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1. Since the Renaissance the study of ancient measures has been conducted in a spirit of rationalistic and cosmopolitan ideals: besides solving antiquarian and practical problems, it aimed at finding some universal rational principle above political divisions. This tone of metrology was set formally by Budé in 1514; his pupil Leroy assigned to the study of Egypt and Babylonia the task of tracing the origin of the arts and the sciences. Operating in this spirit French metrologists of the Enlightenment, by considering the structure of ancient metrics, concluded that there had been in the Near East a culture particularly gifted in mathematics from which the metric system had originated. At the beginning of the nineteenth century Böckh concluded, partly on the strength of numismatic evidence, that ancient metrics had been conceived in Mesopotamia, had been adopted in Egypt at the beginning of Egyptian culture and imported into Greece through the Phoenicians when Greek civilization was emerging from darkness. Because of this he envisioned the continuity of Oriental and Greek culture and the general unity of ancient civilization, before it was documented by other types of investigation. Hence, when the excavation of Nineveh and Dur-Sharrukin, initiated in 1842 by Paul Emile Botta, revealed the world of cuneiform documents, metrologists quivered with expectancy: one hoped not only to trace the fons et origo of measures, but also to obtain a key to unsolved problems of Hebrew, Egyptian, and Graeco-Roman metrology. But Mesopotamian metrics revealed themselves as more complex and obscure than those of the other countries of the ancient world.

2. One explanation of the difficulty is, as I have determined, that the Mesopotamian system has undergone a step of evolution beyond that of neighboring countries. The system adopted in these countries corresponds mainly to that of pre-literate Mesopotamia. Beginning with the Early Dynastic period measures were adjusted to make them fit into a consistently sexagesimal computation. The metrics of other countries are only partly sexagesimal; the sexagesimal factor appears in the metric system partly because the first purpose of an organized structure of measures was to be able to calculate the grain needs of the population by the day, by the month, and by the year, and partly because five units of wheat correspond to six units of barley. The sexagesimal computation originated by making the metric system consistently sexagesimal; I shall show that this phenomenon explains the difficulties of Mesopotamian metrics and that by taking it into account the difficulties can be removed.

I may note that it is in the field of metrology that one first became aware of the phenomenon of diffusion; metrologists were diffusionists for at least a century before diffusion began to be seriously considered by historians and anthropologists. The theory of diffusion has achieved respectable status only after the discoveries of the last twenty years have proved that the most decisive transformation of human life, usually known as the neolithic revolution, originated in a restricted area of Syria, northern Mesopotamia and Iran, and from there spread through the world. I have tried to show that the metric system is only one of the aspects of the neolithic revolution and is closely linked with the adoption of agriculture as the main source of food. The march of agriculture and the march of the metric system through the world move on parallel lines. Metrology also reveals an apparently paradoxical aspect of diffusion which is being considered today by a few anthropologists: the more distant an institution is from the center of diffusion, the more archaic are its features. The Roman system of measures is more primitive than the Greek one and much more primitive than the Hebrew one. The English system of measures is closer to the original one than that of France before the Revolution.

The understanding of the evolution of Mesopotamian metrics from a partly sexagesimal to a totally sexagesimal system has been beclouded by the injection of racial theories. When the use of sexagesimal computation in Mesopotamia was first discovered, excessive importance was ascribed to this fact, without considering that sexagesimal multiples and submultiples are found also in Greece. If the problem of computation had been considered concretely, examining how calculations are performed on the abacus, it would have become evident that on the abacus one can calculate both decimally and sexagesimally and that the two computations can be combined. The abacus indicates that a multiplication or a division by 60, must be broken into two steps using the factor 6 and 10 separately; in the Mesopotamian system the mina has sexagesimal multiples and submultiples, but there are intermediary units, such as the saton (Sum. sat; Akk. sútu) and the akálu calculated by the factor 6 or 10. In Mesopotamian metrics the calculation by multiples such as 16, 32, 64... is also important, as noted by Father Deimel in his Šumerische Grammatik; this reflects the fact that a cube can be divided into 64 parts with ease and into 60 parts with difficulty, and that there was an instrument of calculation, the diagrammismos, which is a primitive slide rule constructed according to logarithms with base 2 and hence allowing easy multiplication and division by 2, 4, 16, 32... All that occurred in Mesopotamia is that one developed a system of notation according to sexagesimal multiples and submultiples; but this is a development of written culture that has nothing to do with primitive racial characteristics. The importance of this notation has been distorted by stating that it is an example of positional reckoning unique in the ancient world; this is not true, since positional reckoning is essential to the abacus. If the abacus is set for decimal computation one multiplies and divides by 10, simply by moving the symbol that corresponds to the point in our decimal notation; the abacus has the advantage that one can multiply and divide by 60 in the same manner, if the abacus is set for sexagesimal computation.

There are scholars who link the number system with ethnic traits, whereas number systems are an intellectual development and are unusually international, being connected with trade. A study byt Giuliano Bonfante has shown that Indo-European languages show traces of quaternary, quinary, decimal, vigesimal and sexagesimal computations in their earliest strata. The quaternary computation is particularly interesting since the number eight, octo in Latin, has a dual grammatical form and must have meant “two times four,” the number five is an added number, being quin-que in Latin and pén-te in Greek, and the number nine means “new number.” Numbers and methods of computation can freely move from one culture to another according to the development of mathematical thought.

When the question arose whether it was true that the cuneiform script used to represent a Semitic language, Akkadian, had been earlier used to represent a non-Semitic language, Sumerian, the matter was discussed in an atmosphere of intense racial prejudice. The defenders of the existence of Sumerian (I think François Lenormant was the first) introduced the additional argument that in Mesopotamia one used sexagesimal computation, whereas Semitic computation is decimal. This unfortunate remark, the value of which was formally denied by Lehmann-Haupt in his defense of the existence of Sumerian as a language, was seized by the racialists, and by the end of the nineteenth century it had developed into a general theory of a distinction between Semitic and non-Semitic mathematics. Through history the Semitic and Jewish mathematical mind would be characterized by purely abstract conceptual thinking, whereas the non-Semitic mathematical mind operates through visual images.

