Source: Von Soden, Wolfram (1985) Chapter 11 Sumerian and Babylonian Science. In: The Ancient Orient - an introduction to the Study of the Ancient Near East. William B. Eerdmans Publishing Company, Grand Rapids, Michigan, USA. Translated by Donald G. Schley.
Soon after the invention of their writing system, the Sumerians began to compile smaller lists of cuneiform signs. With a system of word signs, sign lists are simultaneously word lists, having even a certain somewhat topical material arrangement. With the gradual transition to cuneiform, the signs, which were increasingly employed as syllabic sings, were becoming less pictorial. Thus, lists arranged according to the signs could remain simultaneously word lists with a topical arrangement of the signs only in the case of a minority of signs. For this reason, distinct lists of objects were created as early as the 3rd Millennium. These contained primarily compoud words: in addition to objects designated by determinatives, including those objects made from wood, reed, leather, metals, stone, wool and so forth, the lists enumerated plants with particular subgroups, such as trees and grains, as well as domesticated and wild animals, and certain classifications of people with designations for body parts, geographic names, stars and divine names. The tendency toward a fifmly established sequence within the individual groups, however, had still not been fully realized by the Old Babylonian period. Among the local scholastic traditions, which from the beginning had diverged widely from one another, that of Nippur came increasingly to prevail after the time of the Third Dynasty of Ur. The word lists migrated to some extent with the writing system to both Elam and Syria, where independent native traditions developed, as the archives of Ebla (about 2400 Before Common Era) impressively show, though they preserve the adopted lists in a form which has undergone manifold changes.
When such lists were first compiled, practical criteria may have stood in the foreground, and these always retained a great significance for the scribal schools. At the same time, however, these considerations were increasingly surpassed by goals of a more theoretical sort. The Sumerians believed in a means of ordering the world which brought with it confirmation of the working of the gods . The lists had the task of making this order manifest in connection with the main groups of objects and living creatures, including the gods. This could be accomplished, however, only by people who knew how to handle the lists. The Sumerians were unable to present their ideas in a connected fashion, either in the realms of nature, abstract matters, and theology, or in those of mathematics or jurisprudence.
Thus, Sumerian science lacked the conceptual framework of formulated principIes (what in the West has been called źnatural laws"), and simply ordered nominal expressions one after the other in a one-dimensional fashion, without any kind of elucidation. Verbs in finite form and abstract terms are found only in those sign lists which are not topically ordered, but not in the lists which have been ordered according to systematic criteria. Mythic literature served to illustrate the conception of order . During the Neo-Sumerian period, the compilers of several lists were apparently concerned to comprehend the nominal expressions in many areas nearly completely as possible; in other cases, as with the stars, they were satisfied with a small selection of that which was accessible to observation; the reasons for these variations are still unclear.
History, for its part, was presented in the form of king lists, which were composed on the basis of the fiction (Lishtar┤s Note: Instead of fiction, I prefer myth and oral mythologized tradition) that there had always been only a single king in the land. For the earlier as well as the later period, the king lists set simultaneously reigning dynasties in successive order without any explanation. Nor were mythical and historical kings differentiated; three to four place numbers for regnal periods are occasionally encountered, even for historical monarchs. In mathematics, an equally equally one-dimensional arithmetic table replaced the one-dimensional lists. .
The Semites in Syria and Babylonia carne to know the Sumerian sign and word lists, but they only partially understood the sense and function of the lists. These people recognized quite early, however, that one could create two-dimensional lists by the addition of a second column, or line, in their own language, as was done at Ebla; these two-dimensionallists could then aid the study of the other language. The Sumerian words and expressions were rendered with Akkadian or, as the case may be, Eblaite words, genitive constructs, or brief relative clauses, which in turn were only of provisional assistance due to the vast differences in the languages. The bilinguallists thus became the first lexical aid in human history, and for a long time nothing similar followed outside the cuneiform cultures, since the Greeks had little interest in other languages; not until the Renaissance did Western lexicography begin to develop. Until a short time ago we only knew of bilinguallists from the second millennium, so we assumed that the beginnings of lexicography lay in the early part of the Old Babylonian period. The discovery of the archive of tablets from Ebla forced us to revise our position: at about 2500 Before Common Era, Sumerian - Eblaite lists of considerable scope already existed. Here, as in later Babylon, verbs were presented by juxtaposing the Semitic infinitive to the Sumerian verbal root. Unfortunately, many Sumerian words in these lists were left untranslated, including particularly frequent words as well as those used less often. According to the present reconstruction, the bilingual lists were first created in northern Syria around 2400 Before Common Era; afterward, they were created anew in Babylon shortly after 2000 without knowledge of Eblaite. It is not unthinkable, however, that the bilinguallists of Ebla were patterned after northern Babylonian models which have yet to be discovered.
