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UNITS OF LENGTH


1. Because of the uncertain results of the application of Newton’s method in Mesopotamia, Oppert was hoping to find the equivalent of the Egyptian measuring rods which allowed to verify in a final manner the value obtained by the study of Egyptian monuments. But a discovery of the kind is not likely in Mesopotamia, since the climate and the soil is not favorable to the preservation of these objects and since richly furnished tombs are not typical in the area. It was an unexpected boon when in 1880 the excavation of Lagash by Ernest de Sarzec brought to light a group of statues of the Sumerian regent Gudea (2050-2000 B.C.) of which two (Statues B and H) present him holding on his knees a rectangular writing tablet on which there is placed a stylus and, along the side opposite the body, a graduated measuring rule. The two rules are identical, but that of Statue B is broken at the tenth finger. One of the tablets is empty, but on the other (Statue B) there is drawn the plan of a building, The statues bear Sumerian inscriptions concerning the dedication of a temple by Gudea. The statues are today the most widely known example of Sumerian art.

Seated statue of Gudea, 2150–2100 B.C.; Neo-Sumerian period. Probably Tello (ancient Girsu), southern Mesopotamia
Diorite; H. 17 3/8 in. (44 cm)

Metropolitan Museum of Art, New York

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 la plus grande diligence according to André Parrot, whereas to me it is shockingly vague and imprecise, particularly in relation to architecture. As to the rule, Heuzey reported that, considering it “outside any system” of metrology, he found it composed of sixteen fingers. He reported in round figures that the total length is 270 mm. and that the graduated part is 265. He excluded from the length of the rule one end beyond the graduated portion, but did not exclude the other end, which he interpreted as a sixteenth finger. He gave evidence of the proper spirit by not making any statement about the divisional lines.

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 Sumerian Grammar is the one most currently consulted by scholars. He reports (ZA 23 (1903), 113) that while in London he examined the rule and gives the length of each finger; he concludes that the fingers have an average length of 17 mm. He excludes from the reckoning one end of the rule, but includes in it the other end as a sixteenth finger. Even though 17 x 16 = 272, he concludes that the rule is 270 mm. long. Reading his report one would conclude that he examined in London some plaster reproduction of the rule, and in fact many Mesopotamian collections possess a full-size reproduction of the statues with the rule. But since his figures are most astounding, I was forced to engage in a little detective work and found that in reality he measured the photograph published in the report of the excavation; the photograph is about natural size, but slightly enlarged.

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.

2. Metrologists of the new school did not pay any attention to the subdivision of the fingers. Haupt refers to it incidentally by the incorrect statement that “some are divided into sixths.” Only the first finger is divided into sixths, leaving one undivided finger between divided fingers, it is followed by a finger divided into fifths, one into fourths, one into thirds and one into halves. In total, out of fifteen fingers, five are subdivided. The finger divided into sixths has a sixth further divided into 2 parts, or twelfths, and a sixth divided into 3 parts or eighteenths of finger. Aurès properly assessed the meaning of these subdivisions of the finger: they have the purpose of allowing to read the plan of the building according to a scale. But he drew the false conclusion that the rule does not give any absolute measure, but only a proportional scale. The correct inference is that the rule is presented in the statues with the very purpose of giving an idea of the size of the building, the plan of which appears in the tablet of Statue B; this explains why such minute divisions are drawn, but are at the sime time drawn so inaccurately as to their mutual spacing. The number of the subdivisions by itself must have given an indication of the scale. The Egyptologist Borchardt, who has done valuable work in dealing with the metrology of the Pyramids of Gizah, assumed that the scale must have been a standard one. He examined the plan of a building drawn on a tablet found in Babylon and concluded that it was on a scale of 1:360 and from this concluded that the rule of Gudea probably was calculated for the same scale. However, he should have tested his interpretation on the plan for which the rule of Gudea was intended, the plan of Statue B. In my opinion a test confirms Borchardt’s hypothesis.

Plan of the Girsu temple in the lap of Gudea’s seated statue.

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.

3. There is a large body of Mesopotamian maps and plans. Plans of fields and buildings were attached to contracts; at times diagrams of the fields were inscribed on the boundary stones (kudurru). A few maps of cities have been considered by archeologists in relation to their excavations. A general survey of these documents would be highly desirable; there is an essay on the subject by Unger who unfortunately is not interested in determining the metric facts, but in proving that in Mesopotamia one saw the world with an ethos different from ours. The metrology of these documents would reveal much about techniques of landsurveying and of construction. In my opinion planning of land reclamation was the most telling social activity in Mesopotamia.

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 Isis, but received none. It seems to me that the division up to 1/15 of finger in Egypt is the counterpart of the division up to 1/18 in the rule of Gudea. The explanation is that a minute of march was calculated in Egypt as 150 cubits (525 x 150 = 78.75 m.), whereas in Mesopotamia it was calculated as 180 cubits (506.25 x 180 = 91.125 m.).