3. The other reason for the partly inconclusive results of the study of Mesopotamian metrics is to be found in the methodological crisis of cuneiform studies. The great pioneers of Akkadian and Sumerian studies dedicated so much attention to metric problems that they can be considered professional metrologists; on the other side scholars who had specialized in the metrology of other areas tried to become acquainted with the new field of cuneiform studies, as for instance the Egyptologist Justus Lepsius (1810Ė1884). But the tone of Mesopotamian metrology was set mainly by François Lenormant (1837Ė1883) and Julius Oppert (1825Ė1905).

Lenormant as son of an archeologist who had been with Champollion in Egypt and of a distinguished niece of Madame Récamier, continued the metrological thought of eighteenth century France. He started in the field of Greek archaeology but shifted his interest to cuneiform studies when he realized that these could contribute to the solution of problems of Greek numismatics. Lenormantís position gained general acceptance when Mommsen added to the French edition of his history of Roman coinage an appendix dealing with Assyrian metrology (originally published as an article in German in 1863) in which he stressed the importance of Mesopotamian metrology for the understanding of Greco-Roman monetary weights. I shall show that Mommsen was correct to the point that questions that are at present obscure and controversial in the history of Athenian and Roman coinage can be solved through correct conclusions about Mesopotamian weights.

Oppertís intellectual position is overlooked by biographers who are distracted by his specific contributions to the decipherment of cuneiform-written languages and particularly by his decisive contribution to the discovery of the Sumerian language and Sumerian culture. His main position becomes clear when one considers that he entered the field of scholarship under the guidance of his famous uncle Eduard Gans; it was because of him that Oppert studied law, even though his first passion had been mathematics. Gans was a collaborator of Hegel and a historian sympathetic to the ideas of the Enlightenment and the French Revolution; in the years around the July Revolution he lived in Paris where he associated with liberal politicians and was a member of the salons of Madame Récamier and the Duchesse de Broglie, the daughter of Madame de Staël. It was these connections that allowed his nephew to settle in France and be readily accepted as a Frenchman. As a professor of Roman Law, Gans was the actor in one of the major intellectual controversies of the nineteenth century: against the romantic notion of Savigny that law is a spontaneous historical creation of the peopleís soul, he defended the conception of law as expression of conscious rational organizing activity. I may best stress the significance of Gansí criticism of the historical school of law by quoting the opinion of an opponent, Professor Carl Anton Bernoulli, the devoted biographer of the two great reformers of ancient studies, Nietzche and Bachofen: “History of culture may even today have reasons to express regret that at that point victory was scored by Logos and that the entire political and economic development of Central Europe and hence of the entire world stood under the sign of Logos and its indomitable will and insatiability.” When one considers Gansí influence one can gather that throughout the multitude of specific technical investigations of cunieform texts, Oppert was preoccupied with the origins of rational thought. It is for this reason that he was particularly concerned with Böckh. Böckh used his authority to sponsor the young Oppert, who was vituperated in Germany after he had refused to abjure Judaism and had settled in France, since he wanted to avoid being identified either as an apostate or as a Jewish sectarian. In French academic circles one of his most active sponsors was Letronne whose major interest had been Egyptian metrology and its significance for the study of Greek and Roman numismatics.

4. Oppertís monumental and epoch-making study of the culture of cuneiform-writing nations includes about thirty articles dealing with measures. These articles are still today an inspiring model of correct methodology in dealing with Mesopotamian metrics, but they do not arrive at a final conclusion on the one issue Oppert considered fundamental. According to the principles of Böckh (Oppert specifically states that he shares his Grundideen with Böckh) he assumed that the entire system of measures could be deduced once the exact value of the cubit was known, but he could not achieve a positive determination of this value.

In his first essay of 1853 Oppert came near the correct solution. He found that in some texts the kurru (Sum. GUR), the cube of the cubit, is equal to 300 minai; so that if one assumes a mina of 482.34 grams, which is suggested by Mesopotamian sample weights and by Greek authors, one can calculate the kurru as 144,702 c.c. or as the cube of the Egyptian royal cubit of 525 mm. The argument is logically perfect, but the mina that is contained 300 times in a cubic cubit is not the normal Mesopotamian mina, but a smaller mina that is 5/6 of the former and is called Euboic mina by the Greeks. It is remarkable that Oppert came so close to a solution soon after cuneiform documents had become available in a certain quantity.

Oppert tried to find a confimation of his reckoning by applying Newtonís method which had been so successful in Egypt. He devoted himself to the interpretation of architectural measurements and also, following Newtonís suggestion, assumed that the size of most bricks would be in simple numerical relation with the unit of length. Under Oppertís influence the engineer and archeologist Marcel Auguste Dieulafoy (1880-1920) dedicated himself to the application of Newtonís method to Mesopotamian buildings, taking as a starting point his own excavations in Iran. Oppert conducted debates protracted through years with another ingénieur des ponts et chausseés turned archeologist, Auguste Aurès, who made his lifelong task the metrological analysis of the monuments of the ancient world. But, in spite of the efforts of all these gifted people, the results were steadily contradictory. This provided Rev. Johns, who in 1901 wrote the manifesto for the new school of metrology as applied to the Mesopotamian area, with a pretext for denouncing the validity of Newtonís method. But Oppert answered the following year reaffirming, three years before his death, his belief in the scientific soundness of the method. The emphatic condemnation of the method by Weissbach caused a total abandonment of the line of research initiated by Oppert, Aurès and Dieulafoy. In 1912 came the discovery of the Smith tablet, which gives the dimensions of the Tower of Babel and provides a textual confirmation of the validity of Newtonís method, if such is necessary. Dieulafoy published a commentary on it in 1913, just before the dimensions of the Tower obtained in the field by Koldewey became available; Dieulafoy was near a triumph in a long effort, but the following year he offered his services to the French Army and was no longer able to publish any article before his death in 1920.