For a long time, the Sumerian lists of objects were handed on in monolingual form, and not until late in the second millennium were they first prepared with the Akkadian column. Conversely, lists of different types, arranged according to signs, and even lists of grammatical forms, which were conceived from the outset in bicolumnar torm, were transmitted as early as the Old Babylonian period. Certain of these lists attest a multifaceted concern with the Sumerian language and with their own. Still, grammatical rules were never formulated in terms of precepts, and one learned instead from the multitude of examples, which of course were not always of equal merit. In the age following the Old Babylonian period, certain types of lists were canonized by the creation of series of tablets, most of which were named after the initial line and which consisted of up to forty numbered tablets. To these were added completely new compilations of lists. The compilers of these new lists collected synonyms and homonyrns, for example, or Akkadian root words with their multifarious usages and their real or supposed derivations, without shrinking from assembling wild etymologies. To put it mildly, these lists are still in need of thorough study. Very brief explanations, introduced by the determinative pronoun sa, comprised a completely novel element in the later lists. The equivalencies of the earlier lists, rightly understood, often present indeterminate relationships. This happened because the compiler was unable to formulate his knowledge clearly, owing to the fact that the Sumerian and Akkadian words often were not actually equivalent. In the later lists we find many hundreds of partial equivalencies of the type, zi-zi = qa-ta-pu sa basburi, "to pluck, [said] of apples:' Naturally, even such equivalencies as these must be read critically.
During the first millennium, numerous commentaries led beyond the lists. These commentaries maintained the form of the bicolumnar lists only in part. They also contained many citations from the bilingual lists and the lists of synonyms (see below) and included the verbal infinitive along with many verbal forms. Factual commentaries of different sorts, which also contain clarifications of many words, existed alongside the predominantly philological word commentaries. We will have to refer frequently to these commentaries below. Along with the commentaries, the bicolumnar Akkadian synonym lists first carne into being during the first millennium and were transmitted primarily in Assyria. The synonyms enumerated in these lists are overwhelmingly "partial synonyms":a fact which is rarely mentioned.
These same lists often survey little-used words of literature and poetry and therefore become a particularly important aid for understanding works of these genres. That Akkadian could for a time become the language of diplomacy and commerce from about 1400 to 1200 Before Common Era, even as far as Egypt and the Hittite Empire, was made possible by the fact that the schools there took over, selected, and even expanded considerable portions of the Sumerian object lists and the bilingual Sumerian-Akkadian lists. Since the native languages then had to be surveyed, these were introduced into third or even fourth columns. >From the Hittite capital of Hattusas we possess many Sumerian-Akkadian-Hittite word lists alongside merely Akkadian-Hittite lists; there are even quadrilingual Sumerian-AkkadianUgaritic-Hurrian word lists from Ugarit. These are quite helpful, of course, despite their extremely fragmentary state of preservation. It would have been quite simple to introduce into such lists the Aramaic which prevailed primarily in the West during the Neo-Assyrian period.
We know of no such lists, however, but only smaller groups of West Semitic words in the Akkadian synonym lists. In isolated cases, very late copies of lists contain Greek transcriptions. Still, classical antiquity neither adopted the bilinguallists nor offered something better in their place.
The purpose of the topically ordered, monolingual Neo-Sumerian lists was not to present ideas of the cosmic order, but rather to depict inventory rolls according to the main categories in the world of objects and living creatures. The Old Babylonian period expanded the corpus of compiled lists. Nevertheless, the development of these into bicolumnar and bilinguallists did not occur until toward the end of the second millennium. During this process of transition and expansion, however, there were many kinds of additions, omissions, and transpositions. In many cases particular principles were presupposed in the arrangement within individual tablets as well as within entire series of tablets, which were named after their beginning line urra = bubulla, "interest obligations." In addition, external associations often played a role, as did perhaps even chance. Trees were treated exhaustively in Tablet III, but the rest of the plants were not found until Tablet XVII. So also, most domestic and wild animals carne in Tablets XIII-XIV, but birds and fish not until Tablet XVIII. There are also many kinds of explanatory additions, though much more frequently these are completely lacking or are encountered only in commentaries running parallel to the lists.8 One would scarcely have been able to read the work at many places without preliminary instructions. Altogether the work comprises a comprehensive survey of the animate and inanimate world, geography, and stars, as well as artificially produced objects, victuals, and many other things.
Similarly, the work was perceived early on as inadequate form for some important categories; thus, further compilations were created, though generally not in the form of \vord lists. These will be treated below. Furthermore, occasional distinctions between the real and the mythical world were overlooked, especially when dealing with animals. In later copies, supplements were only sporadically inserted.
