodotos speaks of cubit which is mevtrion and Loukianos speaks of koinovn or ijdiotikovn, they mean the basic foot which exists in two varieties, corresponding to the Greco-Roman and to the Egyptian foot. From an Egyptian foot of 300 mm. one derives a Mesopotamian cubit of 506.25 indicated by the Tower of Babel. But since Weissbach had calculated the Mesopotamian cubit as 500, the length of the cubit of the Tower of Babel became a problem. Thureau-Dangin, who was always trying to reconcile the irreconciliable, tried to explain the difference. Since he agreed with those who thought that the rule of Gudea was the absolute reference standard and had tried to agree with Lehmann-Haupt, by saying that the rule of Gudea indicates a cubit of 496 mm., he tried to explain the dimensions of the Tower of Babel by the following theory: one did not measure the side of the ziqqurat, but merely multiplied the length of a brick by the number of bricks, not taking the space occupied by the mortar into account. The Smith Tablet gives detailed information, according to two standards, about the length and the area of the basis of the ziqqurat, and further gives the dimensions of the following six levels; it is obvious that the Tablet intends to be precise, and further if the builders had been as imprecise as Thureau-Dangin claims, the Tower of Babel would have had the destiny ascribed to it by the Bible, in spite of any mortar. Weissbach accepted the theory of the bricks and the mortar. In the camp of Koldewey there was trained a younger scholar, Eckhard Unger, who took upon himself the task of refuting Weissbach point by point. He wrote a volume on the topography of Babylon in which he combines the archeological evidence with the written evidence and thereby disproves Weissbach’s absurd position. But Unger thought that he should also refute Weissbach in the field of metrology. If his commentary to the Smith Tablet does not add anything to what had been already said by Weissbach, his specific effort in the field of metrology was most harmful. He accepted the metrological ideas of Father Deimel, with whom he had worked on the texts of Shuruppak, but these ideas had been developed without any thoughtful consideration. In 1916, while studying the weights of the Museum of Constantinople, he came across the Nippur bar, which is a most important standard for weights, but interpreted it as a standard of length supporting Father Deimel’s contention that there was a cubit of 518 mm. Concerning the Tower of Babel, Unger took it as evidence of Deimel’s theory that the cubit was a variable entity and at times had been 508 or 510 mm. The total result was that, just when there had become
available evidence that could have settled in a positive way the issue
of the length of the cubit, scholarship was totally disorganized and what
had been achieved was lost. The present state of confusion is documented
by the summation found in the recent handbook of Assyriology by Sven Aage
Pallis: “As a unit of length (the cubit) varies somewhat according
to local city areas. The Gudea cubit at Lagash equalled 495 mm. , the
Nippur cubit, which was standardized in the earliest Babylonian kingdom
and after that is called the Babylonian cubit, was 518 mm. The “large
cubit,”
One thing is certain about the kigal: it has the same area as the basis of the ziqqurat, but it has the shape of a cube. The kigal has a surface of 180 x 180 cubits and a height of 180 cubits, whereas the first storey of the ziqqurat has a height of 66 cubits. Weissbach has suggested that the first storey was imagined as extending underground so as to form a cube, and that this partly imaginary cube, located partly underground, was called kigal. Others have advanced vaguer explanations identifying the kigal with the underground foundations of the ziqqurat or with the hole excavated for the foundations. Koldewey in his reconstruction of the ziqqurat draws it as a cube, assuming that the several stories were merely bands marked on the faces of this cube; this theory proves that Koldewey had little respect for textual evidence, but also that in his mystical imagination he had an intuitive grasp of symbols. My opinion is based on the fact that the seven stories of the ziqqurat add up to 180 cubits of height, and that Strabo reports that the ziqqurat was a stadion wide and a stadion high. The kigal is an imaginary cube which is represented by the ziqqurat. It was technically impossible and artistically undesirable to build the ziqqurat as a cube, but one built the first storey as high as possible, making it more than 1/3 of the total height, and constructed the other tapering storeys in such a way that they would