The reason why Oppert and other scholars did not completely succeed is that cuneiform tablets assume the existence of a single type of cubit, since they speak of the cubit (Akk. ammat, Sum. KUS) without formulating any distinction: they do not even mention the foot, even though some of the units of volume and weight are the cube of foot units. The texts do not draw any distinction between different types of cubits, except to state that the cube usually divided sexagesimally into 30 fingers is at times divided into 24 fingers as in the rest of the ancient world. It was concluded that the only problem was that of determining the length of this cubit. Actually in the ancient world there was one type of foot or cubit with different modules, and cuneiform documents reflect a reckoning based on a single module, but in architecture one used all modules. The same happened in Athens where volumes and weights were calculated by the basic foot, but in buildings one used whichever module was most convenient. Oppert was influenced by the example of Egypt where all monuments, from the First Dynasty on, appear calculated according to the royal cubit of 28 basic fingers or 525 mm, and assumed that the same would apply in Mesopotamia. As I have said, in his first metrological essay, written at the age of twenty-eight, he concluded that the Mesopotamians used this very cubit. In spite of his long animated controversy with his friend Lepsius he was overwhelmed by his ideas. Lepsius was an Egyptologist, and Egyptologists have tended to take an imperialist view of Mesopotamian culture; only in the last two decades at most have they accepted the historical primacy of Mesopotamian culture. In the field of metrology, not only Petrie, but the great Egyptologist and clearminded metrologist Heinrich Brugsch struggled to assert the Egyptian origin of the metric system. It would have been better if Oppert had listened to his friend Vasquez Queipo, who as a political exile in Paris had contacts with Oppert while writing his Essai sur les systèmes métriques et monétaires des anciens peuples. Vasquez pointed out to Oppert the existence of a cubit of two feet among the Arabs, but the latter probably was too disgusted with Gobineauís theory that cuneiform documents were to be read in Arabic to accept with equanimity the close connection between Mesopotamian and Arab metrology.

Oppert had come closer to a correct answer than he thought. From the size of bricks he concluded that the Mesopotamian foot has a value of ca. 330 mm. (it is in reality a barley foot of 333 mm., corresponding to a cubit of 499.4), but later he hesitated because he found evidence of a foot of 315 mm. (in reality a wheat foot of 314.5) and also because he had become convinced that some constructions were calculated by a cubit of 548 mm. This last group of constructions is actually calculated by the trimmed lesser foot of 277.5 mm, the double of which is 555 mm.; the existence of ancient calculations of the circumference of the earth based on a unit of 555 mm. had already been noticed by the cosmologist Laplace, and this possibly influenced Oppert to concentrate his attention on it. He should have concluded that at least three modules of foot were used in Mesopotamian architecture , but on the contrary he concluded that there was a foot of 330 mm. from which by an exceptional procedure a cubit of 440 mm. or 5/3 of the foot was derived. If he had calculated the cubit as usual as 1Ĺ feet, he would have obtained the right solution.

A further important step towards the right solution was made by Aurès and Dieulafoy when they had an inkling that cuneiform tablets present a learned system of metrics, whereas in architecture one used more practical methods. The tablets in their sexagesimal computations used as unit of landsurveying a double-cane of 12 cubits, called SAR or GAR, whereas buildings appear constructed by using a rod of 10 feet as in the rest of the ancient world. Dieulafoy further concluded that the cane (Sum. GI(N), Akk. qanu) of 6 cubits must be equal to a rod of 10 feet; since he noted the use of the artabic foot, he was a step away from the solution. A cane of 6 natural barley cubits (3,037.5 mm.) or 6 trimmed barley cubits (2,996.4 mm) was used in sexagesimal computations, but in actual construction work it was considered equal to a rod of 10 artabic feet (3,077.9 mm.)

5. A completely fresh approach was introduced by Lehmann-Haupt who in 1889, as a young man, published the best essay of his career and one of the best in the history of metrology. He observed that the foot one can find embodied in the bricks has a value of 328-334 mm. , and that from this one can derive a Mesopotamioan cubit of about 495. He studied the evidcence that indicates the use of this cubit, but the most important discovery was the reading of texts that clearly indicate that the double qa (volume of a double mina of water) is a cube with an edge of 6 fingers. Hence, there cannot be any doubt that the cubit contains 250 minai, or 125 double minai or qa. The stumbling stone met by Oppert in his first essay had been removed.

Since the approximate weight of the Mesopotamian mina is well known, the length of the cubit can be determined with a reasonable approximation. But Lehmann-Haupt believed, as had Oppert, that one cannot read Mesopotamian mathematical texts with certainty unless the measures are known with the greatest precision. Hence, he chose as his task the precise determination of these values. There is a special difficulty in determining the weight of the Mesopotamian mina, since sample weights indicate a value varying within an unusually wide range. I have determined that the range is a diesis and that the mina varies between 486 and 518.4 grams. Oppert, in 1874, on an empirical basis set the range of the mina between 495 and 518. Lehmann-Haupt concentrated his attention on sample weights; he obtained a research grant to study the collection of the British Museum. He arrived at the correct conclusion that the lowest value indicated by the sample weights was the correct one, and that the other values were special forms (Sonderformen) of the mina increased by fractions for particular reasons. But he hesitated at drawing the conclusion that the correct Mesopotamian mina was equal to the Egyptian mina or hin, calculated as 485 grams or c.c. He was deviated from the right conclusion by assuming that the mina which is calculated in the documents as 1/250 kurru is the correct one; I have determined that this calculation is a later development and is the very explanation of the existence of the increased special forms.

At this point Lehmann-Haupt in the anxiety to arrive at a solution violated the strictly mathematical method of the old school. He was impressed by the discovery of the measuring rule of Gudea that he thought indicates a cubit of 498 mm. (it probably agrees with the trimmed barley cubit of 499.4); from this cubit he should have derived a mina of 494 grams. But he knew that this weight was too high and hence he compromised and fixed the value of the Mesopotamian cubit at 496 mm. and that of the mina at 491.17 grams. He introduced a datum that does not have support in any form of evidence. The demonstration that one should be more than careful in such matters, is that after Lehmann-Haupt had chosen as a compromise these two figures, in 1909 Thureau-Dangin examined the rule of Gudea and thought that it indicates a cubit of 496 mm. and later Bieliaev proceeded to a statistical analysis of the weights of the British Museum and, in spite of the technical refinement of his statistical method, arrived at a mina of 491.14 grams, the weight he believed he should find.