At the same time, because of their bicolumnar nature the lists could have functions completely different from those of the SumerianAkkadian word lists. Thus the great "god list:' perhaps formed in the twelfth century by the insertion of much later additions into various monocolumnar Sumerian god lists, begins with an = Anu and generally lists in the left-hand column divine names which stand in quite different relationships to the god in the right-hand column, which often remains the same for many lines. There are variations on divine names, gods who bear essential similarities (such as the gods of the Elamites, Kassites, and other peoples), but above all, many names of originally independent gods who had evaporated into the syncretistic theology within the framework of a polytheism which reinterpreted much, and which made many divine names subsidiary names to other gods or simply relegated them to the status of hypostases of other gods. More will be said of this theology, which the Babylonians were unable to develop systematically. Further differences are found in the functions of bicolumnar works of astronomical instruction. This list form is used in certain bicolumnar lists of pharmaceutical plants and stones which are no longer bilingual, in order to present side-by-side alternatively applicable f1oral, faunal, or mineral drugs, in most cases without explanation . Bicolumnar king lists play only a subordinate role beside the monocolumnar king lists which the Babylonians and Assyrians had taken over from the Sumerians with some modifications. These bicolumnar king lists juxtapose the actual or sometimes conjectural concurrent rulers of Babylonia and Assyria without indicating the length of time they reigned concurrently.
In summary, we could say that the bicolumnar lists offered the Babylonians quite diverse possibilities of expression, but that these lists were seldom able to bring to tolerably adequate expression what should have been understood from them. The same is especially true even for the Sumerian and Akkadian grammatical forms preserved in many instructive lists.
To the Sumerian lists of words and nominal expressions, the Babylonians added not only the previously identified lists of similar types, which generally were bilingual, but often quite comprehensive compilations of lists which arranged hundreds and even thousands of similar verbal phrases in serial order without tying them together logically or syntactically in the way we have been accustomed to do in academic study since the time of the Greeks. Moreover, no conclusions at all are drawn from the heaps of individual expressions, and no conclusions are formulated as general principles of knowledge. That conclusions and knowledge, as well as premises, were not formulated should not mislead us into thinking that the Babylonians were not interested in such forms of knowledge. Their mathematics, especially, shows clearly that they had at their disposal a type of knowledge which comprised many details, yet which was not formulated in terms of basic principles. Because of our schooling, we will perhaps never understand how they were able to realize such knowledge without either predicates or deductions. We must, however, recognize that this was possible under the determinative presuppositions of Babylonian culture. Even knowledge without formulations could be quite fruitful, though only to a limited extent. We must now attempt to explicate for ourselves some areas of science which the Babylonians especially nurtured, but which we would scarcely be prepared to regard as sciences. It could thus be considered sensible to set the word "science" in the folllowing treatment in quotation marks; I would not want to do this, however, since this too frequently signifies a degree of denigration which would be inappropriate here.
The term "science of omens" will estrange some from the outset because the belief in good or evil omens sent by the gods, which was present everywhere in antiquity, is a superstition to us. Manifold references to omens of the most diverse sorts are found throughout ancient literature, and people were convinced that these had proven true. Lesser or greater collections of omens with their interpretations were frequently compiled, and sporadically appear even as early as the Sumerians. Yet the Babylonians and Assyrians were the first to order thousands and later tens of thousands of omens with their respective interpretations according to similar categories, thereby creating a science of omens which the Hittites took over in many particulars and which stimulated the assembling of some collections. These collections must be treated here briefly according to formal criteria.
Each omen consists of a conditional clause with a final clause containing the interpretation: for example, "When the blind are numerous in a city, there will be trouble in the city"; or "When a serpent falls upon a sick person, it draws that person's sickness out; he will regain his health." In all probability only a small minority of omens were ever observed. The rest were added in the endeavor to comprehend particular categories of omens as fully as possible, since some of these could possibly take place once. What is important to us, however, are those rare cases when historical events are referred to in connection with an omen. By the arrangement of interpretations of the omens, some principles can be established, as, for example, left = good, right = bad, and vice versa. Quite often, however, no rational principle can be discerned, though one must note that there is still a dearth of studies on this subject.
In the Old Babylonian period, the collections of omens were for the most part still rather small. Omens which took place without human agency, such as encounters with animals or anomalies of birth, were given less attention, and astrology was almost completely absent. People were mostly concerned with inducing omens, primarily through inspection of the liver of sacrificial sheep, but also in figures which were formed when small quantities of oil were poured into a basin of water, or even in the curves of a rising plume of smoke. In the case of liver divination, a question which could be answered either positively or negatively was probably always posed prior to the slaughter of the sheep. The majority of these questions concerned public life, for example, the prospects of a military campaign or the acceptance of a public office. A person inquired about the appearance of twelve different parts of the liver.