reach the height of 180 cubits. The reason why the ziqqurat was ideally conceived as a cube will appear more clearly when I shall explain that the Ark in the story of the Flood was a cube of the same dimensions of the kigal. The term ki-gal in Sumerian means “great land, great earth. “ In some documents, the “nether world” is called kigal and there is a Sumerian infernal divinity called “Mistress of the kigal,” Eres ki-gal; but I doubt that this use of the term kigal is directly connected with its use in relation to the Tower of Babel. The name of this ziqqurat, E-temen-an-ki, “Building of the foundation-block of heaven and earth,” makes clear the meaning of kigal. It is the temen, the “foundation” of the world. When the Mesopotamians erected an important construction they placed deep underground, where it could not be lost, a temen; it contained the history of the construction, and its dimensions, and an appeal to the future generations to preserve it and to reconstruct it with the same dimensions, if it was destroyed. The function that the temen had in relation to a building, the ziqqurat had in relation to the cosmos. The idea of the temen corresponds to the social experience of the Mesopotamians who after each destructive flood had to rebuild the dikes and the canals and to retrace the boundaries of the fields with the same dimensions. The world is conceived as ordered The table of surfaces included in the Smith Tablet includes
not only units that explain the surface of the iku and its submultiples,
but also multiples of it: one of 3 I have explained that the are basic Hebrew and Greek myths based on Mesopotamian and Egyptian traditions, in which the khowledge of the system of measures is presented as highly valuable, but extremely dangerous, since the wise master of measures ends by possessing the secret of divine wisdom and is struck down by the divinity as a competitor. This theme appears, reduced to its minimal core, in the biblical story of the Tower of Babel (Gen.11; 4-8), The builders say; “Come,let us build ourselves a city and a tower with its top in the heavens; let us make a name for ourselves lest we be scattered all over the earth,” and God observes: “This is the beginning of what they will do. Hereafter they will not be restrained from anything which they determine to do. Let us go down, and there confuse their language so that they will not understand one another’s speech. “ The notion that the Tower prevents scattering all over the earth may posibly be a reference to the fact that ziqqurat presents in concentrated form the measurements of the universe. I feel more confident about the possibility of a correct interpretation of the biblical reference to the confusion of languages; it seems to me that this is an obvious reference to the fact that in Mesopotamia knowledge was transmitted in a language, Sumerian, which after the year 2000 B. C. was comprehensible only to a few experts. Mathematical knowledge in particular was expressed in a purely Sumerian vocabulary, and did not progress in any appreciable amount after the end of Sumerian civilization. This last fact my not have been known to the authors od The confusion of languages is concrete experience to any reader of cuneiform texts; In particular mathematical texts are linguistically so ambiguous that Thureau-Dangin traslitterates them in Akkadian, whereas Neugebauer translitterates them in Sumerian. The statement of the Smith Tablet that its contents must be revealed only to those who are initiated to Wisdom indicates the mysterious and dangerous character of the metrological information. These remarks throw an important light on a problem of
Roman history. It has been observed that the Roman system of measures
contain elements similar to those of Mesopotamia and not found in Greece.
I have observed that the Roman system of landsurveying is based on sexagesimal
units, even though there is no known evidence that the Romans ever computed
sexagesimally. The minimum unit of surface is a square with a side of
60 feet. The Romans considered that cities could not be settled and lands
could not be cultivated unless one constructed a grid of roads, real or
imaginary, dividing the area into rectangular elements. This pattern had
in its middle a rectangle, the
Measures
of the kigal Etemenanki Length and width by tested result:
60-60-60 the length; 60-60-60 the width, by the suklu cubit. To
obtain the whole: 3 (times 3) = 9; 9 times 2 = 18 (sata). Since you do
not know ( the meaning of) 18: (it is) 3 PI of grain-seed by the little
cubit. Kigal Etemenanki; height as length and width. The area of the
kigal is divided into 9 squares with a side of 60 cubits or a
subban.