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 iugerum is composed of two squares (actus) with a side of 120 feet; the iugerum castrense is a square with a side of 180 feet. On the other side one has glossed over the current use in Mesopotamia of the acre or square with a side of 100 cubits, similar to the Egyptian aroura. One is so much under the influence of the notion that sexagesimal computation is a racial trait that Thureau-Dangin, having found in a tablet of Assur a tablet of itinerary distances with a UŠ, “stadion,” of 600 cubits, merely emended the figure and thereby missed the significance of the document. In this tablet the beru, double hour of march, is divided into 30 UŠ quadruple minutes, which in turn are divided into 5 ašlu, “cord,” of 10 GAR, double of the qanu of 6 cubits The lowest unit is the sixth of finger called “grain,” as in Arab metrics. We have seen the sixth of finger in the rule of Gudea.

4. For some peculiar reason nobody has linked the details of the statues with what Gudea narrates in an inscribed cylinder (Gud. Cyl. A, lines 4, 7-5, 10). Gudea relates that he had a dream in which a man ordered him to build a temple; then a woman who held in her hand a tablet and a stylus performed thoughtfully some calculations and was followed by a man who presented another tablet with a plan. Apparently the Statue H that presents an empty tablet portrays the tablet on which the abstract calculations are performed; since on this tablet there lies a rule as on the tablet with the plan, it follows that the calculations concerned the dimensions. One can draw the conclusion that in Mesopotamia there was a division of roles between the mathematical planner and the practical architect. This would allow to explain one of the great difficuties which has been met in applying Newton’s method. In mathematical texts the unit is the barley cubit adapted to a system of sexagesimal multiples and submultiples, but buildings appear most often constructed by foot units and according to decimal reckoning. As Dieulafoy noted: “The cubit was a sort of legal standard. . . . In practice architects and masons preferred to count by feet. “ It has been noted that both in the Mesopotamian and in the biblical story of the Ark there is a division of roles, by which a god or God gives the general dimensions to the builder.

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 (qaneh ha-midah)” (Ex.40:3). This is significant since the major Mesopotamian gods are often presented holding in their hands a measuring rod and a reel of line In my opinion this image must be linked with the portrayals of kings holding measuring instruments; further, in some documents kings boast of having performed themselves the measurements for the construction of a building. I would draw the tentative inference that landsurveying was originally performed by the king and that this was the origin of the concept of the divinity as the architect of the universe. But E. Douglas Van Buren, in the volume in honor of Bedrich Hrozný (Archív Orientální 17 (1949), 434-450), tries to prove that it is not certain that what Mesopotamian gods hold in their hands is a measuring rod and a line; even though he may be right in dealing with specific details, what is particularly significant is that he should have gone to a great trouble to prove not conclusively, as he specifies, that it is not a matter of measuring instruments, but of “symbols of divine power.” This indicates how the idea of measure is repellent to the contemporary scholarly mind. Van Buren did not consider that the same type of images is found in Egypt; there can be no doubt that the objects held by gods and kings are measuring instruments, because they are so described in the corresponding texts.

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.”

5. After the discovery of the rule of Gudea the problem of the exact length of the Mesopotamian cubit should have been no longer a problem, not because the rule in itself was absolutely reliable, but because it allowed to interpret with certainty the Greek texts that report that the Babylonian cubit is a royal cubit of 27 fingers. There were some doubts about the exact interpretation of these texts, but these doubts can be removed once the value of the cubit is known with a good approximation from the rule of Gudea. Pliny (VI, 30, 121) in paraphrasing the texts of Herodotos uses the words pedes ternis digitis mensura ampliore quam nostra; this should have made certain that the term of reference is the Greco-Roman cubit or basic cubit, but instead it created perplexity among scholars. By collating all passages of Pliny that touch upon measures I have established that repeatedly he writes foot when he means cubit.

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 (Descent into Hades, 16) calls the basic cubit is called “vulgar and common.”

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:


anniti
šusi ša 24 šusi-meš

1 kuš ammat še-numun

“This is the finger of which a 24 finger-mass
(is) 1 cubit, cubit of seed-grain”

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.
trimmed  499.408. 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

6. Scholars of Mesopotamian metrics consider themselves less fortunate than those of the Egyptian ones, for whom the basic problems have been solved by such operations as the measuring of the Great Pyramid; but actually the case is the opposite because a similar quadrangular construction, the most famous monument of Mesopotamia, the Tower of Babel, has been measured and furthermore there are unequivocal cuneiform documents giving its dimensions, whereas no Egyptian text gives the dimensions of any measurable pyramid.

