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Why Study Metrology?

La metrologia non é scienza, é un incubo.
(Metrology is not a science; it’s a nightmare).
-G. De Sanctis

In 1923, Wilhelm Kubitschek, archaeologist and numismatist, author of the most comprehensive study on ancient measures of time, wrote:

There are scholars such as Theodor Mommsen and Hultsch, as Dörpfeld and Nissen, who have presented the problems of metrology in a comprehensive, clarifying and self-contained form. But, because of the way it has been handled in the last decades and particularly in the last few years, metrology is today probably the most unappealing field of ancient scholarship.

This is something I did not know when Angelo Segrè first introduced me to the problems of metrology in Greek papyri. I was then in my last year of secondary education, and I thought that it would be pleasant to apply my classical education to the solution of problems that for their formal rigor appealed to my personal temper. It took me many years to discover that I was engaged in a field that, within its limits, was as dangerous as the study of astronomy in the age of the Reformation and Counter-Reformation. I began to realize this only when I undertook the writing of a doctoral dissertation to be submitted to Harvard University. I had been educated in such a sacred respect for Mommsen and had such a deep personal admiration for August Böckh that, quite innocently, I could not believe that anyone could seriously impeach the validity of their method. At the University of Rome, I had become aware of the ideas held by the literary faculty, and I had been told how the teachers of ancient history, Julius Beloch, Gaetano de Sanctis, and Ettore Pais, used to talk to the students: their condemnation of the philological method, their warning against reliance on auxiliary disciplines and their scorn of the constructions of Roman law. But their utterances were mixed with such crude anti-German quips and with such offensive references to Mommsen that the students were inclined to discount them as political moods or personal peeves. In the Italian intellectual climate, even the most extreme positions can be expressed without great harm, since all ideologies are met with a degree of skepticism. It was for this reason that the erratic genius of Beloch was welcomed at the University of Rome, whereas Mommsen and Wilamowitz had considered his ideas so dangerous for scholarship that they had prevented him from obtaining a chair in Germany. It was only when I came to America that I discovered that the principles of the Roman school of classical studies had been accepted by some outside Italy with a dogmatism that was more deep rooted, because it had become unconscious or inarticulate.

In my thesis the disagreement with De Sanctis’ school was embodied in two points. One contention was that the structure of ancient systems of metrology was such that all units of weight and volume could be calculated long or short with a difference of 10 per cent; the short calculation was called in Greek inscriptions pheidolos from the verb pheidomai, “to be chary.” The existence of this terminology gave rise to the construction of an imaginary character called Pheidon of Argos, a figure of great importance, because his imaginary date was used as an anchor point by ancient Greek chronographers and was used, for instance, to fix the date of the first Olympiad. The second contention was that many important Greek texts, as, for instance the Athenian decree on coinage in the Delian League, had been badly understood because of an erroneous interpretation of the phrase metra kai stathma kai nomisma (or nomos). This phrase, which is the key one in ancient metrological texts, corresponds to the phrase numero pondere mensura of Roman law and is found in important passages of the Bible and of the Talmud. It is a phrase constructed according to the principles of Semitic syntax and consists of three synonymous terms linked by an explanative vau (literally translated into Greek by kai) and conveying a single idea. I tried to present my point of view in a form as limited as possible, making as many concessions as possible to the other side. I was so discreet that I did not mention the word “metrology” more than three or four times, but the disagreement about the value of my kind of research remained, and my thesis was sharply criticized from a methodological point of view. To be more exact I should say that the criticism was epistemological: it was a matter of deciding whether the Greeks or any other human beings could have thought in the way I described. In the following years I learned that this is the very essence of the debate on metrology. In this field one can rely on evidence more reliable than that usually available in ancient scholarship, and as a result there is substantial agreement among specialists about all essential points; but other scholars refuse to accept the conclusions drawn from the evidence because these do not suit their way of thinking.

I had just begun to ponder the criticism of my thesis when I went to teach at the University of Chicago, and on that occasion I paid a visit to Professor Jacob Larsen. When I described to him what my interests were, he told me that metrology had been completely debunked and added that I had “better read what’s been written on the subject in recent years.” This advice was not intended to be friendly, but it proved useful, because then, for the first time, I began to read in chronological order all that had been written on the subject of ancient metrology. Up to that time, I had concentrated my attention on the works of authors whom I considered competent and responsible. Reading all that had been written in this century was a painful process, since I found myself submerged in a realm of total irrationality, but it allowed me to arrive at an understanding of why a highly technical and impersonal research could meet deep-seated emotional hostility.

I had pursued the study of metrology because I knew it was a promising field, providing a solid method of investigating several topics of ancient history, but I did not suspect that I had involved myself in a controversy touching upon basic issues of intellectual life. At moments, I felt that I should abandon my research, since my task was overwhelming, but what I found was so outrageous in terms of my values of justice and truth that I concluded I should continue it.

The basic points of ancient metrology were reconstructed in the seventeenth century by two successive holders of the Saville Chair of Astronomy at Oxford, John Greaves (1602-1652) and Eduard Bernard (1638-1697). Their work is connected with the development of the ideas of Newton, who also was interested in ancient metrology. The achievement of these two scholars, men of extraordinary encyclopedic learning and of more than human capacity for work, was such that Christian Eisenschmidt as early as 1701 could say, with reason, that to write about metrology after Bernard was like writing the Iliad after Homer. The modern study of metrology was initiated by Böckh, who amplified the work of his predecessors by taking Greek inscriptions as his main starting point. Bernard had also been active as an editor of Greek inscriptions, but his information in this area was necessarily limited; he relied mainly on Greek and Oriental literary sources, many of which he discovered himself through his activity as a collector of ancient manuscripts. Following the principles already formulated by Greaves, Böckh stressed two main points. The first, that there was one single system of metrology, which had been developed in Egypt and completed in Assyria by connecting the Egyptian units of length, volume, and weight with units of time and with angular measurements; this system was received as a unified whole by the Greeks. The second, that the system developed by the Egyptians was conceived like the French metric system, in that the unit of length, by being cubed, gives the unit of volume, which, filled with water, is the unit of weight. On a different level, Böckh was one of the figures mainly responsible for the establishment at the beginning of the nineteenth century of the concept of philologia, the concept that classical culture is characterized by certain general basic ideas and that these can be best approached by the development of specialized branches of investigation, each with its own methodology. One of these branches is metrology, which Böckh established as a formal discipline. Up to the end of the nineteenth century, generations of scholars pursued metrological investigations accepting the basic structure outlined by Böckh.