The area is also described by the volume of grain needed to sow the
area; the amount is 2 sata for each of the nine squares. since there are
several kinds of saton, the 18 sata are defined as 3 PI (the term is the
equivalent of the Hebrew ephah) or talents of 36 double qa each.
Hence it is a matter of a saton of a saton of 6 double qa. Since the PI
is a cubic foot unit it is necessary; to define the unit of length by
which it is calculated; the barley cubit is here called the little cubit.The description of the kigal is reported as follows: In this second calculation the cubit is 1½ barley
cubit; this longer cubit is callet “great cubit” and The second time the linear unit of measurements is the
GAR or double cane of 12 great cubits. Sinse there are 10 GAR on each
side, the are is divided in 100 squares called The ziqqurat Etemenanki was constructed so as to enbody the essence of the system of measures, and the Smith Tablet expands the idea by bringing in ceveral types of units. For this reason the interpretation of the Smith Tablet and of the architecture of the ziqqurat has been a hopeless task for those who reject the old school of metrology. Neugebauer who takes an ambiguous position between the old and the new school, never mentions the Smith Tablet even though he deals with problems for which this text is most relevant. In dealing with units of volume and weight and with seeding
rates, I shall discuss again some aspects of the metrics of the Smith
Tablet; but here I may observe that some Old-Babylonian boundary stone
1 The formula is the same as that used in the Smith Tablet. The amount
of seed is 30 double qa for an iku; both the Weissbach and those who followed him, in order to explain the different units used in the Smith Tablet, ascribe them to two independent systems of measures, a “newer” one and an “older” one. The “older” system would have been the one used before the reconstruction of the Tower of Babel. That the ziqqurat was smaller and was later enlarged, changing the side from 120 barley cubits to 120 great cubits, is a fact, but the date of this enlargement should have been determined by an archeological investigation. There are tablets in which Assyrian and Neo-Babylonian kings boast of having reconstructed the ziqqurat after it had been totally destroyed, but one cannot trust any of them since more than one claims to have been the true builder. According to Unger the Smith Tablet would refer to the ziqqurat built by Nabopolassar, whereas according to Weissbach it is that of Esarhaddon. Meissner and Walter Schwenzner, having noted that the Smith Tablet uses units found in the oldest documents of Mesopotamia, arrive at the opposite conclusion; the Smith Tablet does not describe the ziqqurat as it existed in Neo- Babylonian times, but an older ziqqurat which at the latest belongs to the Kassite period. In 1930 Dombart has tried to reconcile the different views by claiming that the Smith Tablet describes two ziqqurats, the newer and the older at the inside The truch is that the system of measure did not change throughout the history of literate Mesopotamia. As to reconstruction of the ziqqurat, the only thing certain is that it had the dimension of 180 barley cubits at least as early as Esarhaddon.
The only one who has called attention to this fact is
Alfred Schott in a footnote When the epic of Gilgamesh became known, scholarship had gone over to the new school of metrology, and the opposition to the image of the metric cube prevented a full understanding of the texts. How could the Ark have been built as a metric cube, if the idea of linking length, volume, and weight was first introduced by the French Revolution! In the Bible the Ark is called tebah, a term that Septuagint
renders by kibwtov”, “box,” and Josephos, followed by the
Vulgate, as The ship that thou shalt build; has been considered incomprehensible. Later I shall explain the therm
O Enki, master over prudent words, to thee I will give praise.