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 fast quadratisch. The reported dimensions are 86.10 and 85.90 x 77.30 and 79.00 m., but mention is made of a socket protruding 1.90 m. all around. As usual a great number of detailed dimensions are provided, but they are referred to a unit called the “stone” that keeps changing value. It is a case of not seeing the forest because of the trees; the most interesting datum has not been clarified. One may wonder if it was a case of a near-square of 160 x 172 trimmed barley feet (theoretically 79.905 x 85.898 mm.), with a diagonal of 235 (exactly 234.913).

Not all scholars approved of Koldewey’s ideas; the Orientalistische Literaturzeitung referred to him as Narrenschiff der Assyriologie, and no more emphatic reference could be made in the German language to his mental jumble. But often responsible scholars are withdrawn and do not care about the power politics of learned societies, so that here again it was Oppert who had the task of fanning the fire of indignation at professional meetings. Concretely Oppert criticized Koldewey’s plan of attack on the ruins, on the basis of an interpretation of Herodotos’ report; this later unwittingly had unfortunate results for the evaluation of Herodotos’ statements, as I shall explain below. Oppert was so successful that by 1903 there was not one Assyriologist willing to work under Koldewey, and this was a serious problem since he was left a large staff of architects, but not one person who could read cuneiform texts for him. The situation changed after Oppert’s death, but usually linguistic collaborators fell off with Koldewey and in particular Weissbach was among the two or three who reacted acrimoniously. This feud affected in a specific way Weissbach’s view of linear measurements.

7. In Germany, particularly under the influence of Zimmern, there had been developed a mystique of Babylon as the holy city; it had a connection with non-academic tendencies, such as the convictions of those who wanted to erect Babylon against biblical religion, and the political program expressed by the Berlin-Baghdad railroad and the Kaiser’s visit to the holy places of Islam. Part of this mystique was the belief that Babylon had realized the ideal of the kolossal in the Wagnerian sense of the term, and Koldewey was truly the man to operate in kolossal manner. Personalities of this type have the advantage over normal people of displaying a tireless drive, and thanks to it for eighteen years mountains of rubble were removed from the ruins of Babylon. Zimmern had understood the structure and the importance of Mesopotamian metrics in the history of world culture, but had given an esoteric interpretation of them; for instance he claimed that sexagesimal computation was introduced because it corresponds to the number of times the apparent diameter of the solar disc fits into the arc of the sky. Zimmern had stressed that our method of time measurement is obviously of Mesopotamian origin, and this influenced Koldewey to try to introduce time recordings into the technique of excavation. However, out of this cloudiness some important concrete results were achieved.

The Tower of Babel was measured and it was ascertained that its basis has the following dimensions (in meters):

North 91.66 m.
East 91.52
South 91.10
West 91.44
————————
Average 91.43

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;.

North 61.10 m.
East 61.15
South 61.20
West 61.15
————————
Average 61.15
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 iku and a side of 120 barley cubits. There was a standard unit of surface, the iku, which had for side 10 double-canes of 12 cubits. This unit of 120 cubits, often called ašlu, “cord,” in the texts, is the sexagesimal multiple of the double cubit, which in turn is composed of 60 fingers. Calculating by the natural barley cubit of 506.25 one would expect a length of 60.75 m. for each side; the reported dimensions differ by only 0.40 m. , and would indicate a cubit of 509.5 mm. It may be that the cubit had been calculated slightly longer, or it may be that earthquakes and the sheer weight of the mass tend to spread the bricks to the outside. There was also an iku calculated by the great cubit, a cubit equal to 1½ barley cubits, and hence having a side of 180 barley cubits or 120 great cubits. This iku is frequently used since 180 barley cubits fit into the system of itinerary units, being one minute of march. The later Tower of Babel was calculated by this iku. As it has been observed, whoever rebuilt the ziqqurats. piously respected the dimensions, but changed the basic standard. I shall show that the dimension of an iku has a cosmic meaning. It does occur in other ziqqurats. If we consider the dimensions of the three best preserved sides as the reliable datum, they would indicate a cubit of 508.55 mm.

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 ex post facto by Friedrich Wetzel who was one of his main collaborators); Koldewey and his supporters, as for instance Andrae, reacted by asserting that Herodotos believed the tales told by his guides. That Herodotos was a gullible tourist is a legend repeated from book to book without being investigated; I have examined the matter in detail in relation to Herodotos’ visit of Egypt to conclude that he reported factually what he was able to see in a conducted tour of a highly policed state, and that he was deliberately misinformed by Egyptian priests who were concerned with Athenian policy in relation to Egypt. But apparently in Babylon there was no prejudice against foreigners and no restrictions on their movements.