Usually the result was then a partial "yes" and a partial "no." In such cases, the yes and no characteristics were counted, and the greater number determined the answer. If the result was six to six, the liver divination was unsuccessful and had to be repeated, if no additional features permitted an answer to be inferred. One could also derive more sharply differentiated answers from the lists of actual or fictitious liver diagnoses which had become quite comprehensive as early as the Old Babylonian period, and which were ordered primarily according to the parts of the liver. lndividuals were concerned with omina addressing the fate and relations of the family, house and property, and the chances of recovery for the sick. ln the later period, none of the Old Babylonian omen collections was adopted in toto, but they were nevertheless widely exploited for new text compilations, even in Asia Minor. New comprehensive texts are first attested from the period after 1200 Before Common Era, but the great series of tablets known primarily from Assyria were most likely not assembled until the first millennium. The liver divination texts comprise a great part of the aggregate omen literature down into the Hellenistic Age. Further, many omens are based on a combination of features, and clarifications are often inserted or collated for special commentary tablets. Only sporadic mention is made of oil divination.
Besides liver divination, the observation of the far more numerous non-induced omens emerged in the first millennium. These omens, supplemented through thousands of others construed according to particular schemata, were compiled into the greatest tablet series of Babylonian literature, whose most comprehensive form comprised far more than ten thousand terrestrial and astrological omens. To these must be added several thousand birth omens, calendar omens - held to be especially important for the choice of the best possible day or month - and diagnostic omens, in addition to somewhat smaller classifications, such as physiological omens and dream omens. Clear organizational principles are recognizable in all of these series, even if these are not strictly adhered to in every case. Nevertheless, only specialists with years of schooling, who are called "seers" or "gazers" ( as are those who divine by sacrifice; Akk. bãrú), were able to work with these masses of texts. lt took many generations to compile this massive amount of material, and the great series in its entirety, with its hundreds of serially numbered tablets, was probably first brought together in the eighth and seventh centuries in Babylonia or Assyria.ll These collections associate the immense number of omens with a much smaller number of mostly quite general interpretations from the spheres of public and private life.
If it were merely a question of mantic prophecy in the narrower sense of the term in these collections, supplemented by the commentaries, the collections would hold a preeminent position in a history of superstition, but they would command quite limited interest beyond this.
However, the omen collections are of far greater importance. The desire to understand as fully as possible the ominous constellations manipulated by the gods, even to the extent that one could even organize trade arrangements by them, led to ever more precise observations. Thus for the sheep livers, of which no two were alike in every respect, even the smallest oddities were observed, registered, and recorded on clay tablets. Other organs were observed as well, insofar as a diagnosis could be drawn. The same was true of new-born infants and their anomalies, as well as miscarriages. The body structure and behavior of various animals in highly diverse situations was observed very preciselyas well, and special attention was paid to snakes. The result was a level of zoological knowledge which was quite unusual in ancient times. Many plants carne under observation too, though they did not receive the same attention as animals. Several kinds of omens were deduced from water, particularly the floodwaters of the rivers, as well as from meteorological phenomena of all types. In accord with the Babylonian worldview, weather omens were incorporated into the astrological omen series.
Humanity was studied with special intensity, and in this regard the science of omens worked closely with medicine . The basic questions regarding human behavior had to do with morality and ethics. We learn much about the moral values then in force (, as well as of the consequences of outbursts of temper, from the interpretation of good and evil omens, which were important for the fate of the individual. Finally, dreams were also recorded in very great numbers. Since people are able to remember only a small part of these, a great many dreams admittedly may have been invented for the omen collections. From dreams, sicknesses were also diagnosed. One can derive many observations relating to psychology and the study of human behavior from all of these omens and their interpretations. Still, one can speak of no more than the beginnings of these and other modern sciences nurtured on the fringes of divination in ancient Babylo.
The situation is completely different in the case of astrology. In contrast to the later periods, the early Babylonians did not deduce from the stars the fate of the individual - that happened on occasion first in the Seleucid period - but rather, the fate of noble families, the state, and larger groups, and not least of all the prospects for the harvest. In these areas, astrology primarily supplemented liver divination. But astrology could not attain a greater significance until astronomy, which was pursued from time to time for astrological purposes, had access to a sufficient number of observations. That would scarcely have been possible prior to 1200 Before Common Era. Astronomy will be treated in its own right (see below). Here, reference will be made solely to the many thousands of astrological omens which we know from the first millennium.In hardly any other instance has superstition been as fruitful for the emergence and development of a science as in the case of astronomy, which was scarcely nurtured, in contrast to opinions often represented regarding the Sumerians.