By a quirk of fate, the attack against the study of ancient metrology was launched in England, where the study was born. In 1892, William Ridgeway published his sensational work, The Origin of Metallic Currency and Weight Standards. It has the pretension of great encyclopedic learning, but in reality it is a conglomeration of hastily collected information of all origins badly put together. It is difficult to criticize its methodology, since the author proclaimed to have introduced a new scientific method called “inductive” ; his writings indicate that by this term he means a method based on intuition of what must have been the truth. In the first lines, Ridgeway proclaims that Böckh’s “theory was undoubtedly suggested by the fact that the French Republic had established a new scientific metric system.” This statement is as inaccurate as most of those that follow, but it is considered sufficient to dispose of Böckh’s work. Ridgeway did not bother to inquire about Böckh’s English predecessors. He considers that it is absurd to assume that the Egyptians and the Assyrians could, from early times, have had a “scientific” system of measures as that described by metrologists. As a proof of this, he describes the systems of currency used by several primitive societies; the argument consists in applying to highly developed cultures the anthropology of preliterate societies. As pointed out by reviewers, the author did not like the idea that Oriental cultures could have had any influence on Greece; metrology must be, rather, the invention of the “Aryan” races. For this reason the author imagines the existence in the entire Aryan area from India to Spain of a system of metrology based on the amount of gold corresponding to the value of a cow. The Babylonians and the Egyptians would have developed their own systems beginning with the Aryan cow unit. This piece of writing was greeted by several English scholars as the fanciful work it was. But in the following years the prevailing attitude of English scholars began to change. On the eve of the First World War, England was possessed by an inferiority feeling in respect to German industrial and scientific achievement; this feeling of inferiority had its reflection on the field of classical studies in which many began to talk of the necessity of freeing themselves from the influence of German scholarship. It was said that the heavy, technical “German” method of scholarly investigation destroyed appreciation for classical works and corrupted human beings by mechanizing them. The archaeologist Sir William Ramsay proclaimed that there were two methods of scientific research: one, called the “method of exhaustion,” by which the researcher considered all possibilities before choosing one; and the other by which the researcher conceived a new idea. The first method required “continuity of working and belonged to the Germanic races; the second method required “ingenuity” and belonged to the Anglo-Saxon races. With the second method one arrived at discoveries, whereas with the first method one could only perform useful work. It is obvious that according to these methodological principles the work of Ridgeway is the expression of superior scholarship.

It must be noted that these ideas were presented by Ramsay in 1914, a period in which he was active organizing in the United States a revolt against the alleged Germanization of scholarly techniques introduced by President Eliot of Harvard. Up to 1912, he had been a member of an Anglo-German group, headed in Germany by Theodor Wolf, of the Berliner Tageblatt, formed to prove that there were no basic economic conflicts between England and Germany and to further intellectual cooperation between the two countries. Ramsay’s passage to the prevailing camp of anti-Germanism was marked by the Oxford History Lecture of 1913, in which he declared that henceforth the English Empire must not be based on economic considerations but on “faith” and “moral values” ; he used these terms as empty of any content as they are in Fascist terminology.

As English classicists were whistling in the dark, they realized that there was one field in which their scholarship was superior to the German, that of numismatics. It happened, however, that the brilliant achievements in English numismatics had been made by people who were gentlemen scholars or operated in the tradition of gentlemen scholars; they considered it quite unpleasant to have to bother to learn the arithmetical technicalities of metrology. In general, there is little good feeling between metrologists and numismatists, because their two fields infringe upon each other but require completely different skills and types of memory and imagination. The metrologist, engaged mostly in a speculative work that requires pencil and paper, has to remember huge series of numerical texts in order to be able to arrive at a synthesis; the numismatist must have an extraordinary memory about material objects, in order to be able to classify them, and must develop a feeling about them that includes a particular sense of touch. I suspect that here we deal with the distinction, pointed out experimentally by the electro-encephalograph, between individuals who think in terms of abstractions and individuals who think in terms of concrete images; brain physiologists remark that intellectual communication between the two types may be difficult. Plato noticed this distinction-and the resulting difficulty of mutual understanding. Much progress would be achieved if numismatists and metrologists would develop a respect for the achievements and the limitations of their respective fields. But this has not been generally so up to now, and the existence of a team composed of a numismatist and a metrologist, such as Kurt Regling and Carl Lehmann-Haupt, is a rare occurrence. In this situation, English numismatists thought that they could proclaim numismatics to be a field in which Englishmen had nothing to learn from the Germans; this meant that English numismatists had no longer to ponder the metrological treatises written by German scholars. It is quite significant that it was the numismatist Percy Gardner who in 1903 delivered the most important appeal for the liberation of English classical studies from German influences, in his essay Oxford at the Cross Roads. This book ends with the conclusion that henceforth English “intelligence” must substitute for German “amassing and ordering of facts.” It seems that Oxford always had its share of Percy Gardners, since a biographer of Bernard reports that “his erudite pursuits rendered him an object of ridicule in gay society.” Bernard’s primer of metrology was criticized for being hard reading; to this Thomas Smith, who with Bernard had edited the Greek inscriptions of Palmyra, replied, neque enim elementa in puerorum aut iam discere incipientium usum scripsit.

As a result of the political situation, the defense of Ridgeway’s work became a matter of prestige for many English scholars and for numismatists in particular. In the heat of nationalist passion, Ridgeway became a hero and, at the end of 1914, was elected president of the Classical Association. In his Presidential Address, he took the occasion to denounce as pro-German the English scholars who had dismissed his papers as unscholarly: “My only offence was that I had ventured to dispute what the Germans had said.” He then proceeded to compare the reception given to his work by respectable English scholars to the attitude of English biologists who, in their subservience to Germany, subscribed to “Weismannism” and refused to accept the ideas of a friend of his who aimed at proving the inheritance of acquired characteristics. This little detail proves that there is some method in this world of madness; the Lysenko affair in the Soviet Union also consisted of condemning “Weismannism” as “kowtowing to foreigners” (inostranshchina). It is rather significant that Ridgeway proceeds by warning Englishmen that Greek history teaches that unless they temper their democracy with some return to aristocratic institutions they risk losing the war. The ideas of Ridgeway continued to be accepted as truth by English numismatists even beyond 1918 and have influenced all their writings up to the most recent ones. It has been accepted that the proof that Ridgeway failed to provide about the existence of the cow standard was provided by Arthur Evans in 1906 (Minoan Weights and Currency), who claimed that some bronze ingots found in Greece represented an oxhide and had the value of a cow.

When I wrote my Harvard thesis, I knew that I could not achieve anything in the field of metrology unless I refuted Ridgeway’s theories, but I decided that, instead of engaging in polemics, I should take a constructive position. A careful perusal of Ridgeway’s work convinced me that his analysis of anthropological evidence had confusedly pointed out an important fact of Greek history, namely, that before the reception of the system of metrology the Greeks had used utensil money such as is used by many primitive people. Therefore my thesis consisted, first of all, of a detailed archaeological analysis of the types of utensil money used by the Greeks. On the basis of this analysis, I proceeded to a review of the conclusions of C. T. Seltman’s Athens, Its History and Coinage, a work that contains many important numismatic results, badly distorted by being combined with a total acceptance of Ridgeway’s theories. I devoted a special appendix to Evans’ theory of the oxhide ingots. Heinrich Willers, who is not a friend of Böckh’s method, wrote, “Evans’ work is one of the most fantastic ones of modern metrology.” I did not say anything of the sort, but through many months of patient research I was able to prove that the ingots, which with a great effort of imagination could be said to resemble oxhides, were plain ingots of smelted metal that had that shape for metallurgical reasons. I was able to point out the use of smelting techniques producing ingots of the same shape in several periods and in several parts of the world. I think that I can hardly hope ever to prove a case with equal assurance. But those who reported on my thesis asked me how I could dare to contradict Sir Arthur Evans so blatantly. It is obvious that if I had to bow to Evans’ judgment in this matter, I had to accept a fortiori the positions of Ridgeway and Seltman.