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 ašlu, or 14,400 cubits of perimeter; King Nabonidus boasts of a similar activity and gives the figure of 20, and, since this unit usually corresponds to four minutes of march or 720 cubits, one arrives at the same figure. Nabonidus also states that the length has been prescribed from antiquity. Since these kings would not have mentioned a length less than the actual one, one may surmise that they reckoned by great cubits, so that the circuit would be 10,935 m.; hence the figure given by the kings may be less exact than that reported by Greek writers.

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 Herodotus’ Description of Babylon (this is the title of the Englisch translation), in which he does not bother to investigate any of the studies about the length of the cubit used by Herodotos in describing the monuments of Babylon (of which there are more than a dozen) or about the length of the Mesopotamian cubit, but draws from a cursory reading of classical dictionaries that in the ancient world the cubit could be either 444 or 495 mm. As to the stadion he gives the figure of 198.38 m. on the strength of Lehmann-Haupt’s article on “Stadion” in RE, an article which apparently he did not read since its author delves into the variety of stadia used in the ancient world. This is the kind of documentation used to prove that Herodotos’ data are unreliable and the product of irresponsibility.

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 ašlu and 1 subban, units of 120 and 60 cubits. King Nabopalassar too claims to have rebuilt the ziqqurat with a dimension of 1½ ašluby the correct cane of 12 cubits. “ The Smith Tablet too makes clear that the calculation of the side by units of 60 cubits was the essential element, and reports the length as 60-60-60. Given that there was a fixed tradition about the length of the basis of the Tower of Babel, it is not surprising that Greek authors reported the exact figure, a stadion

8. The dimensions of the ruins of the Tower of Babel, together with the Smith Tablet, could have solved most of the pending problems of Mesopotamian metrics, but they became the special preserve of Weissbach who dedicated the rest of his life to the interpretation of these data under deeply emotional circumstances.

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 Das Stadtbild von Babylon. He might have reasonably argued that an archeological excavation, the results of which are not integrated by a thorough study of the written evidence, is inconclusive; but he pressed the argument to absurdity by suggesting that nothing could be gained by the excavation of Babylon that could not be gathered from the study of cuneiform texts. As a sort of challenge he presented his own picture of the city of Babylon and predicted that nothing much would be added to it, unless new documents were discovered. He also added as a corollary point that the excavators were not searching for written texts in the ruins; he asserted, and repeated this assertion in later writings, that Koldewey, because of his concern with architecture, had refused to tear apart constructions, such as the city walls, in which one would have found inscribed tablets and cylinders in great number. Weissbach, who could see the world of science only in terms of war between two camps, erected an unnecessary opposition between the study of documents and archeological evidence.

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 Heraus mit den monumentalen Zeugen! (Come out with the monumental evidence !). But just when the monumental evidence became available in a conspicuous form, Weissbach rejected it.

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,” ammatu rabitu, was 555 mm.; it is often called the royal cubit. “

9. The Smith Tablet in lines 1-15 gives some dimensions of the temple surrounding the ziqqurat. In the part that is recognized as the main one, lines 13-24, it gives the dimensions of a cube called Kigal (Akk. Kigallu); these dimensions are given twice; the first time, lengths, areas, and volumes are calculated by the barley cubit; the second time they are calculated by the great cubit. Lines 25-35 describe details of ziqqurat such as chapels and stairs. The width and the height of each of the seven storeys of the ziqqurat are listed 36-42. Lines 43-44 and 48-50 mention the writer of the tablet (a member of a well-known family of scribes), the date (229 B. C. , in the reign of Seleukos II Kallinikos), the document from which the tablet was copied (a tablet from Borsippa, one of the surviving centers of the old culture), and the warning that the information must be revealed only to the initiated. In this closing section, there is inserted, lines 45-47, a table explaining units of surface that are submultiples and multiples of the area of the kigal.

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 numero, pondere, mensura, and the cube is the symbol of the metric system connecting length, volume and weight. The cube is the symbol and the standard of the metric system by which the world is born out of chaos. This is the reason why the most important element of the ziqqurat is the length of its side, which is a basic unit of length, and the surface of the base, which is the standard unit of landsurveying. I make the Mesopotamian notion of cosmic order less mystical than others would; it is an expansion of the operations of landsurveying and land reclamation that made land fit to be cultivated and inhabited in Mesopotamia. The ziqqurat of Babylon has the surface of a standard plot of land surrounded by a draining ditch, an iku.

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 iku, one of 3 x 6 iku, and one 18 x 60 iku. These units have no application in the construction of the ziqqurat, but indicate that the ziqqurat is a standard of the system land surfaces.

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 templum, which was conceived as corresponding to a cosmic templum embracing the entire universe. The correspondence of these Roman practices with Mesopotamian practices is too obvious to need further expounding. Since these Roman practices are of Etruscan origin, this is a further element in favor of the Oriental origin of the Etruscans. One can even surmise that the iter limitare, the band of uncultivated land that according to early Roman law must surround every field, is a substitute for the Mesopotamian water ditch.