Theology will be treated only briefly here, and under formal criteria; its contents will be dealt with in the chapter on religion. Theology was primarily the teachings about the gods, but the Sumerians could only express these in monocolumnar, one-dimensional lists of deities without suggesting any clarification. The mostly bicolumnar Babylonian god lists reveal essentially more, since they have been illuminated in numerous ways, so that much more can be deduced from them about the relationships of the gods to one another. Nevertheless, they still leave the reader ignorant of much crucial information. The first millennium added cultic commentaries to these lists, drawing quite colorful pronouncements from the lists of gods, the myths, and the rituals) but scarcely exhibiting a systematic viewpoint. Wildly rampant speculations frequently based on etymological wordplays, often find expression in these pronouncements. These scarcely ever had a binding character) and they are only witnesses to Babylonian science in a very limited sense. Central theological ideas, which must be deduced from prayers and mythic poetry, were never formulated or linked together systematically.
There was fertile ground for a scientific approach to history in Babylonia and Assyria insofar as there was often a pronounced interest in the distant past. This interest was expressed among the Sumerians, although only in the monocolumnar one-dimensional king lists and in mythic poems relating to earlier kings such as Gilgamesh. Political criteria were determinative for the exclusion of a number of dynasties from the lists. The alleged regnal years were not always correct, even for the period after the middle of the third millennium, and the listing in successive order of dynasties which were actually contemporary certainly led to false understandings for periods in the more distant past. Both the Babylonians and Assyrians continued these lists.
The year lists down to 1530 Before Common Era served primarily practical purposes, but were interpreted for the king lists in the same way as the eponymal year lists in Assyria, which were constructed for similar reasons. Interest in particular kings was expressed primarily in epic sagas, among which those on the kings of Akkad, Sargon, and Naram-Sin were especially beloved and were repeatedly revised. However, from the Sumerian period on, times of trouble also served as themes of such poetry, for example, such events as the incursions of Elamite armies. The wrath of the gods was often referred to in these poetic compositions.
The king lists were enriched early in the second millennium by additional information, for example, concerning a change of dynasty. It is not entirely correct to regard as chronicles later texts which, from a particular perspective, briefly recount significant events for selected kings. After about 1100 Before Common Era, we find texts in Assyria as well as Babylonia which give brief reports primarily on wars during the preceding 250 years or so. An Assyrian chronicle from the eighth century treats the conflict between Assyria and Babylonia after around 1500 Before Common Era with a strong anti-Babylonian slant, and similar works exist in Babylonia. The so-called Babylonian Chronicle begins with the year 747 . This work registers the most important events for each king in annalistic form, but subsequently gives shorter or more detailed treatment to each year. Some political bias can frequently be detected behind the otherwise very factual reports. Moreover, no recollection of the list form can be recognized in any of these works, though the texts themselves offer merely the raw materials for an actual historiography. From the seventh century on, even the "astronomical diaries" (see below) contain short historical reports.
Geographical lists of lands, cities, bodies of water, and occasionally mountain ranges were handed down in Babylon, and for a brief period in Ebla, from the middle of the third millennium. These were altered in later centuries through omissions and additions, but from the Old Babylonian period on they offered an increasingly historical geography, which is still more oriented to earlier than to contemporary names.
Conversely, the itineraries and lists of Assyrian provinces from the later period are not part of the geographical literature. Some narrative texts, and especially Assyrian campaign reports, show that the landscape of foreign lands was observed as well.21
The names of trees and other plants, animaIs of alI kinds, and minerals were included by the Sumerians in their expanded monolinguaI word Iists, and were recorded by the Babylonians in essentially more Comprehensive, mostly bilingual, and sometimes very briefly expanded Iists. The principIes which determined the arrangement are only partially recognizable for us, primarily because we are unable to interpret very many of the names. In comparison to the other categories, hoWever, we know most about the Iand animaIs, under which the insects and Worms are ordered; we know Iess of the birds, and even Iess of the fish. The body parts of animals are treated along with those of people.
The distinctions made between a great many types in all areas attest to intensive observation, although naturally all types were not treated in the same manner. The initial words of word phrases allow us to discern a pre-scientific order among the Sumerians, Who in any case had at their disposaI only a Iimited number of words to be used as names; for example, ur designates dogs, woIves, and so forth, as well as the great predatory cats. In the first millennium, the word Iists were supplemented by the above-noted Iists of floral, faunal, and mineral drugs, which present a far greater number of plants than the other lists. Where these Iists are ordered according to the illnesses that the drugs served to combat, numerous drugs are to be found. Names derived from foreign Iands testify to the importation of many medicinal herbs at an early date.
Medicinal commentaries contain further important disclosures. The works sammu sikin-su and abnu sikin-su - "the plants with respect to their appearance:' "the stones with respect to their appearance" which emerged in the first millennium, bring new insights and serve to facilitate the recognition of plants and mineraIs. In the case of the plants, the Iist names severaI parts from the flower to the root and Compares these without any differentiation to the Corresponding parts of other plants, following the pattern, "Plant a: its flower is plant b, its stem is plant c," and so forth. Naturally, the inquirer thereby gains little exact knowledge. The schema for the mineraIs is simpler still. Nevertheless, these descriptions presuppose multifarious observations, though the scope of both works cannot be discerned from the portions preserved. On pharmacology, see below, section 8.