The link between This very well, the Pulal,
was its well of sweet water, The Ark in the story of the Flood has the shape of a
cubic
The division of the Ark into 7 decks of 9 rooms each may have a connection with number magic. W. H. Roscher has written several studies on the mystical meaning of the couple of numbers 7 and 9 in Greece, and Father Franz X. Kugler has dealt with a similar symbolism in Mesopotamia. But these numbers may have a metrological explanation which I consider the original one. In metrics a cube is often divided into 64 parts by dividing each edge into 4 partes; this originates the discrepancy diesis between the division of a cube into 64 partes and its division into 60 parts according to sexagesimal computation. The discrepancy is reduced to a leimma when the 60 parts brutto are calculated netto and become 62.5. The nomber 63 may be a compromise between the figure 62.5 indicated by metrics and the figure 64 indicated by geometry. That one aimed at dividing the Ark into 60 parts is suggested by the total volume of 6,000.000 cubic cubits netto. The Babylonian priest Berossos in the Seleucid period transmitted a different version of the story of the Flood in which the Ark is described as 5 stadia by 2 stadia. Nobody has tried to interpret these data even though the figures are eloquent. In Mesopotamia it was common to express volumes by the units of surface assuming that they have the height of a cubit; this explains why Berossos does not mention the height. Interpreting the Greek term stadion of our sources of Berossos’ narrative as a equivalent of US and giving to US its most common value of 720 cubits, four minutes of march, the volume of 5,184,000 cubic cubits. This is the volume that one would obtain if the volume of 1,728,000 cubic cubits by the great cubit is converted into cubic cubits by the barley cubit, using the conversion rate 1:3 instead of 1:33/8, as it was often done for the sake of simplicity in reckoning. In the biblical version (Gen.6:11) the Ark has a rectangular
surface, 300 x 50 cubits, but the area is the same as that of the Ark
in the Epic of Gilgamesh. The surface is an From essay to essay up to the recent books by Parrot on the topic of the Ark, it is repeated that the biblical Ark has the same proportions of length and width as the Ark of Berossos; but the relation 1:6 is not the same as that of 2:5. The Bible states that the Ark is divided into cells, but does not state their number. But since the area is divided into 6 squares and the Ark has 3 decks according to the Bible, one would expect 18 cells; but the cells must have been the result of a further subdivision by 5, since the commentaries of the Midrash speak of 90 or 900 cells. The height of Noah’s Ark is only 30 cubits, 1/4 of the height according to Mesopotamian tradition. Possibly there is a metrological explanation of this difference; if a formulation of volume as that found in Berossos was interpreted by making the US equal to 360 cubits (single stadion or double minute of march), the result would be a reduction of volume to one fourth. My interpretation of the metric data concerning the Ark
reduces to simplicity a question on which there has been spilled a great
quantity of ink. In defence of the value of traditional metrology, I may
quote the interpretation offered by Haupt who contributed to the establishment
of the new school. The question of the Ark was his favourite topic, and
his position is summed up in the essay Concerning the relation between Ark and ziqqurat, Haupt
concludes that the ziqqurats represented ships turned upside down and
were a reminder of “the vessel that brought the Sumerian invaders
to the northern shore of the Persian Gulf. “ But the Egyptian pyramids
too represent inverted ships. Ark, ziqqurat and pyramid would be instances
of a universal symbolism of the ship, of which the ship of the Argonauts,
the solar ship of the Egyptians, and the
The dimensions are expressed in GAR of 12 barley cubits.