Another line of attack against metrology developed in the context of German and Italian scholarship. At the end of the nineteenth century, the leading representative of philologia in ancient historical studies was Mommsen, who tried to further, in particular, the study of Roman law and metrology. Against this kind of scholarship Nietzsche lifted his voice and with him the entire nihilist trend of thought of Germany at the turn of the century. In the field of ancient history this movement of revolt found its expression in Beloch. Beloch’s main passion was politics; he advocated the establishment of a popular dictatorship and thought that Germany had been totally corrupted by French and Jewish ideas. One of these ideas was constitutional government and the rule of law, which German ultranationalists blamed on the German reception of Roman law. The study of Roman law was also linked at the moment with the name of Mommsen, who was particularly obnoxious to German right-wing radicals for his courageous championing of intellectual freedom and for his opposition to intellectual chauvinism. Hence the necessity to condemn Mommsen with the entire concept of philologia. Metrology was a clear embodiment of the evils of the philological method. It is worth noting that at the same time French nationalists were attacking Mommsen and his type of scholarship, as an instrument of German imperialism; he was accused of being a spokesman for Bismarck, under whose rule he was actually brought to trial.

The two founders of metrology, Greaves and Bernard, had relied mainly on their extensive knowledge of rabbinical literature, and Böckh had stressed the similarity between ancient metrology and the French metric system. This clearly proved to Beloch that he was dealing with an idea concocted by his mortal enemies, the French and the Jews. In German academic circles, Beloch was a prophet before his time, but he found a friendly reception at the University of Rome, where some classicists had adopted Nietzsche’s motto Ceterum censeo delendam esse philologiam. There he could pander to Italian nationalism by inveighing against the “German philological method.” From the German Jugendbewegung, the movement of revolt against all intellectual, social, and moral traditions, Beloch imported the term Abschreiber, “copycat,” which was translated into Italian as scimmione, “ape,” and with this word the Roman school disposed of all “philologists” who were described as abstract and pedantic squelchers of the creative spirit. It was natural that the study of metrology, with its technical and mathematical rigors, should be quoted as the worst example of scimmionismo.1

There was also another specific reason for Beloch and his pupil De Sanctis to direct their fire against metrology. In 1891 Aristotle’s Constitution of the Athenians was discovered, which they greeted as an opportunity to do away with the philological method in the field of Greek history. They set down the principle that this text should be the basis of the study of Greek history. This procedure, which one could well accept on practical grounds, to them meant that the study of Greek history could be reduced to politics without consideration for Greek intellectual history and that one could study a single text in isolation without all the baggage of auxiliary researches required by the philological method. An incidental reason for stressing the significance of this text is that allegedly it emphasizes the importance of dictatorship in Athenian social progress.2 In reality, Beloch and De Sanctis were the least fit to appreciate a text of Aristotle, for whom formalism and constitutional government were of paramount importance. Only now, after fifty years, scholars are beginning to recognize how little progress has been made in the interpretation of the Constitution of the Athenians. The text of Aristotle bothered Beloch and De Sanctis in that it contained references to Solon’s metrological reforms and hence seemed to require a knowledge of this most condemned auxiliary discipline. De Sanctis tried to disentangle himself by asserting that Solon’s social reforms had nothing to do with his monetary and metrological reforms, but, even when relegated to a lesser place, metrological questions continued to exist. It was necessary to prove that the passages of Aristotle could be interpreted without reference to the formal structure of ancient metrology, and that all that had been written up to then about metrology was an imaginary and arbitrary construction. Beloch and De Sanctis were not afraid to do this, since they had already intimated the same about the system of rules developed by scholars of Roman law.

The parting shot for the Roman school was fired in 1909 by Willers in his Geschichte der römischen Kupferprägung. Willers was a numismatist who had reasons for disagreeing violently with Mommsen’s study of Roman coinage, since this work is weak from the numismatic point of view, as Mommsen himself admits in a prefatory letter to the French translation. As I have said before, metrologists are usually weak as numismatists, but the reverse is also usually true. The great contribution of Mommsen’s work is his incidental study of Greek metrology, which allowed the development of Greek numismatics, up to that time only a poor sister of Roman numismatics. Willers thought that, having revised part of Mommsen’s work on Roman coinage, he should attack the entire science of metrology with which Mommsen was associated. For this reason Willers added to his respectable book a few prefatory pages that are a wild manifesto against metrology. This manifesto is based on what Willers had heard in Italy from the mouths of Beloch and De Sanctis. It does not contain any textual reference, but it gives in three pages an imaginary history of metrology that is a modified version of Ridgeway’s theories; Ridgeway’s work, however, is not quoted, probably because it was not accepted as respectable in Germany and Italy. Willers makes the following declaration:

The competent reader will be surprised by my repugnance for the so-called comparative metrology, whose dogmas have been forced upon numismatists, attempts having been made to include coins in its scope. A sort of apotheosis of this discipline is the booklet by Hultsch entitled Die Gewichte des Altertums in ihrem Zusammenhange dargestellt. This method is nothing but a mathematical playwork, and in the course of time it has brought about a complete crippling of research on Greek monetary standards. La metrologia non é scienza, é un incubo, properly complained an Italian historian, but I would rather call it a methodological frenzy. It is still beyond our knowledge how much the Egyptian and Babylonian weight systems have influenced the Greek and Italic ones but this much can be clearly seen already today; namely, that this influence cannot be expressed in a simple fashion-in terms of fractions. In any case, we must, in the first place, derive the Greek and Roman weight system from the monuments and meanwhile leave the Orient completely to one side.

In this way, one disposed of the work of generations of scholars who had shown that the Greek and Roman system of measures was the Egyptian and Babylonian one. It will, of course, be impossible to prove the identity of the systems if one sets the rule that scholars of Greek and Roman metrology must ignore the system of the Orient. As to the alleged crippling of research on Greek monetary standards, it is a fact that studies had flourished up to just this point. Willers’ manifesto was echoed by Beloch, with an increase of invective, in the chapter “Metrologisches” of his Griechische Geschichte. The only point remarkable in Beloch’s statement is that he tried to develop in the spot a new system of Greek metrology and that his construction, as far as it contains documented statements, follows the conclusions and the techniques he condemns. This last point was made in 1915 by Ettore Ciccotti, a Marxist historian and Socialist politician, who in 1914 joined the ranks of the ultra-patriots of the Mussolini group. In order to prove his conversion to the side of anti-German academic chauvinism, Ciccotti, after ten years of scientific inactivity, came out with a book directed against metrology, Vecchi e nuovi orizzonti della numismatica. In this book, he demonstrates that there have been two attacks against metrology, that of Willers and Beloch and the English one, and that the latter is much more radical. It was obviously the right political move to uncover that the German Beloch had remained a Teuton after all. And, in fact, in 1918 Beloch was suspended from his chair at the University of Rome, a victim of the wave of fanaticism he had helped to stir up in Italy; it is to be noted that this event had a sobering effect on De Sanctis’ position. Ciccotti’s book must be read with his popular article of that same date, “Per l’emancipazione della cultura italiana.” In this article, he advised Italians to follow the example of English classicists, and of English numismatists in particular, who renounced competition with the overwhelmingly superior German scholarship, and to concentrate on the production of works of vulgarization and interpretation of history. He quoted at length the ideas of William Ramsay, but added the warning that this call for works of “genius” must not be “an excuse for laziness and improvisation.” This last reservation is a reflection of the fact that the majority of Italian scholars put up a good fight against the attempt to discredit the philological method. One may cite as an example the uncompromising position of Giorgio Pasquali. Beloch stated that his internment as an enemy alien in Italy in 1918 was the greatest misfortune of his life, because it prevented him from emerging as a political leader in Germany at the moment of the defeat, by means of the organization of a popular revolutionary movement based on hatred of Frenchmen, Jews, and Socialists; one may speculate whether English numismatists, Ciccotti, and metrology have to be blamed for the fact that the Third Reich was not established under the leadership of Professor Beloch.