The great lists of terrestrial omens ( see above) treat flora and fauna at length. Here the primary concern \vith animaIs is their behavior, \vhile with plants it is their location, especially unusual locations. Unfortunatel:., as is else\vhere the case, floral and faunal omens based on actual observation are found alongside a great many others which were invented according to some analogy or other. The latter are easy to recognize if they make obviously absurd pronouncements, as, for example, the claim that someone had observed a lamb with ten feet; but in many other cases the invented omens can be recognized only \vith difficulty, or not at all. There is still need for someone to undertake a comprehensive evaluation of the omens. Certain literary texts give quite valuable pointers for identifying birds, and also render the birdcalls in vocalized form. Collective descriptions of the body structure and behavior of certain types of animaIs are completeIly lacking: these lay beyond the possibilities of Babylonian science.
The Babylonians never possessed even the beginnings of an understanding of physics, though they did have at their disposal some knowledge of physical principIes, such as the laws of leverage, which had to be used in transporting the heaviest blocks. One can speak of Babylonian-Assyrian chemistry in only the most limited sense that many kinds of experiences \vith the properties and behavior of elements, and their relationships, had been assembled. This accomplishment in the middle of the second millennium made it increasingly possible to reproduce chemical relationships going well beyond those of metallurgy, which had been known at a far earlier date. Thus was attained the means of working \vith many kinds of glazes and cosmetic media. They must have learned much from chemical analysis; but we also possess, primarily from Assyria, collections of formulas for the production of glazes and cosmetic pastes. Yet these collections of formulas should not be reckoned among the scientific writings in the strict sense of the term.
As for the scientific study of humanity, the focal point is either groups and communities or the individual person. The study of individuals attained a considerable significance in Mesopotamia, but scarcely the beginnings can be found for the collective focus. Thus, in the area of law, we are quite familar with collections of laws but find no discussion of legal questions of a more fundamental sort. One finds programs for better conduct of the affairs of state in some royal inscriptions, but nothing which one could designate as the beginnings of a political science. It scarcely needs mentioning that even the very presuppositions are lacking for more wide-ranging approaches to knowledge, such as philosophy with its various subdisciplines. Still, the so-called wisdom texts contain interesting pronouncements regarding these fields, as well as pedagogy and ethics (see below..
In the same way, there was no intensive concern for the healthy individual outside the religious literature. All manner of individual observations on psychology are found in the omen collections, especially among the physiognomic omens, which often deal with human behavior. Particular interest in the anatomy and physiology of the human body is shown predominantly within the framework of that form of medicine concerned with the means of healing illnesses; especially intensive concern was devoted to this area. It must at the same time be noted that, in contrast to Egypt, surgery is only rarely treated in the great mass of medical texts. As in Europe during the Middle Ages,surgery was considered more of a tradesman's activity. The doctor (Sum. a-ZU, "fluids expert"; Akk. asu) ,worked primarily with orally taken or externa1ly applied medicaments of the most diverse sort, and with magical means. lndeed, medicine and magic were so intertwined that it is completely impossible to draw a sharp line between the tWo. Here Babylonian-Assyrian medicine can be shown to be archaic on the one hand, while on the other the combination of medicine and magic anticipates modern psychosomatic methods. The magical practices stimulated the patient's will to be well, without which no successful healing can be expected.lncantations and prayers supplemented treatment with drugs, and one can scarcely distinguish bet\veen the magical and actual medical effects of these applications. Our understanding of the methods of that period is made much more difficult by our inability to interpret many words for plants and minerals. The situation is even worse with the designations of diseases, which primarily denote the external appearance of a disease, and so in our own medical terminology are ambiguous ( cf. the treatment of leprosy in Leviticus 13-14, where "leprosy" can apply to a house or garment, as well as the human body); in many cases we do not even have a clue as to the meaning of the word.
Still, an intensive study of the numerous pertinent texts would certainly bring forth new knowledge and information. Only occasional, modest collections of prescriptions and diagnostic texts, which lack exact descriptions of symptoms, are preserved from the Old Babylonian period. These lack any systematic organization and have the appearance of the records of individual doctors. The texts from the last third of the second millennium are more numerous and often far more comprehensive, as we1l as better arranged, and attest to considerable advances in medicine and pharmacology. The great medical works, however, did not emerge until the first millennium, and the copies on hand mostly stem from the time after 700 Before Common Era. Letters provide us with extremely important supplementary information to the medical texts, since they often report on individual cases in great depth and make known to us famous doctors of their age, as, for example, Urad-Nanâ, who served in the royal court of Nineveh after 680 Before Common Era. Occasionally these letters even contain the patients' questions to the doctor. There are two large groups of medical texts. Those in the first group present the diagnostic omens and generally give only a few symptoms of the illness. They also state quite briefly whether the disease can be healed and, depending on the case, how long it will take, or whether death will come after a shorter or longer period. In place of this last statement one often finds "the hand of the god ( or the demon) X"; the hand of each god was not equally malevolent. Such a reference may intend to indicate either that the help of the designated god should be sought, or that a ritual should be carried out against the particular demon. One such example reads,
If he [ the patient] is sick all day long, then his head is "devouring" him he lays his hand repeatedly on his stomach and cries out, he stretches his hand out again he will die.