I shall discuss the dimensions of the seven storeys of the ziqqurat in relation to the dimensions of the Ark. The lines dealing with the dimensions of the kigal are more significant for metrics. They read;

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:
The second time Measures of the kigal
Etemenanki. Length and width by tested
result; 10 GAR length, 10 GAR width
by the are cubit. To obtain the whole by the
amount of seed; 10 times 10=100 (musaru);
10 times 18 ( sheqels) = 30 (qa); Since you
do not know ( the meaning of) 30 (qa): (it is) 1 simid
for 1 iku by the great cubit. Kigal Etemen-
anki; length, width, height, by the great
cubit; each part agrees to 10 GAR.

In this second calculation the cubit is 1½ barley cubit; this longer cubit is callet “great cubit” and ammat are. The two terms ammat suklu and ammat are and translitterations of the Sumerian name for the little and the great cubit. The term ammat are means either “march cubit” or “multiplication cubit” ; if the explanation as “march cubit,” which is the current one, is correct, the reason for the term is that the ammat are has a multiple that fits into the system of itinerary distances: 120 great cubits make a minute of march. As Thureau-Dangin has observed, a great cubit is equal to 3 feet and is a step. It is believed that the term ammat suklu for the little cubit, is a repetition of two terms meaning “cubit” ; Oppert noticed that suklu occurs in contexts where the meaning “cubit” is expected. But I am more inclined to think of a Sumerian term meaning barley, like se and bulug ( Akk. buqlu). Where one finds suklu in the sense of cubit, one could compare it which the therm se’u, “grain” that is regularly used for qa se’u, “pint of grain. “ The main point is that the kigal is described twice by two different cubits, related as 1:1½. There is general agreement on this question, except that Father Deimel introduces a third cubit of 620 mm., a gratuitous creation of his, and Theodor Dombart calculates by four different cubits. The reason why two different cubits are used is clear; the older ziqqurat had a side of 120 barley cubits, and one wants to stress that the proportions have been preserved in the more recent ziqqurat, but calculating the side by 120 great cubits. The surface would be called iku in either case.

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 musaru; the musaru, “enclosure, orchard, cultivated field,” is a common agrarian unit equal to a square with a side of a GAR. The amount of seed is 18 sheqels per musaru, and the total is 1800 sheqels or a simid which is a talent unit equal to 30 double qa. The fundamental point in these calculations is that the sheqel and the qa of the second reckoning are of the type called royal and they are larger according to the cube of the great cubit. The texts makes clear that the volume of seed of the second reckoning is calculated ammatum rabitum, “by the great cubit. “ This is a point that Weissbach and all the supporters of the new school could not admit, and therefore they have thrown the interpretation of the text into a state of total confusion.

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 (kudurru) on which there is inscribed the area of the fields thy enclose, define the units used by the formula;

1 iku 30 (qa) ammatum rabitum

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 qa and iku are calculated “by the great cubit. “

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.

11. Since followers of the new school totally confused the rather simple question of the size and shape of the Tower of Babel, it has not been possible to see that it has the same dimensions of the Ark in the story of the Flood. According to the version contained in the Epic of Gilgamesh ( Tablet X I) the Ark is a cube and has the same dimensions of the kigal Etemenanki; it is described as having the surface of an iku with width, length, and height of 10 GAR.

The only one who has called attention to this fact is Alfred Schott in a footnote (ZA 40 (1931), 15 n.), in which he also observes that the Ark is divided into 7 decks like a ziqqurat and that each level is divided into 9 rooms, which correspond to the formulation of the Smith Tablet by which each side of the iku is composed of 3 segments of 60 cubits so that the entire area is divided into 9 squares. But Schott considered his association of Ark and ziqqurat as a cube as too daring and ended his statement with a qualification that is obscure to me, but which substantially means that what he said must not be understood literally. Two years later (ZA 42 ( 1933), 140 n. I) he took a more conventional position by trying to interpret the text of the Gilgamesh epic so as to understand that the Ark has the shape of an inverted trunk of a pyramid and hence somehow resembles a ship

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 lavrnax, “box, trough. “ Most linguists link tebah with the Egyptian db’t, “chest, box, coffin. “ The Bible calls tebah the Ark of the Covenant which, according to my interpretation, is nothing but an empty rectangular box corresponding to a unit of measure and representing the divinitey as numerical order of the universe. Interpreters have had difficulty with these lines of the Gilgamesh Epic:

The ship that thou shalt build;
Let its dimensions be measured,
Let its breadth and length be proportioned,
Like the apsu, cover (the area) with a sassu
The last line;
Ki-ma ap-si sa-a-si su-ul-lil-si

has been considered incomprehensible. Later I shall explain the therm sassu, “firmament,” but here I shall concentrate my attention on the fact that the Ark is “like the apsu.”