The attack against metrology, which was conducted in the name of anti-Germanism in England and in Italy, took an anti-Semitic tone in Germany. The attack began as a dispute on some Assyrian metrological texts about which F. H. Weissbach disagreed with Carl Lehmann-Haupt. Weissbach, who was a sound scholar in the field of textual interpretation, decided to attack Lehmann-Haupt in the field of metrology. Weissbach had no competence in metrology, so he questioned the validity of metrology in general. Lehmann-Haupt used arguments from the field of metrology, in which he had a breadth of information unrivaled since the age of Bernard. The result was a polemic that lasted for years, with replies and counterreplies in which Weissbach made sweeping statements against the method of metrologists and Lehmann-Haupt and Kurt Regling tried to explain why, if one accepted Weissbach’s view, any metrological research would be impossible. For instance, Weissbach claimed that numerical relations do not prove anything and that “one must accept as proven only what is spelled out explicitly in words” General verbal formulations of accepted social practices belong to the highest level of culture, as Aristotle points out, and one would, consequently, never find the documents required before the age of Socrates at least. The general rules of Roman law began to be formulated in the Byzantine age and were, in some cases, formulated by Romanists of the nineteenth century. A clear refutation of Weissbach’s contention is provided by an inscription found at Thasos, recently published by Mabel Lang, which consists of three words and four numbers and is, possibly, the most important metrological inscription ever discovered.

One has to read about fifteen hundred pages in order to follow the dispute between Weissbach and Lehmann-Haupt, but the concrete issue under dispute is a single one. Lehmann-Haupt had realized that all important units of weight and volume exist in two varieties related as 24:25 or 96:100. He considered this discovery his greatest contribution to scholarship; he made it before the publication of Aristotle’s Constitution of the Athenians came to confirm it by definitely proving that in the Solonian system there were two minas of 432 and of 450 grams and that other units were adjusted accordingly. This confirmation was displeasing to Beloch and De Sanctis since it implied that one should study Solon’s reforms in the light of general metrological practice. Therefore when Weissbach denied the existence of the relation 24:25, he found enthusiastic approval and was thereby encouraged to defend an impossible position. Since the evidence about the use of the relation 24:25 is overwhelming, Weissbach was forced to question every single technique of evidence normally used in metrological investigations. For instance, since Lehmann-Haupt tried to prove his point by the examination of sample weights, Weissbach replied that such a difference between weights could be the result of accidental causes and, further, that one should accept as evidence only weights that were marked with inscriptions stating that they were official weights and stating expressly the number of the units and the nature of the units. Such a stricture is tantamount to asking epigraphists to limit themselves to the study of inscriptions that have been found in their full text.

The correctness of Lehmann-Haupt’s opinion on the relation 24:25 was proved in 1942 on theoretical grounds by August Oxé, who demonstrated that not only all weights but all units of volume were of varieties related as 24:25. In the thirties, Colonel de La Chaussée, in a series of articles in La Revue Numismatique, proved the existence of this relation on the basis of some of the best known ancient sample weights. In 1934 N. T. Bieliaev arrived at the same conclusion by a statistical analysis of weights excavated at Susa in Iran. I intend to show that the instruments and the methods of calculation used account for the relation 24:25. But, in any case, the single arguments used by Weissbach are not very important; what proved important is that he attacked Lehmann-Haupt in a manner that Lehmann-Haupt mildly called “unparliamentary.” Even Ciccotti granted that the language used went beyond what is acceptable in scholarly disputes. I do not know whether Weissbach intended to use anti-Semitic innuendoes, but the fact is that references The matter became worse when Oskar Viedebantt, who had begun as a follower of Lehmann-Haupt and published useful, though not outstanding, research, came into conflict with his mentor. Lehmann-Haupt accused Viedebantt of having appropriated the results of some of his studies3 and, in turn, Viedebantt blamed Lehmann-Haupt for his failure to obtain a university position. As a result of this miserable story, Viedebantt proclaimed himself the founder of a “new school” of metrology opposed to the “old school,” of which the representatives were, first of all, Lehmann-Haupt and then all other metrologists present and past who had followed Böckh’s ideas. The “new” school was composed of Weissbach and Viedebantt. In his first manifesto of the new school, Viedebantt subscribed to Willers’ position and declared that his school had as slogan Heraus mit den monumentalen Zeugen! Viedebantt, in spite of his slogan, did not produce any monumental evidence, but filled pages and pages with abstruse and often irrelevant numerological calculations, which occasionally are arithmetically incorrect. The English numismatists G. F. Hill and C. T. Seltman, who reviewed with enthusiasm Viedebantt’s Antike Gewichtsnormen und Münzfüsse (1923), because of his richness of contumely against the “old” metrologists, should have been punished by being asked to explain some of its pages. I know that they would have had a hard time doing it, particularly in view of the fact that their works prove that numbers definitely are not their forte. In a way I have done more justice to Viedebantt’s work, since, like Kubitschek, I have spent many a painful week in trying to interpret it and at times have found in it a useful reckoning. The prevailing frame of mind of the scholarly world in such matters is indicated by the review of Pericle Ducati, who praised the book while granting that it was beyond his ken. He declared, E questo non solo libro di scienza, ma di fiera battaglia. I can well see the “fierce battle,” but as to “science” I am of the opinion that it has been lost in the scuffle.

The seriousness of Viedebantt’s approach is indicated by the fact that, when he was about to break with Lehmann-Haupt, he claimed that he would have arrived independently at the discovery of the general occurrence of the relation 24:25 and he “was in condition of showing a heap of manuscripts” written before his becoming acquainted with Lehmann-Haupt’s position. This is a rather strange statement since Lehmann-Haupt had dealt with the relation in his earliest works, written when Viedebantt was still a minor. But most peculiar is the fact that Viedebantt, after he became a follower of Weissbach, dedicated the first pages of his Antike Münzfüsse to berating Lehmann-Haupt for believing in the existence of the relation 24:25. He did not explain how he intended to deal with the evidence concerning this relation he had gathered in the mentioned unpublished manuscripts and with the evidence he had published in the article “Hin” of the Real-Encyclopädie.

A more serious effort to establish a new metrology according to the pronunciamentos of the Roman school was made by Angelo Segrè. He started as a scholar of Roman law, but for reasons better known to himself he initiated a quarrel with the other scholars of the same field, one of whom was his uncle, by saying that they were reactionary and not aware of social and economic reality. Similar things had been said by Beloch and are a standard part of Fascist ideologies. In this way Segrè succeeded in spoiling some excellent legal studies and continued to do so up to his last one, which dealt with the Hellenistic katagraphe. Being blackballed by the Romanists, Segrè became a protegé of De Sanctis, under whose guidance he wrote his major work, Metrologia (1928). In the process of writing this work, Segrè became involved in a welter of absurdities; by the time he had accepted De Sanctis’ theories and let him edit the manuscript, there was little left of the original work. He had to believe that there was no close relation between the metrology of the several ancient countries and that there was no interdependence between measures of length, volume and weight, but the underlying, unexpressed idea of the entire work is to the contrary. The most important metrological discovery, namely, that the volume of the artaba depends on the relation of length between foot and cubit is buried in a footnote. On the basis of this footnote I was able to determine that measures could be calculated long or short with a difference of 10 percent; Greek inscriptions distinguish between calculation pheidolos and drakto. The situation caused such great personal distress to Segrè that at times he abandoned metrological studies for periods of years. Certain formal inaccuracies and erroneous quotations are evidence of the emotional stress under which he wrote his main work. About ten years ago he kindly suggested that, using his notes, I publish a revision of his treatise, but I found this tempting offer unacceptable, because I would have been in the situation of Procopius writing the secret volume of his court history. I can only say that Segrè’s inability to resist the cruel pressures of our age has resulted in a tremendous loss to scholarship. I do not hesitate to compare this case with that of Copernicus, who was compelled to deny the significance of his work. Segrè undoubtedly was unique in variety of skills and breadth of learning. As evidence of this, I can point out that after the publication of his Metrologia, friends competent in the field of physics suggested to him that he should abandon the ungrateful study of metrology and dedicate himself to theoretical physics, in which, in spite of his age, he could still achieve a fame similar to that of his brother.