The omen series begins with incidents which should enable the incanter to approach the case of the patient, then cites many diagnoses from the head to the feet, as well as the internal organs, then many maladies with various symptoms, and finally a great number of infantile diseases. As with other portents, there are certainly many invented combinations of symptoms here. But there is nowhere any mention of what the doctor can do or usually does. The collections of prescriptions, which were not assembled in as great a tablet collection as the diagnostic omens ( comprising forty tablets), also begin each section with a brief, or in some cases very detailed, diagnosis. Several magical-medicinal prescriptions, and sometimes incantations which the doctor can try usually follow upon these. Occasionally, the series of plants, trees or woods, or minerals are very long.
A very large part of the tablets which have come down to us are tablets which individual doctors or incanters had abstracted for themselves from larger compilations. The prescribed medicaments frequently were mixed with water, milk, beer, or more seldom wine, and point to a developed pharmacology. It is of course improbable that all the given components of any prescription were always available. Not a few medicaments contained substances completely similar to those used today for the same sicknesses, and the doctors of the first millennium were able to build upon the experiences of many previous generations. That is true, for example, of the application of fish gall for the healing of blindness caused by a speck upon the cornea.32 Beyond the diagnostic omens and the various prescription texts with numerous commentaries appended, there was no further medical literature in Babylonia and Assyria. The situation was the same in medicine as in other areas of science: knowledge formulated in terms of general principles was not deduced from the many individual observations which each doctor knew how to apply. Nor was there any physiological theory as was found among the early Greeks. For these reasons, narrow boundaries constricted ancient Oriental medicine despite all of its respectable achievements. At the same time, however, it attained an entirely unique position in the history of medicine.
Babylonian mathematics presents us with particularly difficult problems, because in many respects it is completely different from that of the Greeks and ourselves. In the early period, mathematics was determined by entirely practical demands, namely the measuring of fields and the necessities of administration, which already by the time writing was invented required quite complex means of reckoning. Because only a limited amount of fertile ground was available in Mesopotamia, land parcels had to be measured with great exactitude so that the land could be used to its best advantage. Not only were there rectangular and triangular parcels, but also some in the form of irregular polygons. In order that the area of such fields could be calculated, they had to be broken down into triangles and rectangles, once the boundaries had been measured and recorded. The sum of the areas of these simple figures was then the same as the total area. One Old Babylonian tablet, in a sketch not true to scale, depicts a field which had been divided into four rectangles, three trapezoids, and seven right triangles.33 Moreover, even cubic entities, such as pits, walls, and the like, had to be calculated quickly, or at least estimated, so one could know how much material had been excavated, or how many bricks would be needed, or even how many workers were needed and for how long. The yields of the harvests had to be figured too, along with great quantities of livestock and fish, as well as payments in kind, often to thousands of workers.
While reckoning in Syria, at Ebla, and in Assyria was done primarily according to a numerical system based on ten, the Sumerians and Babylonians used mostly a sexagesimal system ( one based on sixty), which had as its basic numbers 1, 10, 60, 600, 3600, 36,000, 2,160,000, and so forth, and as the reciprocals to this the fractional numbers ex. 1/60, and so forth. The smaller cardinal numbers originally had not only their own numerical names, but also their own numerical symbols which could be repeated for the multiples of these numbers and used in varying combinations. After about 2200 Before Common Era, however, the numbers also carne to be written in cuneiform signs, and, like other cuneiform signs, could not be allowed to exceed the normal height of aline. Thus, the vertical difference between the perpendicular wedge of the 60 and that of the 1 disappeared. Sometime later, this development provided the mathematicians with the occasion to retain only the broad, slanted wedge of the 10, and the vertical wedge for the (respective) 60-,3600-, etc., multiples of 1 as well as the fractions of 1 (1/60, etc.). In this manner, a purely positional system of numerical writing was invented, as was later found in the decimal systems of the Indus valley, the Arabs, and our own. Since, however, no sign was employed which corresponded to our comma, the positional value of numbers with multiple places was not normally evident. Thus, a sexagesimal number such as 58 45 40 corresponded not only to the decimal numeral 208800 + 2700 + 40 = 211540, but also to the sixtieth multiple of the sarne, and so forth, as well as to V60 of it, and so forth, inasmuch as no designation followed to make the numerical value clear. The Babylonians understood the problem in such a way as to make a virtue of necessity, and thus to reckon with great sophistication without any unequivocal place va1ue, since as far as they were concerned a protracted reckoning of the place value was of no concern in the case of the intermediate sums. Only the fina1 sums had to be unequivocally identified. Moreover, within the sexagesima1 