The first storey has a surface of 15 x 15 with a height of 5½,
slightly more than one third of the total height. The second story is
only l GAR narrower all around and is 13 x 13 with a height of 3. the
following four storeys are only l GAR high and form a separate unit; the
surface of the lowest one is that of the older ziqqurat, 10 x 10 GAR or
120 x 120 cubits (surface of and In the Bible the statement of the dimensions of the Ark
is followed by a line (Gen.6: 16) which is considered incomprehensible:
“make a It becomes possible to understand the quoted line of
the Epic of Gilgamesh, “cover (the area) with a The biblical verse “make a 14. Before considering the dimensions of other ziqqurats it is expedient to consider in general the application of Newton’s method in Mesopotamia. The condemnation of Newton’s method by Mesopotamian scholars is based on preconceived assumptions about the non-rational charater of Mesopotamian thought. The use of the method was condemned in relation to Greece for the same reason; as a prominent Greek archeologist put it to me in a nutshell: “Obviously the Greeks cannot have thought like Newton. “ This has created not only a distortion in the interpretation of ancient cultures, but also a serious handicap in the techniques of archeological investigations. Newton, from a single Mesopotamian brick that had reached him, tried to guess the unit of length used in Mesopotamia, but today Mesopotamian archeology cannot use the size of bricks as a principle of chronological distinction because the metrics of bricks have not been studied. It is obvious that one cannot establish a typology of bricks unless one knows the metric units by which they were calculated. Neugebauer and Sachs have published tablets from which it appears that there were typical proportions in the size of bricks, but no attempt has been put forth by them or by anybody else to connect this information with the archeological material. Oppert, Dieulafoy and Aurès had reached the conclusion that most usually a brick is one foot long; and in fact in the first millennium B. C. one finds most commonly bricks of the length of a barley foot, followed in order of frequency by bricks of a wheat foot. One the basis of this conclusion one should try to establish which proportions of the three dimensions were favored in each period. From archeological reports of sites dating from the second half of the third millennium B. C. , one can discern that at least thirty different sizes of bricks were in common use at some time within that span of time. On the basis of my classification of the modules of length one can easily see that most of the bricks have as their major dimension either a foot or a cubit (1½ feet), the foot having a module of 15, 16, 17 or 18 basic fingers or being an artabic foot of 162/3; one can, however, find bricks calculated in fingers of any of these feet. I shall quote an example from one of the earliest periods for which there are available reports. In Stratum IIIb of Uruk (Proto-literate period) there were found bricks of the following dimensions in cm. 16 x 6 x 6 17 x 7.5 x 7.5 19 x 8 x 8 24 x 11 x 10 One can see how the first three types support my interpretation: the number of fingers must be the same while the module of the foot changes. I presume a size of 10 x 4 x 4 fingers; the first finger, 15.4 mm. , is obtained by dividing by 30 an artabic cubit; the second, 17.34, is finger of trimmed oil foot, and the third, 19.92, of natural wheat foot. As one can see, when the bricks are measured in centimeters and the figures are rounded to the next centimeter, the interpretation becomes a difficult task. My contention is that with the table of possible fingers I have drawn, the excavators could arrive at an exact figure. The fourth type of brick appears to have been calculated as 14 x 6 x 6 fingers of the second module listed above; by such a proportion 3 bricks on their long side equal 7 bricks on their short side. As a further example from the early period, I may mention bricks used in the construction of the so-called White Temple of Uruk: 26 x 11 x 6 29 x 12 x 8 These bricks probably are calculated as 15 x 6 x 4 fingers, the module being the trimmed oil foot and the natural wheat foot. The size suggest sexagesimal computation: 4 bricks on their longest side equal 15 bricks on their shortest side and 10 bricks on the intermediate side, with a total of 60 fingers in each case. To quote an example from an even earlier period (Obeid Period), the bricks used in the construction of Temple VI and Temple VII at Eridu are reported to have the following dimensions in cm: 23 x 13 x 6 43 x 13 x 7 28 x 23 x 6 23 x 17 x 6 42 x 18 x 6 28 x 23 x 6 23 x 30 x 6 25 x 21 x 6 27 x 21 x 6 Since the figures are rounded to the centimeter, the longer dimensions provide a more reliable datum. It seems to me that one can conclude with some amount of assurance that the most common dimension is 23.1 cm. or the half of the artabic cubit of 462 mm. I would explain the other dimensions by assuming that the artabic cubit in some cases was divided into 24 fingers of 19.6 mm. and in other cases into 30 fingers of 15.4. If this interpretation is correct, it would follow that sexagesimal computation was used as early as the Obeid Period. The issue is of such importance