Metrological studies continued in the peace of isolation in distant Romania, where Mihail Sutzu (Soutzos) dedicated his long life (1841-1933) to them. His achievements are great, and among them is that of having reduced all ancient weights to multiples or submultiples of a single Egyptian unit; this particular achievement was the basis of the last and most comprehensive study of Hultsch. In the following thirty years, Sutzu arrived at other similarly important results, which have not yet been considered by scholars. His position as a member of one of the great princely families of Romania may explain his aloofness from academic controversy, but in spite of his nobility of approach, he reveals an awareness of economic reality possibly inherited from his Phanariote Greek grandfathers. It is to be noted that this metrologist, too, was accused of kowtowing to foreign scholarship. Romanian nationalist and anti-Semitic extremists tended to be pro-German, so he was accused of frantzuzisme. Luckily, he had the strength to make this public declaration in the organ of the Liberal Party: “Since there are some who aspire to make an insult of the word frantzusit, I shall shout, and well aloud, so that nobody may fail to notice, I am a frantzusit and I consider this a glory.”4 I wish Segrè had had the same psychological security instead of wasting his life in fear of personal criticism of his work.

The only contemporary upholder of metrology is another isolated scholar, the Russian exile Bieliaev, an encyclopedic mind whose activity extends from the teaching of metallurgy to Oriental archaeology and Russian history. He has pointed out that the same weights with the same subdivisions are found in early Rome and in India of the third millennium B.C. He has traced the connecting links in Sumer and in Egypt, and determined that the same units were used in medieval Russia. Unfortunately most of his essays have appeared in the Seminarium Kondakovianum, the most distinguished, but little known, organ of Russian exile scholarship.

The history of the vicissitudes of metrological scholarship forces one to ask why there has been such an explosion of irrationality in a field that is so dry and technical. It is not extraordinary that somebody has claimed that Böckh, Brandis, Lepsius, Mommsen, Nissen, Hultsch, Dörpfeld, Häberlin, Brugsch, Lehmann-Haupt, Regling, Kubitschek and others spent the whole or a good part of their lives furthering a sort of conspiracy aiming at the befuddlement of the scholarly world, but it is extraordinary that such a paranoiac view was widely accepted. Incidentally, for some reason, the French metrologists De Sacy, Aurès, Decourdemanche, Thureau-Dangin and so on, are usually considered not even worthy of a dismissal.

My studies of ancient metrology have led me to two general conclusions: first, that metrology was born mainly from the practices of the international merchant class of the ancient world and, second, that metrology provided the foundation for the scientific rational vision of the world.

I think that these two aspects of metrology can explain the a priori prejudice of some classicists.

When one considers Max Weber’s description of the frame of mind necessary to the development of capitalism, one sees quite clearly that metrology corresponds to the main elements of it. Without entering into details about the history of a period for which I claim no competence, it seems to me that the spirit that Weber describes as the prerequisite of the capitalistic age is nothing but classicist rationalism as recreated by Humanism. Weber himself suggests this when he lists a rational legal system such as Roman law among the prerequisites. He agrees that the conception of universal society as formulated in the age of the Antonine Emperors best corresponds to the needs of a capitalist order. Metrology is closely linked with an outlook that corresponds to that of the modern capitalistic scientific world. It is for this reason that there are people who, with the same logic for which Jews are blamed for modern capitalism and science, recognize in metrology something Semitic. The sociologist Talcott Parsons has properly pointed out that phenomena such as Fascism, chauvinism and racial bigotry are the expressions of attitudes of rebellion against the increasing demand for rational behavior made by modern society; specifically he remarks that they are reactions against what Weber called “the process of rationalization.” Parsons states:

The reaction against the ideology of rationalization of society is one of the principal aspects at least of the ideology of fascism. It characteristically accepts in essentials the socialist indictment of the existing order described as capitalism, but extends it to include leftist radicalism and the whole penumrba of scientific and philosophical rationalism.
This also explains, to some extent, the nature of the attacks against metrology.

It should be the historical task of classicists to point out that the world of Copernicus, Galilei, Descartes, Newton, and Leibniz is their world, and to remind this world of its spiritual foundations.

On the contrary, the field of classics has often become the refuge of people with resentments against scientific progress, with a resulting hostility toward some fundamental aspects of ancient thought.

Herman Diels notes this in the preface to Antike Technik.

Alfred Espinas, who was one of the most influential thinkers of the French Third Republic, has indicated that the period of Greek bloom from the seventh to the fifth century B.C. was a period of rapid technological change which was closely linked with the development of Greek thought, and Rodolfo Mondolfo, who is a fine specialist of pre-Socratic philosophy, has written that the difficulty in interpreting the remaining quotations of pre-Socratic philosophers results from the fact that they were often lifted from the context of technological treatises.

Similar ideas are also presented by Pierre-Maxime Schuhl and, in a more popular version, by Benjamin Farrington.

These highly important views have even less chance of being considered than the achievements of metrological research.

This bias of classical studieshas been studied in relation to the birth of Italian Fascism.

The historian Luigi Salvatorelli (who is the most outstanding chronicler and analyst of the Fascist phenomenon in Italy) has written that Fascism was, first of all, a reaction by the class of parasitic job holders with academic degrees against the involvement of Italy in the stream of international capitalism. He noted that this ”humanistic petite bourgeoisie” was the product of a classical education emphasizing only the rhetorical skills, and saw itself threatened by the possible rise of true bourgeois elites with all sorts of technical skills, including technical skills in classical studies.5 Thus it was that the main butt of the future fascists was the philological method and the industrialization of Italy with the help of German technology and capital.6 It must be noted that it is in this context that anti-Semitic literature made its first appearance in Italy. Salvatorelli, who began his academic activity as historian of the Christian Roman Empire, points out that in Italy classical education of the rhetorical type, connected with an ancient history that emphasized the political side, gave ”an artificial representation of the ancient world” and created a complete ignorance ”of the new scientific-industrial world, of capitalistic civilization, of the economic and moral values of entrepreneurs and workers... and hence, reciprocally, this capitalist civilization often ignored and despised cultural values.”7 These remarks about the Italian political scene throw a good deal of light on the state of classical studies in general, and in a particular way should explain also why metrology met and meets such opposition. The attack against metrology began in England, where classical studies had taken the aspect of dilettante exercises, and received general support in a moment in which it was felt, rightly or wrongly, that England would be worsted in a liberal world of capitalistic competition.