Having taken a false step, Lehmann-Haupt found himself involved in a series of difficulties from which he was not able to extricate himself in forty years of research. Particularly he was was not able to take advantage of a discovery he had made and of which he was justly proud: namely that most weights of antiquity and of the Middle Ages exist in two varieties related as 24:25 (what Oxé called the netto and the brutto variety). Since Lehmann-Haupt properly stated that there are as many lengths of foot as there are talents, he should have drawn the logical conclusion that there are lengths of foot related as the 24-³/25-³. He should have concluded that this is the explanation of the most important problem of ancient metrics, a problem that has beset metrologists since Newton: the mathematical connection between the Greco-Roman foot of 296 mm. and the Egyptian foot of 300. In another brilliant study Lehmann-Haupt collated all ancient sources dealing with the relations among units of length and determined once and for all which relation exists among the several modules of ancient foot. But having set arbitrarily the Mesopotamian cubit at 496.165 mm., allowing for a variation between 495 and 498, he was forced to merge the Greco-Roman and the Egyptian foot into a single unit varying between 297 and 298.8. Thereby his very achievements had the result of obliterating two most certain data, data that had been arrived at with exquisite precision through three centuries of persistent effort.

By the end of the nineteenth century Oppert and Lehmann-Haupt were on the threshold of a solution of the main unknown of Mesopotamian metrics; but Oppert did not progress appreciably beyond the conclusions enunciated in 1874, and Lehmann-Haupt could not develop the brilliant insights of his earlier writings. The reason for this is that they were attacked in toto, but their opponents never did them the kindness of criticizing them on the concrete questions where they could be found at fault. One may quote a verse of Stephan George, a guiding spirit of the new scholarship:

Wer niemals am Brüder den Fleck für den Dolchstoss bemass,
Wie leicht ist sein Leben. . .

And indeed the new school struck blindly against their colleagues without ever measuring where the dagger should fall. After 1874 most of the energy of Oppert had to be invested in the refutation of those who claimed that the Sumerian language and Sumerian civilization had never existed. Even worse was the situation of Lehmann-Haupt who, after the death of Mommsen in 1903 and of Oppert in 1905, found himself isolated among ancient scholars. After 1912 only Lehmann-Haupt and the numismatist Haebertin were upholders of what was by then called the old school of metrology.

6. I have examined in detail the birth of the new school of metrology among Greek scholars at the end of the nineteenth century. The pronoucement of Eduard Meyer that there never was a metric system and that the ancients fixed measures arbitrarily and in different manners in different times and in different areas, was accepted as a dogma both for Greek and Roman history and for the Oriental one. The central tenet of the new school is that the notion of defining the volume as the cube of the unit of length is not an invention of the Sumerians adopted by all ancient peoples, but an innovation of the French Revolution. This is a preposterous contention denied by all the evidence, but the struggle against the role of the cube in ancient metrics is not the result of a technical scholarly dispute, but of an ideological allegiance. The concept of an organized system of measures was identified with the Enlightenment and the Jacobins, so that one could reject the study of ancient metrics with the same positiveness with which one rejects the guillotine. This happened because ancient studies came to be conceived as a foil to the rational quantitative world of Galileo and Newton and all its works; when one considers that the French metric system was prepared by Renaissance scholars on the basis of their detailed studies of ancient and contemproary practices, one can see that the assertion that there was not a metric system based on the cube before the French Revolution affects also the interpretation of the Renaissance. In the new conception, as expressed for instance by Gobineau, the Renaissance stands for heroic vitalism against the frigid logic of the Enlightenment; it is a matter of record that Nietzsche took his psychological model of the ancient Dionysian Greek from Burckhardtís Renaissance herostratic man.

Meyer did not submit a single piece of evidence in order to reject not only all ancient authorities, but also four centuries of classical scholarship. He spoke as if ancient metrology had been born fully armed from the brains of Mommsen and Oppert. Canon Johns who in 1901 in his essay on Assyrian measures summed up all the tenets of the new school in a sort of manifesto, did not advance any argument beyond impassionate rhetoric. Weissbach, who declared that indeed he would accept the old school of metrology if there were in Mesopotamia one text, even as late as the Persian Empire, linking length with volume, but had found none, was and is considered a responsible scholar and his metrology has become authoritative. Paul Haupt who distorted the texts in a crude way in order to deny that the cube was in Mesopotamia a symbol of cosmic order, created a school of American pupils willing to defend to the bitter end his beliefs about Mesopotamian measures.

I have considered how the interpretations of the Greek world as protest against modern scientific society is linked in the works of Beloch, De Sanctis, and W. S. Ferguson with the adherence to the new metrology; the new metrology played a similar role for Mesopotamian studies. The area of disagreement with his opponents was defined by Lehmann-Hhaupt in 1903 in the essay Babyloniens Kulturmission einst und jetzt, in which he specifies that the cultural influence of Mesopotamia through Greece reaches into our contemporary life, as it can be most easily demonstrated through the history of mathematics, astronomy and metrics. To stand for scientific precision and for quantitative order was a mission then and now. The adoption of the French metric system repeats the adoption of the identically structured Sumerian system in the ancient world; on the other side the French metric system is the first break in four thousand years in the continuity of the conventional basis of the system, as illustrated by the French pre-revolutionary pound, which is identical with the Sumerian mina. It was in early Mesopotamia that the vision of the universe as numerically ordered and predictable was first formulated. Against this interpretation of Mesopotamian culture, there developed not only the new school of metrology, but a more general view that cuneiform mathematical texts must be interpreted as superstition, numerology and magic. Today one no longer defends the specific interpretations of Hugo Winckler (1863-1925) and Hermann Volrath Hilprecht (1859-1925); instead there have been developed less concrete but more sweeping interpretations of the type propounded by Thorkild Jacobsen, in which the apperception of cosmic order is voided of mathematical and scientific contents and presented as animistic psychology. But the truth is that even Sumerian mythology, as revealed by the investigations of Samuel Noah Kramer, is a transparent reflection of concrete technical practices of agriculture, land reclamation, surveying and economic organization. If one assumes, as is the current opinion, that mythology must deal with subconscius emotional conflicts and with infantile sexuality, Sumerian texts have to be interpreted well below their overt meaning.

7. Lenormant and Oppertís contribution to the discovery of the Sumerian language is not disconnected from their interest in measures, since the metric system is the most characteristic creation of Sumerian culture and since the discovery of the art of writing grew out of their methods of recording measuring operations and of recording methods of metric computation. For this reason the destiny of metrological research is deeply bound with the Sumerian question.