that further tests are well in order. I have limited myself to suggest a method by which one can strive towards a taxonomy. The problem could be approached by taking new measurements of the bricks, since the data provided by archeologists are often vague; furthermore, one can better express by proper fractions the size of the bricks when one knows which sizes one can expect. I suspect that whereas the efforts to create a typology on the basis of absolute sizes has failed, one may find that certain proportions expressed by the number of fingers, even though the length of the fingers may vary have prevailed in given periods in given areas. If this proves true, a rigid criterion for dating archeological materials would become available. The study of architectural dimensions would be particularly useful to trace cultural connections and breaks; but, whereas one has spent a great deal of time and patience in measuring skulls in order to construct fanciful racial theories, nothing has been done with metrics. In my opinion a completely new word of documentation would be opened if one measured the dimensions of every regular object and the volume of all vases. My assumption is that in general any manufactured object conforms to a standard. But limiting the horizon to purely architectural data,
I may note that E. Heinrich The buildings of the earliest strata of Tepe Gawra (early
Obeid Period, before the introduction of the potter’s wheel) prove
not only that the dimensions of important buildings were calculated in
round figures and that, hence, Newton’s method is valid, but amazingly
prove that there are buildings calculated by the higly refined reckoning
by the Stratum XII, White Room 12.30 x 11.75 m. Stratum X, Temple 12.30 x 11.15 Stratum IX, Temple 13.00 x 11.40 The significance of these figures is confirmed by the largest structure of Stratum XI which is 11.50 x 11 50. There cannot be any doubt that the three buildings are calculated as 40 x 42 trimmed basic feet: 296 mm. x 40=11.84 m. ; 296 mm. x 42 =12.43 m. For buildings that are perfectly square it is not equally easy to determine the module of foot used. In Stratum XI there is a Temple measuring 9.75 x 9.75 and in Stratum XIA a Temple, 8.40 x 8 25 m. It seems to me that a likely explanation of these dimensions is by the natural oil foot of 281.25 mm. ; 30 feet = 8.43 m. ; 35 feet = 9.84 m. The metrics of the acropolis of Stratum XIII can be interpreted with reasonable assurance. The façade of the Eastern Shrine is reported to be 20.50 and may be 70 feet (20.72 m.); the facade of the Central Temple is reported to be 14.50 m. and may be 50 feet (14.80 m.) The Northern Temple presents a highly refined architecture in all details; it is a trapeze with the two parallel sides of 8:13 and 8.66 m. , and the other two of 11.80 m. One can presume a dimension of 28 (8.29 m.), 30 (8.88 m.), and 40 (11.84 m.) feet The two internal walls define an area of 25 x 12 feet. The few data available for buildings of the Protoliterate period in Uruk reveal a specific pattern and hence can be interpreted with considerable assurance. Terrace in Eanna 22.50
x 18 30 m =75 x 60 artabic feet The variety of foot changes but the preference for the relation 75:60 (5:4) is a definite feature. The unit could have been a cubit instead of a foot; in such a case the dimensions would be 50 x 40, 50 x 120, 50 x 40. Quite striking is the fact that the dimensions of the White Temple and of its Central Hall have their perfect equivalent in the outer and inner dimensions of Temple C in Eanna: 22.30 x 17 50 22,20 x 17 18.70 x 4.85 18.20 x 4.60 The inner measurements ot the two temples are 64 x 16 trimmed basic feet with a proportion 4:1 The coincidence of the figures proves that the excavators have been accurate in reporting the data. The shift from artabic foot to trimmed basic foot is also indicated by the Limestone Temple of Stratum V and Temple C of Stratum IVa which are similar in architectural outline. The Limestone Temple has a hall measuring 62 x 11.30 m. , or 210 x 40 trimmed basic feet (62.16 x 11.84 m.) Temple C has outside dimensions which seem to be 56 x 22 m. ; most likely they are 180 x 70 artabic feet (55.57 x 21.55 m). The occurence of the factor 7 both buildings is worthy of notice. The calculation of buildings by the trimmed basic foot and by the artabic foot in the Proto-Literate period suggests that one still calculated volumes by the basic talent and by the basic pint, and not yet shifted to the sexagesimal reduced pint. The trimmed basic foot is the edge of the cube of the basic talent netto, and the artabic foot is the height and the diameter of a cylindrical vase of the same volume. I have tried to trace the earliest occurence at Tepe Gawra of the barley foot, the typical foot of Mesopotamian metrics. As far as I have been able to determine from the published reports the earliest occurence is in Stratum IV, which belongs to the Third Dynasty of Ur (ca.2250 B. C.). In the main construction there is a cella 7.9 x 6.7 m. ; this room is almost certainly calculated as 24 x 20 natural barley feet (theoretically 8.09 x 6.74 m.). The cult chamber is reported to be 12.8 x 10.7 m. and hence 38 x 32 feet (12.81 x 10.78 m.). Other dimensions of details of the same complex may be explained by the natural barley foot.