It is significant that Eduard Meyer, who wrote in defense of the most crude form of philosophical positivism, dismisses all metrological studies in a few lines: “I hold as unjustified the assumption of Nissen and Lehmann-Haupt, approved by Thureau-Dangin, which unconscionably ascribes to the old Babylonians the modern speculation that derives the system of weights from the unit of length. In reality, all measures have been established arbitrarily before the existence of metric systems...”8 This statement is as dogmatic as the entire methodology of Meyer, who, together with diligence in compiling detailed historical research, had very fixed notions on the course of history, in spite of his proclaimed positivism, and for this reason was able to assemble a tremendous amount of facts within the framework of a universal history. One of the basic conceptions of this universal history was the paramount importance of the state in shaping culture; he discounted the influence of economic factors not controlled by the state. It is obvious that for this reason the entire world of ancient international trade and the cosmopolitan science of metrology was something not of his liking. At a minor level, one may note that during the First World War he proved to be a rabid academic chauvinist, and, reversing the argument of English warmongers, claimed that individual liberty and the notion of a world market was an English invention aiming at the total victory of capitalism and hence at English world supremacy.9

The attacks against philological method and hence against metrology, have often been justified on the ground of philosophical positivism. In reality positivism, taken as a serious position, is not an argument against metrology, as it is not an argument against the philological method.

For instance, one can write papers showing statistically that a word is used in a given sense; this is a technique most frequently used by scholars of Roman law.

In my own sphere of research, I have tried to stress as a mere fact that money is called nomos and that this word is synonymous with arithmos, and that arithmos is a synonym of metra, which means ”ratio.” But I have met the objection that these facts are too odd to be presented as such. Most of the prejudice against the conclusions of metrologists stem from the circumstance that often these have to be presented in a positivist form: it is often possible to point out identity of measures in very distant areas and in very different periods, without having the data for tracing the connecting links. The fact that in recent excavations of Indian Bronze Age sites the weights have been statistically tabulated has provided one of the most striking confirmations of metrological theories, because of the identity between these Indian units and the Roman ones. The English archaeologist Flinders Petrie took a positivistic position in matters of metrology, and proclaimed agnosticism in matters of metrological theories;10 for this reason he engaged in the task of tabulating statistically all the sample weights he excavated or could find available in collections. In spite of the fact that his sampling was of necessity incomplete (this type of research should be increased at least tenfold) he determined statistically the existence of a pattern of distribution of weight types which agrees perfectly with the conclusions of theoretical research.11 The last study of Hultsch, that which was the occasion for the attacks against metrology by Willers and Beloch, was written as a purely positivistic statement, aiming at proving on the basis of a long experience with the subject that in metrology one meets only with a limited number of types of numerical relations. Not only is it true that metrological research must often be conducted with positivist techniques, but also that, if one were to search for antecedents of positivism in ancient thought, metrology may be just the field: any system of measures must contain some positivistic elements, even though the ancients tried to justify their system of units on the basis of rational relations with an immanent order of the physical world. Modern positivism has its roots in Newton’s gravitational theory; Newton’s metrological studies may solve the problem raised by historians of science concerning the intellectual development that induced Newton to offer a theory which limits itself to the presentation of a pattern, without discussing causes. In reality the classicists who justify their position by appealing to modern scientific positivism, are using it merely as a pretext for rejecting the idea of order, whereas positivism, even twentieth– century statistical positivism, does not reject the idea of order. Pattern is the central idea of positivism, and the belief in the existence of well–defined patterns of thought and behavior in the ancient world is what is found to be objectionable by the opponents of philologia. The professed positivism of many modern classicists is a device for rejecting the intellectual structures of the ancients and organizing the facts according to the personal ideological assumptions of the investigators.

It is significant that Meyer, who is a voluminous writer, in one line dismisses as the extreme of metrological absurdity a study of Hugo Winckler showing how the ancients tried to connect earthly units of measurement with astronomical measurements. Meyer had to reject outright this fact for which there is abundant textual evidence, called to attention also by other studies, because it emphasizes one of the characteristic aspects of ancient metrology; namely, its connection with the notion of cosmic order and with the striving toward transcendental values.

It is not by accident that the two Oxford scholars, Greaves and Bernard, who founded metrological research were Biblical scholars and men of theological convictions, besides being linguists and antiquarians, and approached the study of astronomy and Greek geometry and mathematics with a religious feeling. It is not irrelevant that Böckh had theological training and was deeply influenced by Leibniz’s philosophy. His main concern in the study of ancient culture was the problem of intellectual harmony and the order of the universe; the influence of Leibniz’ thought in its mathematizing aspect is clearly revealed by the subject of Böckh’s doctoral dissertation, De harmonice veterum. One can clearly see how he brought to metrology ideas about ancient science that he had discovered in his study of Plato’s Timaeus. Greaves, Bernard, and Böckh shared a common faith in universal reason and were concerned with transcending the social and intellectual cleavage brought about, in one case, by the religious wars and, in the other case, by the French Revolution. At the head of his work on metrology, Greaves quotes an epigram by Guillaume Budé:

Una fides, pondus, mensura sit idem,
Et status illaesus totius orbis erit.

Budé (1468-1540), the scholar of Roman law who founded Greek scholarship in France, in first raising the problems of ancient metrology properly summed up with this epigram the spirit that animates metrology.12

It is for this reason that Maimonides was greatly concerned with metrological problems. Many of his conclusions are final and the clearest of the modern treatises of metrology, that by the Spaniard Vicente Vazquez Queipo13 takes its start from Maimonides’ work. Vazquez’ strength is his acquaintance with the Arabic-Hebrew culture of Spain, his weakness is his limited knowledge of the richer Greek materials, for which he misses the flexibility of the system of metrology, flexibility that allows adaptation to the most varied historical situations. One of the difficulties of metrology is the fact that it has both cosmological and practical economic aspects. It was the astronomer and cosmologist Pierre de Laplace (1749-1827), who was concerned also with the practical applications of the Newtonian concept of the world, who was able to determine that the ancients used a cubit of 555 mm.; this conclusion was confirmed about one century later by the discovery of a Greek inscription on which there is cut a reference standard of this length. On the other side, a thinker as unworldly as Spinoza did not understand the spirit of ancient metrology and, partly for the avowed purpose of discrediting Biblical authority, made offhand remarks about the mathematical ineptness of Hebrew metrology. These remarks have entered historical works and, being steadikly repeated without awareness of their origin, have greatly hampered metrological studies. A contemporary scholar who has clearly stated the intellectual value of ancient metrology is Georges Conteneau14 I do not find anything scandalous in metrology, since at the University of Freiburg I received my philosophical education from Husserl and Heidegger, the two most influential philosophers of this century, the founders respectively of phenomenology and of existentialism. Having accepted a position of realism, that is, of confidence in the identity of human thought with reality, I have a view completely different from that of classicists who had absorbed the nihilism and the psychologism of the previous generation of philosophers. This chasm is further emphasized by my training in Roman law and in the philological method, which imply more or less directly a belief in the validity of the structures of reason. From metrology there developed conceptions of the world such as are embodied in the Timaeus, which from Aristotle’s time until recently was considered the most important of Plato’s dialogues. It was the only dialogue known in the Middle Ages, and it is the text considered by scholars to best embody the ideal of Renaissance science. It is in its spirit that Copernicus, Kepler, Galilei, Newton and Leibniz set the foundations of modern science. But something radically new followed the popularization of Newton’s theories. It was a gradually increasing attitude of revolt against reason which found its final affirmation in Nietzsche. One must not forget that it was Nietzsche who initiated the revolt against philologia. The present crisis of classical studies is an expression of a more general crisis of modern thought for which science has completely divorced itself from its humanistic foundations and has degenerated into technology. It is natural that the study of metrology, which is at the borderline between science and humanities, should be under attack.