In order to understand the “Sumerian question” and its implications, one must keep in mind that Mesopotamian studies were born in the spirit of European liberalism as it came to be formulated in the intellectual salons of the July Monarchy. They had their start when Julius von Mohl suggested to Botta the plan for the excavations of Niniveh and Dur-Sharrukin. These excavations were considered so linked with liberal politics that the government of 1848 put an end to them. Mohl who was successively secretary and president of the Société Asiatique and more than any other contributed to create interest in the Orient among the French, was an adopted Frenchman and had married an Englishwoman. His wife, Mary Clarke, had been a member of the salon of Madame Récamier and organized her own salon, which became by the middle of the century one of the most influential ones, if not the most influential; this salon was certainly the most cosmopolitan and through it passed the most significant historians of Europe, such as Tocqueville, Ranke and Grote. Mohl was the brother of three major figures of German scholarship: Hugo was a botanist; Robert, a constitutional lawyer specialized in the role of bureaucracy in the modern state, was Minister of Justice in the Frankfort government of 1848 and later a leader of the liberal party; Moritz, an economist, was one of the most dramatic deputies at the Frankfort Diet and a spokesman for the radical left, and about him it may be mentioned that he championed the adoption of the French metric system in Germany. Botta was the son of Carlo Botta, the most important Italian historian of the beginning of the nineteenth century. Carlo Botta was a decided opponent of the romanticism of Mazzini and Manzoni and believed that the Italian national renewal should be brought about by a return to the thought and the forms of the Renaissance. A soldier of the French revolutionary armies, he was also a scholar of the American Revolution and, having given a son to France, he gave another to America, Vincenzo, professor of Italian literature at New York University. These facts are not accidental, as it is not accidental that one brother of Oppert went to live in China and became a geographer of the Far East and another became professor of Sanscrit at the University of Madras in India.

Liberalism to these people meant the possibility of an enormous expansion of the limits of the human mind; a possibility of expansion by which much new could be added without denying the old. For this reason several liberals of the July Monarchy believed that they could accept the ideas of the Enlightenment and the cult oif science without renouncing their Catholicism, just as Oppert thought that he should not deny his Jewishness. One must not forget that it was under the July monarchy that freedom of the press was for the first time solidly established in continental Europe and that for the first time to be a writer became a regular profession like being a physician or a lawyer. The professeurs who influenced the political scene of the time hoped to see established a society sufficiently free from hatred and violence and with enough universal benevolence to allow the full and free development of intellectual life; this was a political ideal similar to that of Aristotle and Cicero. It may be a very narrow political program for those who are preoccupied with national and social conflicts, but it did what was intended to do for the life of reason.

Mesopotamian studies were a facet of this vast intellectual movement and, hence, were characterized by a positive attitude, whereas in the next generation the affirmation of the values of culture meant the denial of others. The opposite negative attitude was introduced by Count Joseph Arthur de Gobineau, a Frenchman who denounced France to become an adopted son of Germany. The author of the Essay on the Inequality of Human Races (1854) was a representative of the French reaction, taking the word in its original meaning, one of those thinkers who wanted to return to an idyllic past that had existed before the Enlightenment; but he added some new elements to political reaction: the introduction of the techniques of the Gothic novel into the field of scholarship (he was a novelist of distinction) and the idealization of the “mysterious East,” as spiritistic, mystical and bizarre. Gobineau brought together different trends of thought to one central creed, the total denial of modern civilization. Although deriving his title from the noblesse de robe, he fancied himself to be a descendant of Scandinavian pirates who settled themselves as conquerors over a Romanic populace enfeebled by Jews, those African negroes with lightened skin, who had brought Assyrian culture into the Roman Empire. Since Gobineauís ideas have had paramount political consequences and since he has obvious descendants in the field of historical writing, one tends to overlook how many of his specific notions have penetrated piecemeal Oriental, Greek and Roman studies. Even though he was a prophet and his ideas triumphed after his death, he could remark in his lifetime that scholars were sacking his pages without giving him credit.

The most concrete scholarly effort of Gobineau was in the field of cuneiform studies. In those years in which Edward Hincks, Sir Henry Rawlinson, and Oppert were gradually realizing that the Akkadian language could not account for all ancient cuneiform texts and for the inner structure of cuneiform writing, Gobineau in 1858 attacked the three of them in his essay on the Lecture des textes cuneiformes, which he expanded in the two volumes of Traité des écritures cuneiformes, published in 1864, when Oppert had come to the realization of the existence of the language and of the culture that he called Sumerian. Gobineau argued that cuneiform texts were sacred writings written in a cryptic form for “talismanic” purposes, and that if one reads them with the system of transposition of letters employed by the Hebrew Cabbalists they proved to be written in Arabic. He produced a marvel of combinatory devices by which the texts not only proved to be alliterative poetry conforming to strict rules of prosody, but also could be read backwards and forwards, so that what was a blessing read as a curse in the opposite direction. It was Oppertís burden to undertake the task of refuting Gobineau, who made it a question of personal prejudice on Oppertís part. Still in 1933 the Italian Fascist Lorenzo Gigli accused Oppert of having lacked scholarly objectivity.

Gobineau was a prophet even in this field and his theory did not gain immediate acceptance, patly because Mohl threw the weight of the Société Asiatique against it, even though Gobineau was a personal friend of his; but in 1874, when Lenormant published the first sketch of a Sumerian grammar, Joseph Halévy felt that his Jewish racial nationalism was offended by the notion that the culture of Mesopotamia and the first system of writing of the world was the product of people who did not speak a Semitic language. Halévy, too, was an adopted Frenchman, having been born a Turk, but had a completely different background from Oppert; he came to Semitic studies through an anthropological investigation of the Falashas, the Ethiopians of Mosaic faith. He took over Gobineauís theory and gave to it a new turn: the texts read as Sumerian were a hieratic script used by Semites and they were written by the Cabbalistic method of transposition of signs. As Gobineau had accounted for cuneiform writing by saying Toute líAsie est talismanique, Halévy accounted for Sumerian by ascribing to the human race the trait of “universal cryptomania.” Following further Gobineauís theory, he maintained that the so-called Sumerian texts not only were a system of secret writing but contained riddles and plays on words.