Apsu is the sweet water, which is identified with the god En-ki, “Lord of the earch. “ Enki is the god of rational order, mathematics, legal science, and technical crafts. A Sumerian hymn eloquently addresses him by these words:

O Enki, master over prudent words, to thee I will give praise.
Anu thy father, pristine king and ruler over an inchoate world,
Empowered thee, in heaven and earth, to guide and form.

Apsu is creativity, rational order, and more specifically the numerical order of the universe; several scholars agree with this interpretation or approach this interpretation. In the Temple of Solomon the apsu was represented by the Brazen Sea. a tank of water of a given volume; the Brazen Sea on one side is to be compared with the Ark of the Covenant and on the other is similar to the apsu ellu, “divine sea,” in that very temple Esagila where there was the Ziqqurat described in the Smith Tablet. I shall have occasion to explain that the Greek equivalent of apsu is qhsaurov”, which originally was a water tank in a temple; since it was customary throw coins or proto-coins into it, from it there developed the temple treasury. I also shall have occasion to explain that in Greece a qhsaurov” was considered a[busso”, “in connection with the waters of the nether world, immense, bottomless. “ Father Deimel has suggested that the Greek term abuggos”, is derived from the word apsu. But I am more inclined to explain apsu, Sum. abzu, as composed of a-ub-zu, “water-quantity-wisdom. “ Hence a[busso” could be derived from the first two elements of this compound. There are Hebrew and Greek passages in which the maximum of the Wisdom of the master of measures is to know the volume of the water of the sea.

The link between apsu, measures, and the creation of the world numero, pondere, mensura, is indicated by these lines concerning the creation of the moon and the origin of the city Nippur, in the Sumerian poem of Enlil and Ninlil:

This very well, the Pulal, was its well of sweet water,
This very canal, the Nunbirdu, was its sparkling canal,
No less than ten iku each, if measured, were its tilled fields.

The Ark in the story of the Flood has the shape of a cubic iku, because the Flood is tantamount to a destruction and new creation of the world, and the Ark is the principle of measure that creates order out of chaos. For the Mesopotamians the draining of swampy lands by a grid of canals is the creation of the world, and this is the background of the story of the Flood. Below I shall show that the ziqqurat was a symbol of the typical embankment of land and represented the place of refuge in case of floods.

12. In the Epic of Gilgamesh the Ark is a cube with an edge of 120 cubits and, hence, a volume of 1,728,000 cubic cubits. It is not specified whether these cubits are barley cubits or great cubits, but the calculation of the volume of the Ark by Berossos indicates that they were great cubits. Hence we may assume that the Ark had the same volume as the Tower of Babel; by converting 1,728,000 cubic cubits by the great cubit into cubic cubits by the natural barley cubit, the volume is 5,832,00 cubic cubits brutto (multiplication by 33/8) and 6,000,000 cubic cubits netto (further multiplication by 25/24).

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 iku, like the surface of the Tower of Babel, except for an excess of a leimma or1/24; 15,000. square cubits instead of 14,400. This difference is certainly due to the decimal computation of the Bible. In the Hebrew system of measures the agrarian unit of surface is the square with a side of 50 cubits, which is seeded with a seah or saton of grain; hence, the dimensions of the Ark indicate an area of 6 seah or 6 squares with a side of 50 cubits.

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 The Ship of the Babylonian Noah” (Beitr. Assyr. X (1927), Heft 2), published posthumously. He combines the figures of Berossos with those of the Gilgamesh Epic. The latter would merely formulate the vertical section, whereas the length must be derived from Berossos; the Ark would be 120 cubits wide and 120 cubits high with a length of 50 stadia or 1500 cubits. These and other distortions of the texts, allow Haupt to offer a detailed reconstruction of the Ark as a real ship; but given its immense size, he concludes that the ship was not actually constructed, but merely conceived by a Jules Verne of the time. Haupt’s interpretation is accepted by Georges Conteneau in his book on Le Deluge babylonien (2nd ed. , Paris, 1952, 84). Such is the opinion of two specialists of the interpretation of the Epic of Gilgamesh.

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 carrus navalis of Carnival would be further instances.

13. The part of the Smith Tablet, lines 36-42, dealing with the dimensions of the seven storeys of the Tower of Babel, can be interpreted with certainty, if one pays attention to its mathematical rationale. But this has not been attempted, not even by the architects who have tried to reconstruct this ziqqurat.