The problem is discussed by Husserl in his speech on The Crisis of European Culture, which he delivered several times as a summation of his thought after Hitler’s rise to power. In this address he makes the point that the perversion of scientific thought that took place after Newton results from having lost sight of the genetic relation between practical metrology and the mathematical interpretation of the universe, and stresses how important it is for science to have a correct view of this relation. It is likely that Husserl hardly knew about studies of ancient metrology, but obviously he had been able to realize from the reading of Greek philosophy how this is related to metrology.

The central idea of Husserl is that after Newton there took place an intellectual revolution by which the mathematical scientific universe came to be considered an objective reality independent of the mind of man. By this process the world of science became a negation of human rationality, so that modern scientism is linked with antirationalistic tendencies. Phenomenologists did not have to wait for the atom bomb to warn that objectivized science had become a monster that would crush humanity. Husserl, even though he was not a historian by vocation, dedicated much of his research to the origin of Greek science because he wanted to recapture the spirit in which it was born. For the Greeks science was the product of the rational attitude of man, an affirmation of the human mind: the logos discovered in nature is the human logos. This is the essence of humanism according to Husserl. For this reason he pays attention to metrology, because it reveals man’s deliberate option in specific social-historical circumstances to interpret the world in mathematical terms.

Husserl states that an intellectual revolution is necessary in order to enthrone again human reason in the field of science, to destroy the notion that the mathematical world of nature is something with which man is externally confronted. This epistemological problem explains the criticism of my thesis. Since I was concerned with the reception of metrology by Greece in the seventh century B.C., it was objected that I was dealing with the reception of something which it was doubtful existed at all; but in substance the skepticism about my thesis resulted from the fact that my critics could not see the problem. Therefore the textual and archaeological evidence I had collected had trivial meaning for them. Greek sources, however, are emphatic and clear in assigning dramatic significance to the introduction of metrology (metra kai stathma kai arithmos, or simply metra). In the last few years I have been told by several classicists that the problem I am trying to investigate does not exist: without probably having ever given any thought to the question, they can tell me with certainty that measurement consisted merely in chosing arbitrarily some units, which was done independently in each locality. They can make this dogmatic declaration because it corresponds to the asusmptions of modern science: measures are conceived as something that exists objectively in the physical world. Husserl has demonstrated that this is the total denial of humanistic studies, the denial of man’s capacity to construct for himself a reasonable and comprehensive image of the world.

In order to understand the spirit of metrology it may be helpful to keep in mind that Böckh, the founder of modern metrological studies, was influenced by the philosophy of Leibnitz and that one of Böckh’s major writings was a commentary on Plato’s Timaeus. The greatest among the French metrologists, August Aurès (1806-1894), remarks that it is important to understand the significance that the ancients attached to number and measurement and that it is necessary to meditate texts such as Plato’s Epinomis in order to interpret metrological evidence. It is to be noted that he did not agree with this particular view of the world, but he thought its knowledge necessary for historical research: “The ancients attributed to numbers a mystical virtue of which today we can hardly realize the full importance. In this matter, their prejudices were so great that I do not think I am exaggerating when I consider number mysticism as having operated as the essential basis of most of their knowledge.”

I have found evidence of the peculiar significance that numbers had for the ancients in the fact that the letters of the alphabet are always associated by the ancients with numbers. This apparently puzzling aspect of ancient thought became clearer to me when I realized that the alphabet is in some way related to the abacus. I have left this line of research in abeyance, waiting for the results of recent discoveries concerning Cretan and Ugaritic writings, but I have gone far enough to know that the order of the letters in the alphabet is a function of the abacus. All this proves how necessary it is in historical research to put oneself in a frame of mind not dissonant from the ancient one.

Possibly the study of Aristotle may be preferable to the study of Plato as a preparation to metrological studies. I feel that metrology helps in understanding Plato rather than the other way around. Aristotle provides a better insight into the practical aspects of metrology, whereas Plato was interested just in doing away with its practical aspects. I feel that by starting with an Aristotelian outlook I have been able to develop a different metrology from that of my predecessors, in that I have taken into account practical operations. For this reason, I have started from what seems to me the very first step, which is a knowledge of the instruments of calculation. The sources indicate that one first learned to use the abacus, and then learned to use it to calculate volumes, weights, specific gravities, geographical distances, rates of interest, and so on, just as today the engineer learns to use the slide rule for an entire series of different calculations. One of the central ideas of ancient metrology is explained by the much read and little understood Fifth Book of Aristotle’s Ethics, in which the idea of justice is explained by referring to money and to the price structure. This book explains why money is called by the same name that applies to civil law and to natural law (nomos) and why this term is synonymous with arithmos; metrology first developed as an attempt to assure justice in the contract of sale by mathematizing the relation. The origins of the art of legislation and of legal science are to be found in lists that state how many measures of a given commodity would correspond to a measure of another commodity. Once one takes this practical outlook, one can see how, in the Bible, the idea of Divine Providence is linked with the methods used in the rationing of food, of which Greek inscriptions provide the most abundant evidence. Once one keeps in mind the metrological aspects of the idea of Providence, one can see the meaning of the word epiousios in the Lord’s Prayer, a word on the interpretation of which an entire library has been written. One must keep in mind the ethical aspects of metrology to see in the Gospels the metrological reasons for the two miracles of the multiplication of the bread, the Feeding of the Four Thousand and the Feeding of the Five Thousand. In metrology, one must steadily shift from metaphysical and ethical presuppositions to practical aspects. his has been the concern of Greaves and Bernard, who came to metrology from the study of cosmogony but at the same time travelled extensively in the Orient and saw the ancient system of metrology still used by the Arabs. The Talmud, which nobody used systematically for this purpose after Greaves and Bernard, provides an excellent insight into the practical operations of economic life and constitutes an excellent means for interpreting Greek inscriptions. I think that I have been able to achieve the synthesis between the study of Greek economics and the study of Greek conceptions of order at which Böckh aimed. A concrete result of this way of looking at the problem is that I have been able to see that the ancients had an instrument of reckoning, the diagrammismos, which is a primitive slide rule operating on logarithms with base 2. This particular instrument accounts for the existence of measures of volume and weight related at 24:25, a problem to which I have referred earlier.

The fact is that metrology is so central to ancient thought that its study tends to expand in all directions. I am not able to embrace all these facts in one single view, and to give a more adequate picture I must refer to Plato’s writing in which he stresses the importance of the art of measuring in the education of the citizen. Luckily, phenomenological method of Husserl allows one to understand this continuous shift from the practical to the theoretical. Merleau-Ponty says in the preface to Phenomenologie de la Perception, “The entire universe of science is built on the lived world, and if we want to think with exactness about science itself and appreciate its meaning and import, we must first of all awaken that experience of the world of which science is a subsequent expression.”

If one begins by assuming that Plato and Aristotle spoke nonsense and that one can be a scholar of ancient history without bothering to find out what they said, the study of metrology becomes impossible, since one cannot arrive at a feeling for its implied intellectual presuppositions. There are no other equally extensive sources allowing one to arrive at an insight into the realm of ideas referred to by the word metra in Homer, Hesiod, Heraclitus and Pindar. In an indirect way the importance of an insight into views such as those of Plato and Aristotle for the study of metrology is admitted by Segrè who, in order to justify the attacks on metrology, stated that ancient measures were conceived in the spirit of Protagoras.