As E. A. Wallis Budge observes in The Rise and Progress of Assyriology (p. 211), Halévy “was obsessed with the idea that the Semitic people in Babylonia were the direct ancestors of the Jews and the founders of all civilization in Western Asia, and the inventors of the writings, literature, science and the arts and crafts which had been merely adopted by later people.” As the case of Gobineau clearly indicates, anti-Semitism is a form of protest against the modern scientific, industrial, urban society and for this reason it becomes a part of the intellectual baggage of those who turn to ancient history or distant cultures as an escape into an ideal world free from reason, capitalism, socialism and all such evils. It creates opposite reactions among some Jews, but often the reactions incorporate the ideology of the supposed enemy, and Jewish nationalism or racialism often condemns the image of the Jews as intellectual, pedantic and cosmopolitan in favor of anti-intellectual, visceral, parochial and agrarian values. These ideas have played a role in all fields of historical studies, but Mesopotamian scholarship has been particularly infected by this virus.

It is difficult to grasp today how for thirty years Halévy succeeded in dominating Mesopotamian studies. Particularly in the decade 1885Ė1895 he almost succeeded in putting an end to Sumerology. The first volume of Charles Fosseyís Manuel díAssyriologe, published in 1904, is essentially dedicated to a history of the Sumerian question and marks the end of the parabola for Halévyís power. But the consequences of Halévyís preaching are still felt today. It was Lenormant and Oppert who bore the main burden of refuting Halévy, and after Lenormantís death in 1883 Oppert was practically alone. Mohl had died in 1876 and Oppert could not count on that institutional support he had in the past; the Journal Asiatique had refused to print Gobineauís elucubrations but was wide open for those of Halévy. The latter even dedicated one of his works to Mohl who being in the grave could not decline the honor. Other Sumerologists made concessions to Halévy, but Oppert did not compromise on a single issue, even though he was in a difficult position, since Halévy knew how to appeal to the mass of scholars who could not understand the technical problems of Sumerian grammar. Naturally it was easier to follow the cabbalistic games of Halévy than to force oneself to that change of mental habits necessary to understand an agglutinative language. Furthermore, Halévy was more acceptable than Gobineau, since according to the latter it was necessary to understand Arabic poetry in order to read cuneiform texts, whereas according to the former nobody would ever be able to read a Sumerian document because they were hardly readable to the contemporaries, since each scribe could alter the key at will. This is appealing, as is the new school of metrology which frees scholars from the burden of providing a reasonable explanation of cuneiform tablets and of Greek authors or inscriptions dealing with measures.

8. The reason for Halévyís success must be found in the spirit of historical scholarship of the time, a spirit which is best exemplified by Eduard Meyer. As I have shown, for Meyer history is the study of national character and the historically significant character is the Semitic character, characterized by lack of imaginative creativity and an inclination towards sterile logic and reason. Meyer also in the name of empiricism and positivism preached a revolt against the technical systematic methods of the philological school. As I have described, in Greek and Roman studies this meant a revolt against the methods of Böckh and Mommsen; in the field of cuneiform studies this favored the formation of a generation who had contempt for scholars such as Lenormant and Oppert and considered them speculative and unintelligible. It is characteristic of the mood of the academic world that the Greek archeologist Bernard Haussoulier in delivering the official eulogy for Oppert at the Académie des Inscriptions engaged in character assassination by charging him with paranoiac delusions for not having been willing to compromise with Halévy and for having been critical of younger scholars who in the name of positivism wrote studies without knowledge of the problems involved and of the literature on the subject. It is also significant that Meyer, who was well known for his unfriendliness towards Jews and what he considered the Jewish mind, still in 1906, in the preface to his essay on Sumerier und Semiten in Babylonien praised Halévy, even though noting that as a lesser issue his theory of unreality of the Sumerian language cannot be accepted; he praises him for propounding that Mesopotamian culture is of Semitic character from the very beginning. The main argument of the essay is that the earliest pictorial representations of Mesopotamia present types that appear Semitic to the author. Meyer had to uphold the essence of Halévyís views, since the history of Mesopotamia with its succession within the same culture of people speaking a completely different language and possibly of different geographical origins, is by itself a refutation of an interpretation of history based on doctrines of a Semitic national character derived from a contemporary stereotype of the Jew.

In 1892 Lehmann-Haupt wrote what serious scholars came to consider a final refutation of Halévyís theory about the Sumerian language; Weissbach grants that only Heinrich Zimmern and himself did not consider this refutation “totally adequate.” In this refutation Lehmann-Haupt declares in a formal statement that he will not use as an argument the theory that in cuneiform reckonings there are mathematical conceptions that cannot be of Semitic origin and that in general he does not believe in national character as a valid historical theory, specifically expressing his disagreement with Meyer. He remained entirely faithful to this position in spite of the unfriendly political and academic atmosphere in which he happened to live, and his historical writings presented the history of Israel as central to Oriental history, just as Meyer had, but with opposite evaluations, considering that rational forms developed in Israel have positively contributed to the intellectual heritage of the modern world. He steadily opposed the use of characterological stereotypes.

The publication by Lehmann-Haupt of his essay on the Sumerian language created a personal friction with Weissbach in addition to the scholarly disagreements. Weissbachís study on the Sumerian question published in 1898 does not add anything to Lehmann-Hauptís argument and is simply a history of the polemics between Halévy and his opponents, but Weissbach wanted it to be the basis for his claim to glory. And indeed today one generally quotes Weissbach as the one who refuted Halévy, and Lehmann-Haupt is seldom mentioned; this is the price that the latter had to pay for holding unpopular opinions. Lehmann-Haupt had been careful not to reverse the racialist argument used by Halévy, but Weissbach exploited to the full Halévyís irresponsibility: he concludes his book by condemning the “rabbinical-halakic conceptions” and lumps Oppert in the condemnation of Halévy by referring to “the couple of hostile brothers. “ This reference to Oppert is unspeakably vile, since Oppert had nothing in common with Halévy, and proves only that if there were brothers under the skin, these were Halévy and Weissbach, both spiritual descendants of Gobineau.

Weissbach followed a line that was popular in the academic world, since there were many who had to accept that Oppert was right after all, but did not want to recognize his intellectual stature. Oppert had linked Mesopotamian studies with metrology and Lehmann-Haupt had followed on this line, and hence one could charge them both with being visionaries in this area. Weissbach took up these ideas in his struggle against Lehmann-Haupt. Since the latter had tried to demonstrate in detail what all metrologists believed, that the Mesopotamian system of measures was the origin of all metric systems of the ancient world, and at the international Congress of the Orientalists of Stockholm in 1889 had submitted a paper entitled “The Old-Babylonian System of Volume and Weight as Foundation of the Ancient Systems of Weight, Coinage, and Volume,” this contention was denied by Weissbach. Since specifically within the field of Mesopotamian studies one finds that the earliest written documents present a system of metrics that persists intact into Persian times, and since this fact by itself is a denial of a distinction between Semitic and non-Semitic mathematics, the effort of Weissbach is directed at proving that in Mesopotamia there are “older” and “newer” types of units.