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 iku by the barley cubit). Each successive storey is 1½ GAR narrower: beginning with the third storey, the lateral dimensions are 10, 8½, 7, 5½. One would expect the seventh storey to have a surface of 4 x 4, but instead the square is modified into a near-square 4 x 33/4, with a height of 2. This seventh storey is called elu, “high temple,” and sahurru, a term the meaning of which I shall explain below. Its peculiar dimensions must have a mathematical explanation, as it is true in all cases of near-square. And in fact the volume of the kigal temple is 33.75 cubit GAR, exactly 1/100 of the volume of the kigal, 153 = 3375 cubic GAR. Furthermore, this volume is very close to 1/60 of the volume of real ziqqurat which is 2030.25; it would be exactly 1/60 if the volume of the seventh storey were 33.637. The high temple is related in volume both to the imaginary kigal and to the actual ziqqurat by a relation which is centesimal in one case and sexagesimal in the other. The relation between high temple and total ziqqurat must be compared with the division of the Ark into 63 rooms: area divided into 9 squares with 7 levels of height.

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 sohar to the Ark and finish it to a cubit upwards. “ The term sohar has been rendered as “sky light,” “window,” “roof,” “lamp,” “precious stone,” but the only certain fact is that it corresponds to the dual form soharaim, “high noon. “ From the link I have established between Ark and ziqqurat, one can draw the conclusion that the Hebrew term is the equivalent of the Akkadian saharru, which also has been judged obscure and considered of Sumerian origin for lack of a better explanation. The term means “turning point, high point” from the verb saharu, “to turn,” used particularly in relation to heavenly bodies. The elevation of the ziqqurat or of the Ark represents the structure of heaven. The ziqqurat is intended to represent the three-dimensional structure of the universe and to have a height that corresponds to the height of heaven. The ziqqurat of Larsa is called E-dur-an-ki, “Building of the bond of heaven and earth,” that of Borsippa E-ur-imi-an-ki, “Building of the seven guides of heaven and earth,” that of Uruk E-gi-par-7, “Building of the seven mansions,” and others have similar names.

It becomes possible to understand the quoted line of the Epic of Gilgamesh, “cover (the area) with a sassu. “ The term has been explained as “roof,” but there is no authority for this interpretation; the term means “the sun, the sky,” it is an appellative of several stellar divinities and in particular of the solar god Marduk as principle of rule in the universe.

The biblical verse “make a sohar to the Ark and finish it to a cubit upwards,” is rendered by the Septuagint as. ejpisunavgwn poihvsei” th;n kibwto;n kai; eij” ph’cun suntelevsei” aujth;n a[nwqen: “Build the Ark by successive additions and finish to the cubit at the top,” The verb ejpisunavgw is generally used as a mathematical term, “to obtain a total. “ It is used in astrology to describe an aggregation of planets in contact. What is clear is that in the vertical construction of the Ark it is the height that is fundamental and it must come up to the proper dimension to the cubit. The terminology of the Bible does not exclude that the upper levels of the Ark were tapered.

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 (ZA, 49 (1950), 21-44) has tried to reconstruct the developments of the very earliest quadrangular constructions of Mesopotamia, from the early Obeid Period to the White Temple of Uruk, but has neglected to consider the dimensions,even though he has considered the proportion of the parts. The report on the excavations of Tepe Gawra constitutes a welcome exception to current trends in archeology, because the dimensions of buildings are carefully reported.

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 basu of 20. The archeological report notes the existence of several buildings that are almost square, but considers only the rectangular building as evidence of the “architectural ability of these pre-Obeid inhabitants. “ The existence of buildings with sides related as 20:21 indicates that one aimed at obtaining a mathematically perfect diagonal. Furthermore there is a repetition of the same figures in different strata, which proves that we are confronted with highly significant data. The report contains the following data:

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
Temple in Eanna 22 x 54 2 m =75 x 180 trimmed basic feet
White Temple 22 30 x 17 30 m =75 x 60 trimmed basic 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.

15. The Ziqqurat Etemenanki of Bbylon was the largest and probably was also the most elaborate metrically Not many other ziqqurat were calculated by the barley cubit Two ziqqurats are calculated as a square with a side of 100 barley cubits ;

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 iugerum and the Egyptian aroura, is the Mesopotamian acre and is a standard agrarian unit, even though not as common as the iku, by which the Tower of Babel is calculated.

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 subban). There is a vague report to the effect that the ziqqurat of Hammam measures 30 x 30 m.

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 basu of 20 (sides 20 and 21 with diagonal 29) is represented by at least tree ziqqurats. One is the ziqqurat of el-Oheimir at Kish reported to be 195 x 185 English feet (59.44 x 56.39 m.); these dimensions are almost certainly 210 x 200 natural oil feet (theoretically 59 06 x 56 25 m.). The same proportions but in trimmed barley cubits (theoretically 69.93 x 66.60 m.) should explain the so-called ziqqurat of Anu at Uruk, which is actually a high terrace. The excavators have been uncertain about the date of this construction, but it could be as early as the Uruk Period. In any case this would be a very early example of the use of the barley foot in buildings. It is reported that this high terrace has a height of 13 m. , which would be 40 feet (13.32 m.).