Eridu 50 x 50 m Kalah 51 x 51 If the reports are accurate one must conclude that the
first is calculated by the trimmed barley cubit (499.4 mm.) and the second
by the natural barley cubit (506.25 mm.) and the with a side of 100 barley
cubits, which has a surface close to that of the Roman In the region Eanna of Uruk there is a high terrace with rounded corners, belonging to Stratum I3, with a dimension of 50.40 x 45.50. The size is the same as that of the two ziqqurats just mentioned except that one side is 90 natural cubits long. The explanation of this is that the surface of the ziqqurats was calculated also according to the amount of seed, as it appears from the Smith Tablet. In many documents the calculation of surface is made purely by amount of seed. The relation between units of surface and amount of seed is fixed but there is a certain flexibility in this relation, as I shall explain in the section “Seeding Rates. “ There was a flexibility in order to obtain round figures in the volume of seed for each unit of surface. Therefore rates of seeding differ as much as 8:9. This is the reason why in the Smith Tablet there is included a table stating the relation between units of seed and units of surface. In the case of this high terrace probably one took only 9/10 of an acre as the surface in order to obtain a standar ammount of seed, which most likely is 5 sata. A ziqqurat calculated like the Tower of Babel but smaller,is
that of Kar-Tukulti-Ninurta, measuring 31 x 31 m. or 60 natural barley
feet (a Aurès and Dieulafoy have come to the conclusion that in constructions one measured by rods of 10 feet as in the rest of the ancient world. My explanation of this fact is that theoretically one planned buildings by canes of 6 barley cubits (3 0375 m.) and then in the execution of the project one used a rod of 10 artabic feet, which is 3 078 m. The ziqqurat of Dur-Sharrukin measures 43.10 x 43.10 m. according to report. The figure can be trusted because it occurs in one of the dimensions of the ziqqurat of Ur, which is 62.5 x 43. The same dimension occurs in the Court of Nannar, to the side of this ziqqurat, which is 65.7 x 43.6. In turn the major dimension of the ziqqurat of Ur is repeated in the ziqqurat of Assur, 62.23 x 61.50. The dimensions of these constructions are in artabic feet: 140 = 42.59 m 200 = 61.56 210 = 64.64 The ziqqurat of Dur-Sharrukin is a square of 140 x 140 artabic feet; the factor 7 indicates that one calculated the diagonal of the square by the relation 7:10. A square of 210 x 210 artabic feet is represented by the courtyard of the palace of the Kassite kings at Dur-Kurigalzu. The same reckoning by multiples of 7 occurs in the ziqqurat of Nippur reported to be 57 x 38.4 m. It appears calculated as 205 x 140 trimmed oil feet; the theoretical dimensions would be 56.79 x 38.84 m. The two sides are in a relation 5:4, a proportion that occurs in a striking manner in the Proto-literate monuments of Uruk. The same foot occurs in a construction of the Proto-Literate period, the temple on high terrace of Tell Brak, reported to be 27 x 22 5 m. or 100 x 80 feet (theoretically 27.75 x 22.2 m.). Here too the proportion is 5:4. Oppert has shown that in the Neo-Babylonian period the cane of 7 cubits was a standard unit of measurement and that surfaces are calculated by squares of this cane. This cane is well known from the Bible. I have discussed the advantages of this unit in relation to the Egyptian royal cubit of 7 hands. A cane of 7 natural barley cubits is 3.5437 m. , which is almost exactly a unit of 12 trimmed basic feet, 3.5513 m. Hence it is possible that the cane of 7 barley cubits was a practical unit that allowed abstract sexagesimal computations by the trimmed basic foot. Dieulafoy observed that the Persian palaces of Persepolis are calculated by the factors 10, 7, and 6, and properly intimated that the same reckoning was typical of Mesopotamia. The calculation of the diagonal by the The twin ziqqurats of Anu-Adad at Assur have a reported dimension of 36.6 x 35.1 m. , which may be explained as 125 x 120 trimmed basic feet (theoretically 