Against these arguments Lehmann-Haupt had to engage in a hopeless struggle, since those who supported Weissbach were not concerned with scientific evidence. As all the new school metrologists, Weissbach could make statements that were manifestly false and be approved. Lehmann-Haupt not only was intellectually isolated, but was dismissed from consideration with the argument of intractable character. Considering that he was a member of the most notoriously anti-Semitic faculty of the German-speaking world, Innsbruck, it is not surprising that he had some difficulties with his colleagues. The same weapon was used against Oppert, but the former had the advantage of living in an age in which he could find a more benevolent atmosphere at least outside the academic world, whereas Lehmann-Haupt died at the highest point of Hitlerís power. Oppert was described by some of his colleagues as a cantankerous curmudgeon, whereas even in his old age he was lionized by Parisian society for his charm and benevolent wit and was, in spite of his boundless erudition, a bit of a Left-Bank Bohemian. Wallis Budge is not particularly interested in increasing Opperts status (since for an understandable and laudable loyalty he resolves the moot question of the credit for the discovery of the Sumerian language in favor of Rawlinson) but he characterizes Oppert in these terms: “He was singularly free from literary jealousy, and maintained friendly relations with younger scholars who were working on his special subjects, as... Weissbach... But he was a bitter foe to all prentenders to knowledge... on whom he poured his wrath in many languages.” Oppert was willing to be counted when it was a question of truth, even outside academic matters: in a time when Jewish circles in France were afraid to discuss the Dreyfus affair, he, a métèque, was one of the first to champion the case and, at a time when dreyfusard was a name of abomination particularly in the scientific academies, he took care of the English translation of Zolaís Jíaccuse.

9. In general Mesopotamian studies became a battlefield for those who wanted to extol or decry the merits of the Jewish race. Both were interested in identifying the culture and even the racial identity of the Hebrews with that of the Akkadians; this was initiated by Halévy who made the Jews the heirs of the Akkadians and hence the creators of all culture, but the same argument was employed to prove that the Hebrews had not created anything and that all that could be read in the Bible had earlier been said in Babel. But both groups have been interested in reducing the role of the Sumerians and even more in denying the role of mathematics in Mesopotamian culture. Since it is believed that mathematical conceptions do not play any role in the Bible, it follows that any equation of the Bible and Babel must exclude them as a central element in Mesopotamian culture. Furthermore, it is obvious that mystagogues abhor that rationality and logic of thought of which mathematics is a symbol.

The sects of the racialist interpreters of Mesopotamian culture have a link with those who intend to use Mesopotamian practices to prove their particular notions about the nature of biblical religion, with the result that all sorts of religious conceptions belonging, or allegedly belonging, to an Iron Age culture based on an economy of marginal hill farming, have been inflicted upon a Bronze Age culture based on planned estates of fertile lowlands. Here again the awareness of the mathematical aspects of Mesopotamian culture tends to be reduced to zero. Actually the economy of the Hebrews has much more in common with that of the Greeks and this is reflected in some common conceptions of the role of measures in society.

A typical representative of this last trend of thought who opposed Oppert and old school metrology, was Paul Haupt (1850Ė1926) who in 1883 was called from Göttingen to Johns Hopkins University and became the leader of the first group of Mesopotamian scholars in the United States. Haupt was a pupil of the Orientalist Paul de Lagarde, the father of the history-of-religion school of theology, a school that intends to dissolve theology into history of religion. Theology may be or not be pernicious to human progress according to a personís values, but it is a fact that theology is a formal intellectual discipline like mathematics and law, and the dissolution of theology among the members of this school has been accompanied by a dissolution of formal reasoning. Even sympathetic biographers of Lagarde observe that he could not separate his subjective feelings from objective data. He applied himself to ancient metrology proving only that he could not cope with it; he applied himself to metrology because, together with following the mysticism of German national-conservatives, he had a hankering for scientific thought: according to him German national Christianity should be the result of the application of the spirit of scientific inquiry to religion, as exemplified by his study of Giordano Bruno. His pupil Haupt as a Sumerologist claimed that he truly was the one who had discovered the structure of the Sumerian language and that Oppert had Lenormant were less than apprentices who could not solve the problem, since they were confused and lacked method. The truth is that Haupt had an excellent knowledge of Hebrew, and this proved an asset when it was realized that Akkadian was a West-Semitic language and hence much closer to Hebrew than to Arabic, in relation to which it had been studied up to that time; since in the period Haupt wrote about the Sumerian question one studied Sumerian only through bilingual texts, his insight into Akkadian allowed him to obtain important results. But Hauptís claim to superior knowledge of linguistics is unfounded: he relied more on intuition and could not appreciate the technical rationalistic mind of his predecessors.

Haupt made declarations about the necessity of acriby in linguistic study and demanded that Semitic linguistics be raised to the standard of the Indo-European, a demand that has yet to be satisfied today, but these declarations have as little implementation as his declared devotion to science in the interpretation of biblical history; his etymologies are romantic and are further complicated by a desire to annex Sumerian to Hebrew. One can quote scores of examples as the derivation of the Hebrew term for the number one from the Sumerian É-GAL, “great house,” or the derivation of the term Hebrew from a Sumerian IBIRA, “merchant,” through an Akkadian ebir, “itinerant peddlar,” a term to be connected with amber (Open Court 32 (1918), 758). Hauptís most distinguished pupil, Albright, has repeated in several works that Oppert could not refute Halévy because he did not have the solid linguistic method of Haupt. I may observe, first, that one could not refute Halévy at his level and the only method was that of reading consistently Sumerian texts for which there was no Akkadian parallel, which Oppert did; and, second, that in 1885, when the defense of the Sumerian language had become a most unpopular task, Haupt completely withdrew from Sumerian studies, and that, whereas he felt free to use expressions as “not worth the paper they are written on” or less complimentary ones in reference to his fellow Sumerologists, he never was as forceful with Halévy.