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:

Engish feet Metric equivalent

Oil feet Theoretical value

272

82 90 m.
300
83 25 m.

230

70.10
250
69.37

188

57.30
205
56.86

146

44.50
160
44.40


These figures hint that one must hesitate before concluding that Sir Henry was the victim of hallucinations. He reported that the first three storeys have a height of 26 English feet of 7.92 m. whereas the fourth has a height of 15 English feet or 4.57 m. Possibly the figures were 28 and 16 oil feet, 7.87 and 4.44 m.

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.

16. At this point it is possible to approach the problem of the meaning and purpose of the ziqqurat. Unfortunately scholars have thought that because the ziqqurats impress us with their size, they should be discused in a spirit of inspired elevation; pseudo-Longinos states that the Colossus of Rhodes summons up to the sublime and not to acriby. But in truth if there is any beauty in the ziqqurats it is because of their mathematical acriby: one could say with Plotinos “the body becomes beautiful by participatig in the Reason that flows from the Divine. “ About what has been written about the ziqqurat one could quote the words of pseudo-Longinos himself: “Bigness in material objects and grandeur in literary works, both are evils when they are without reason and truth, and they are likely to impress us as the opposite because, as the saying goes, nothing has less flesh than the body of a dropsical. man. “

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 était la manifestation architecturale de l’humanité désireuse sans doute de s’élever au dessus de la terre—les hommes ont toujours voulu adorer sus les sommets—mais surtout anxieuse de préparer à la divinité la voie majestueuse qu’elle emprunterait pour arriver jusqu’à elle. Some may think this language is noble and uplifting, but to me it is the destruction of that very spark of reason that grew in Mesopotamia and of which the ziqqurat is a symbol.

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 apsu and is conceived as a mountain joining earth and sky. There is a line (line 18), which is considered of difficult interpretation, in which the ziqqurat is compared with the water pond of Enki and the container, pu-gin, of Nannar. Enki is the divinity of reason and of mathematical reason in particular; Nannar is the divinity of weights and measures. I have reported how the Ark is said to be “like the apsu “in the Epic of Gilgamesh. At times the apsu is represented also by a tank of water. I have indicated that the Brazen Sea in Solomon’s Temple and the Ark of the Covenant are similar objects. The ziqqurat is compared to the pu-gin; the first element of the term means “container,” whereas the second, being connected with the idea of foot, may mean either “standard” or “movable,” but in both cases the notion is similar to that of the Ark of the Covenant as a portable unit of measure. Responsible scholars have associated the ziqqurat with a tomb, because some texts associated the ziqqurat with an object called-gi-gun4 and other texts seem to indicate that this term applies to the ziqqurat itself. The term has been understood as meaning “tomb,” but there is no basis for this interpretation. We know for certain that the first element of the term means “measuring cane” and that the second element means some sort of construction, like a room. We know that in one case the gi-gun4 is made of cedar wood. Hence, it is possible that the term may have the same meaning of the Hebrew tebah, “box, coffin,” which applies both to a huge cubic construction like the Ark of Noah and to a rectangular trough like the Ark of the Covenant. The gi-gun4 could be both the imaginary cube represented by the ziqqurat and a wooden measuring box as could possibly be the pu-gin.

The Epic of Greation (VI), speaking of the construction of the ziqqurat of Babylon, repeats that it is like the apsu and that it reaches the sky; Tiglathpileser I states that the two little ziqqurats of Anu-Adad are immense and reach the sky. This is to be explined by the fact that the ziqqurat as a unit of dimension ideally reaches the sky or the limits ot the earth, just as the Paris meter reminds us of the circumference of the earth.

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 iku, the square of lan surrounded by water canals; the term iku means both the canal and the area of land enclosed by it. It is the drainage canal that brings land into existence in Mesopotamia, and the ziqqurat stands for a measured plot of land surrounded by water. This is for the Mesopotamians the simple root of the notion of apsu, the notion of a rational measured universe fit for the life of man. The Sumerian city-state was an irrigation unit, as it is demostrated by several studies. The experience of landsurveying, cutting canals, erecting embankments, is the basis of the myths of creation and cosmic order. The ziqqurat is a realistic symbol of. this social activity and of the cosmology that springs from it.

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 (ammah) of your life is broken” (51:13). This mention of the cubit is followed by a reference to God as he who made the earth, established the world by his Wisdom, and in his skillfulness measured the heavens. In the following verses Babylon is described as reduced to a ruin without inhabitants because of both drought and flood (51;36, 42, 43). Jeremiah does not distinguish the two evils, since these were the two dangers that the Mesopotamians warded off by the measured control of waters, of which the ziqqurat was a symbol.


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