37.00 x 35.52 m.). It seems that the trimmed basic foot here is slightly short, as it often happens throughout the history of the ancient world. These ziqqurats were reconstructed on a smaller basis by Shalmaneser III (859-842 B. C.); it is not clear from the report whether they were given a side of 24 or of 26 m. Possibly the excavators were confused by the use of the proportion 20:21; one may risk a guess that the dimensions are 80 and 84 artabic feet (24.60 x 25.84m.). I have already dealt with the high terrace in the region Eanna of Uruk; this high terrace was later covered by a ziqqurat, the dimensions of which are tentatively estimated as 56 x 52 m. Possibly by knowing that these dimensions may be in a relation 21:20, it will be possible to obtain a more precise estimate. Finally, one must consider the ziqqurat of which the most impressive ruins remain today, that of Borsippa. Sir Henry Rawlinson reported exact data about four levels of it, but Koldewey affirmed positively that he could not see any trace of storeys even though the ruins are 47m. high. However, Rawlinson’s figures may be explained in terms of trimmed oil feet:
I have examined all the available trustworthy data about the size of ziqqurats, with the exception of those about the ziqqurat of Mari. I think that in this last case the report by Parrot is too vague to allow an interpretation.
Many of the fancies developed in relation to the pyramids
have been applied to the ziqqurats. One has spoken of tombs or of funerary
architecture. The notion that they are astronomical observatories has
been accepted by Parrot; Günter Martiny (ZDMG, 92 (1938), 572-578)
has tried to interpret the Smith Tablet so as to prove that the Tower
of Babel was constructed in order to aim at specific astronomical points.
Some have spoken more vaguely of an altar of of a divine throne. Parrot
concludes his volume on the subject by declaring that the ziqqurat One finds in the texts some specific statements about
the meaning of the ziqqurat. The Sumerian regent Gudea mentions the construction
of a ziqqurat that has reached the final form of seven superimposed storeys
(Cylinder A, XXXI). This ziqqurat is compared to the The Epic of Greation (VI), speaking of the construction
of the ziqqurat of Babylon, repeats that it is like the We know from archeology that the ziqqurat developed from the high terrace on which there was built a temple; hence the ziqqurat was originally nothing more than an embankment of land. The interpretation of the ziqqurat as cosmic order extending three-dimensionally to heaven must have developed from an earlier ziqqurat with only one level and conceived rather two-dimensionally. The connection of the ziqqurat with the story of the Flood suggests that the high terrace was a place of refuge in case of flood. As Meissner observes, after a flood it was necessary to proceed to a new landsurveying; the high terrace or ziqqurat may have provided a reference point and a standard of measure. The ziqqurat is like the temen, the buried foundation-block which provides the data by which a building can be reproduced after destruction. The temen is also a force for the preservation of a building, just as the ziqqurat is a force for the preservation of a city, so much so that a conqueror takes care to demolish it. Texts indicate also that the ziqqurat was a symbol of the permanence of the social order and of laws all standards of measures were in the ancient world. Concerning the ziqqurat of Babylon we find not only that it was called temen in its official name, but also that Nabopolassar built for it a temen of 30 cubits. Hence the temen can consist not only of an inscribed stone, but also of a measured space reproducing in small size the dimension of the total ziqqurat (the ziqqurat in question has a dimension of 180 cubits). The relation that the temen has with the ziqqurat, the ziqqurat itself as temen has with the cosmos. The ziqqurat was an exalted example of the Jeremiah in his prophecy of doom directed against Babylon,threatens:
“O you who dwell by many waters, rich in treasures, your end has
come, the cubit |