The very discrepant evaluation of Hauptís approach offered by Albright reflects a substantial disagreement on method. Haupt, like his teacher de Lagarde and like his Ameridan pupils, believed in a spiritual approach as opposed to technical rational analysis. From my point of view their effort to reconcile religion with science destroys the essence of science, even though in their opinion they operate on a higher level of understanding. An example of Hauptís scientific method is his article “Was David an Aryan?”, which ends with a negative answer, because “his hair was nor red or blond, but black; and his complexion not fair, but brownish or olive. His stature may have been somewhat low, and his frame light” (ibid.33 (1919), 97). Following the same anthropological science one could argue that David indeed was not a Jew, since the Bible does not in any way intimate that he was flat-footed. Haupt uses a similar technique in dealing with the issue of Jewishness of Jesus.

The specific topic to which Haupt dedicated the greatest attention was that of the Flood and the Ark, a topic that I shall show is most relevant to Mesopotamian metrology. He thought that he would have reconciled science and religion if he could prove that the Flood in some way was an historical event and the Ark was actually built or could have been built. It is true that he made some use of geology and of naval science, but to achieve his purpose he totally distorted the texts and took liberties with mathematics. There are those who think that if it could be proved that when Moses saw the flaming bush, he had actually struck an oil well, it would be of advantage to religion and to science. But whereas our society proves its respect for religion by claiming that all opinions are equally valid, there are recognized objective standards of science by which one can declare that Hauptís interpretations are not science, even though he has a particular liking for such technical subjects as musicology and metrology. This will appear from my analysis of his disagreement with the metrology of Oppert and Lehmann-Haupt.

10. The revelation of Sumerian civilization came at the wrong moment of history. One can well imagine what would have been the excitement if the revelation had taken place in the eighteenth century, when there was an entire literature about imaginary rational people of the Near East; most likely the Sumerians would have been made into a political ideal. Instead today the educated public barely knows the name of the Sumerians and even among historians one seldom mentions them, as is indicated also by serveral contemporary general histories. The Sumerians are a scandal, since the revelation of these wise and intelligent discoverers of the arts and sciences (I am forced to think of the myth of Atlantis), came in a period when ancient history like anthropology is mainly interested in weird practices and murky beliefs, and a great effort is directed towards reinterpreting classical civilization as the realm of the unconscious, the instinctual and the primitive. In a recent work From the Tablets of Sumer Kramer gives a full interpretation of the Sumerians for what they were, yet one notes in it a certain timidity that goes beyond the understandable restraint of a highly responsible scholar; it is not surprising that the book was more enthusiastically received in France than in the United States, since in France rationalist tradition can still defend itself. The Sumerians are a scandal on the present horizon of scholarship for the same reason that metrology is.

The Sumerians have not been popular even with experts of Sumerian language who have tried to introduce into their culture some redeeding foreign element. As one can see even from the published transactions, no topic stirs greater debate at a convention of Mesopotamian specialists than a discussion of ethnic factors in the birth of the culture of the area; each scholar has his own set of races, material cultures, or languages (the concepts are hardly kept distinct) and can move them at will through the map and through the centuries, marshalling invasions as a general would align armies, since at the present state of the data the problem is totally undetermined. The same approach has plagued the study of the tablets that contain the earliest steps in the art of writing, the tablets of Uruk IV, Jemdet Nasr, archaic Ur and Shuruppak (between 3500 and 3000 B. C.). It would have been proper to assume that these tablets are written in Sumerian unless otherwise proved, but on the contrary it took a slow gathering of positive indications to refute the opinion that the texts were not Sumerian. Still in 1952 Ignace Gelb in A Study of Writing insisted that there was an influence by the ethnic element X. I mention these theories because the texts deal with metric information, but no great attention has been paid to their metrology, except to argue that it reveals a non-Sumerian element, which ususally by some devious way proves to be the alleged Semitic mathematical mind.

It is typical of the way one deals with metrology today that scholars who avowedly are ignorant of metrics in general and cannot read the metrics of the specific texts, find in them evidence of non-Sumerian units. The truth is that the metric system of these tablets is the same of later documents: there is a pint with multiples of 60, 120 and 300 pints and there are units related as 5:6. Since this system is not originary and results from an effort to adapt units to sexagesimal computation, it follows that the metric system was well developed when writing began. The contemporary tablets of Susa that present an independent attempt to develop writing and apparently are also Sumerian, reveal the same system of measures.

In a future study I shall show that the alphabet derived from the operations of the abacus. All the alphabets from the Greek to the Korean, from the runes to the Arabic alphabet, preserve the structure of an original alphabet of four vowels and twelve consonants placed by groups of four in the sixteen cases of the basic abacus; on phonetic grounds one must conclude that the original alphabet is Sumerian. It will be possible to consider the origin of writing in a completely different light, and the theory of Friedrich Delitzsch that cuneiform writing developed from sixteen basic patterns will have to be reexamined. I may call attention to his remark about early cuneiform signs, Ein Teil dieser Urzeichen is matematischer Ursprung, and to the main objection against his theory which is: “his explanation is too abstract to correspond to primitive ideas.” There is nothing primitive in the metrology of the earliest written texts and their mathematics reveal a perfect capacity for abstract ideas. For what I have been able to gather I guess that others competent to deal with such problems will be able to trace the origin of the abacus into the Upper Paleolithic. Hence it may happen that the historical search for noble savages will not be able to stop at the Greeks, but will have to move a few millennia backwards.

Ephraim A. Speiser who has employed his keen intelligence to spin around the earliest texts racial theories of the type just described, in a different mood has formulated a statement on “Ancient Mesopotamia and the Beginning of Science” which reveals an insight superior to anything ever written on early Mesopotamia. “The extraordinary development of mathematical and related studies in Mesopotamia is to be sought, I believe, in conditions which antedate the introduction of writing. In fact, I would add, the origin of writing as well as the interest in mathematics are to be traced back, in this case, to a common source. This source will be found inherent in the society and economy of prehistoric Sumerians.” He observes that the several forms of learning, from philology to law and natural science, were devoloped as a byproduct of the effort to transmit and to perfect this art of writing; hence, I would subjoin, there is a mathematical cast to the entire culture. I have tried to show a similar phenomenon in Greece and it is just because the role of mathematization in Greek culture has been so bitterly denied that I have become interested as an outsider in Sumerian culture.

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