The difficulty of metrological studies results from the fact that metrology originated in a given way of looking at the world, a way in which the notion of the existence of a recognizable rational order is implied. It is necessary to look with some sympathy at the effort to see the world in terms of the immanent structures of the mind. This can be explained by an example in which this attitude was carried to an absurd conclusion. Ancient scientific geography developed from metrology, at first as a study of the distances and times needed for commercial travel and navigation. The step, conceived as a fixed unit both of length and of time, provided the link between measures of length and of time, provided the link between metrology and astronomy, allowing for the development of astronomical navigation. From the tables concerning trade routes there developed scientific geography and, very soon, calculations of the size of the earth. These calculations, however, were based on erroneous assumptions, such as that, for logical reasons, Rhodes was on the meridian of the Nile and, being on the latitude of the caravan route from Syria to Mesopotamia, was the center of the world, and, further was on the meridian passing through the Dardanelles and a river of the Black Sea corresponding to the Nile. The same way of interpreting things accounted for the assumption that Carthage, the Strait of Messina, and Rome were on the same meridian. These erroneous assumptions, however, allowed great scientific achievements, such as amagingly accurate calculations of the size of the earth. In any case, a study of this way of interpretation allows the historian to explain what Homer means by metra keleuthou and Hesiod by metra thalasses.

Once this way of thinking is clear, one sees that the basic structure of the Odyssey is that of a geographical poem, giving pointers on orientation and distances. In spite of the huge amount of writing on the subject, scholars have not seen the rather elementary fact that the cardinal points of the Homeric poems are not four but six, according to the sexagesimal method of dividing the horizon. Once this is accepted, according to my reckonings, the location of Ithaca can be determined to the mile. It is clear that in mythology Odysseus is a doublet of Palamedes, the hero to whom were ascribed the inventions of the abacus, the alphabet, metrology, astronomical navigation, money, and all the system of sciences necessary to trade, to which the anciences referred with the phrase metra kai stathma kai nomisma (or arithmos). I hope that after having reconstructed in detail the myth of Palamedes I shall be able to prove that the contention of Emile Mireaux that the Odyssey was written in the early years of the reign of King Gyges of Lydia is a fact.

All this indicates that metrology was one of the central ideas of the ancient world. It is so central that as a researcher I found myself confronted with a frightening Pandora’s box. It is sufficient to consider that a phrase like numero pondere mensura, applied by the Talmud to the contract of sale, is used in early parts of the Bible to refer to the laws of the Hebrews and in late parts to the divine order of the universe. The fact is that metrology accounts for the development of scientific and philosophic attitudes in the ancient world. The field is so enormous that I have given little thought to the fact that metrology was exported from the ancient world into China; this is a fact of which Bernard already was aware. Marin Mersenne, the correspondent of Descartes, who, before Bernard, in 1644 made an unsuccessful attempt to reconstruct the system of ancient metrology, was aware of the wide cosmological implications of metrology and opened his treatise with the words “Cum omnia Deus in numero, pondere, mensura condiderit, hic de Mensuris et Ponderibus tractatus...”

Given the fact that metrology has such widespread implications, it is not surprising that even though for years I have tried to concentrate my attention on the simplest and most obvious documents of ancient metrology, I have found that my conclusions are questioned a priori, since of necessity I have always to refer in a more or less limited way to some general principle. If some scholars have acted like the astronomers of Padua, who refused to look through the telescope at the satellites of Jupiter, it is because if they accept the interpretation of one single inscription or of one single archaeological measurement, they have to swallow the existence of systematic metrology. A great part of the methodological disagreement results from the fact that in metrology one must proceed with the method used in Roman law, the historico-dogmatic method; that is, one must proceed with a survey of the entire evidence in order to arrive at the formulation of basic principles, and these, in turn, must be used to interpret the single texts. It is for this reason that Böckh titled his work as dealing with measures in ihrem Zusammenhange. And for the same reason Hultsch called his final and comprehensive work Die Gewichte des Altertums nach ihrem Zusammenhänge dargestellt; this is the work that was dismissed by Willers and Beloch as mere fancy, coming from the “witches’ kitchen.” The only really important work of metrology in this century was written by August Oxé, at the age of seventy-nine, summing up what must have been decades of research, and it is called Antike Hohlmasse und Gewichte in neuer Beleuchtung (1942). It is to be noted that in spite of the monumental scope of this work, covering all important volume and weight measures of the ancient world, and in spite of the established scholarly reputation of its author, it was not the object of a single mention or book review, to my knowledge. The majority of scholars of the present generation accepts the condemnation of metrology by such authorities as Beloch, De Sanctis and Eduard Meyer without having even an inkling of the method and the achievements of this discipline. The situation clearly indicates that today one must start at the point where Greaves and Bernard and Böckh, too, started. Bernard, in spite of the incredible wealth of information he had accumulated, deliberately set down his main work in the form of a primer (Non pompae sed usui destinatus). Böckh also set down a fundamental statement, which was used by metrologists for the following hundred years. I have to proceed in the same way, keeping in mind that reason under attack can rely only on its own strength.

Luckily I am in the condition of writing a clearer, more unified and practical primer than those written by my predecessors; I can utilize all the accumulation of data provided by the unfolding of scholarship since Böckh’s time. One encouraging aspect of metrology is that the more investigations progress, the simpler the system becomes. I have succeeded in what has been the aim of all major metrologists beginning with Newton, that of explaining all measures on the basis of a single unit of length. Having determined which was the basic ruler, I have been able to trace the few simple formulas by which there derived all measures of volume and weight. Even though my description is purely factual and intended to provide a practical reference handbook, I have outlined a structure which by itself proves what marvellous adventure of the human mind metrology was. I hope to be able to convince ancient historians that metrology provides sources of information which are exact and reliable beyond hope, and to convince them to look at the data with a spirit similar to that shown by Newton:15

Newton withheld his hope
Until the day when light was brought from France,
New light, new hope, in a small glistening fact,
Clear-cut as any diamond; and to him
Loaded with all significance, like the point
Of light that shows where constellations burn.
Picard in France—all glory to her name
Who is herself a light among all lands
Had measured earth’s diameter once more
With exquisite precision. To the throng,
Those few correct ciphers, his results,
Were less than nothing; yet they changed the world,
For Newton seized them and, with trembling hands
Began to work his problems anew.


  1. Beloch’s terminology has been made generally known in Italy by two popular books by Ettore Romagnoli, Lo Scimmione in Italia and Minerva e lo scimmione, attacking the philological method in classical studies. 
  2. This point is made by De Sanctis in the preface to Atthis.
  3. ZDMG, 66; 1912, 638. 
  4. Indépendence Roumaine, 6/19, April, 1906.   
  5. Nazional-fascismo, 1923, p. 21.  
  6. Cf. Ezio Maria Gray, L’invasione tedesca in Italia, 1916. 
  7. Irrealtà Nazionalista, 1925, p. 184. 
  8. Geschichte des Altertums, I, 2, 581. 
  9. England, 1915, p. 78. 
  10. Inductive Metrology, 1877. 
  11. Ancient Weights and Measures, 1924.
  12. De asse et partibus eius.
  13. Essai sur les systèmes métriques et monétaires des anciens peoples depuis les premiers temps jusqu’à la fin du Khalifat d’Orient, 1859.
  14. Manuel d’archéologie orientale, Vol. 4, pp. 1874-77.
  15. Alfred Noyes, Watchers of the Sky

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