system division by 3 and its powers always led to finite sexagesimal fractions which were more exact than the abbreviated, interminable decima1 fractions of our system. In the case of the measures of length, area, and volume, as well as of weights, quite diverse multiples were used, since a very ancient measuring system had been adopted. For instance, the spatial measurement bur corresponded to 5400 = 18 X 5 x 6 X 10 qa (approximately 0.8-11.).34 The primary difficulty for reckoning in the ancient Orient was that one could work OUt addition and subtraction for very large numbers, but the same was not true of mu1tiplication and division. This forced the Sumerians early on to prepare multiplication tables as well as reciproca1 tables, because division cou1d be conceived only as multiplication with the reciproca1 of the divisor.35 In addition, there were tables of powers and roots. Tables other than those necessary for ca1cu1ation had been created at least by the Old Babylonian period, and these al1ow us to deduce a theoretical interest in the properties of numbers. Thus the number 225, which appears as the sexagesima1 3 45, was carried OUt to the tenth power, since there are unusually similar numerical series with this number. The tables of powers for the number 2 led a scholar through to 230, and then formed in addition the reciproca1s to what is for us a ten-place number, which sexagesimally is an even longer numerica1 series. Such unusua1 tables could have no practical interest, but we have no indication of why someone would prepare them.
The situation was similar in geometry, which had grown far beyond the various practical purposes. Nevertheless, this discipline developed without formulated theorems, and a proof of a geometric fact was never attempted. People could work with the Pythagorean Theorem and even knew that there are pythagorean triplets in considerable number, according to the equation [a2 + b2 = c2], in which every number is a whole number. One tablet arranges fifteen select triplets with predominantly high numbers, as for example the decimal 13,5002 + 12,7092 = 18,5412. As for how could someone have come up with this, there are a number of conjectures.The starting point was naturally the basic triplet, 32 + 42 = 52, which was easily ascertained by trial and error, along with its multiples (e.g., 62 + 82 = 102).
The Babylonians of the period before and after Hammurabi added to these tables thousands of texts of mathematical problems, both with and without the accompanying computations. Individual tablets compiled up to 247 problems of similar type without computations. A part of these was algebraically formulated, and among these were multifarious problems pertaining to divisions of inheritances which never appeared in actual praxis. Some texts show that the Babylonians could work with arithmetic progressions. The geometric problems are of a quite diverse sort; many have to do with building construction and excavation, including military purposes such as sieges. Often, however, only the terminology is geometric, as shown by the addition of linear and quadratic quantities, among other things, and such problems are therefore to be understood algebraically. We would formulate many of them as equations, both linear and quadratic. Still, the Babylonians never formed an equation, though they could solve numerous algebraic problems notwithstanding and only rarely had to be satisfied with estimates, which could not be avoided in geometry through circular calcu lations. .Ajmost all problems work with concrete numbers. It is only in rare instances that we find problems without such concrete numbers, in which ",'e ",'ould insert general numbers or variables, such as a, b, and the like.37
The completely unique phenomenon of Old Babylonian mathematics, whose achievement we can only sketch briefly here, has still not been satisfactorily interpreted, largely because this field is examined too one-sidedly, from the perspective of the history of methodology. Such a consideration is, of course, both necessary and indispensable, but it leaves open the decisive question: How is it possible that one form of mathematics, which was far more productive in its inception than Greek mathematics, developed without any systematic formulation of the knowledge of which it made such manifold use? It has often been maintained that oral instruction had supplied the principles of mathematics which cannot be found in any texts. If so, the intellectual structure of oral instruction must have been fundamentally different from that which had determined the form of the texts. This theory is made even less probable by the fact that other scientific texts contain no systematic formulations of scientific knowledge. Thus one comes with difficulty to the assumption that there was in Babylonia a nonverbal form of thought which was able to work quite efficiently without sYstematically formulated principles of knowledge, yet was never able to surmount certain limitations. This conclusion stands in direct conflict with what passes everywhere else as almost certain knowledge. What these limitations signified is shown quite impressively by the fact that after the great advance of Old Babylonian period, Babylonian mathematics stagnated for a thousand years, and in all probability sharply declined in productivity. There are only a few textual witnesses that during this period mathematics remained a subject of instruction.
The most important witness for the nurture of mathematics in Babylonia and Assyria in the first millennium is astronomy. As has already been mentioned ( see above, section 5) , astronomy emerged from the study of astrology. Astrology played a totally subordinate role during the period when mathematics flourished, but it won increasing significance toward the end of the second millennium and thus necessitated a far more exacting observation of the stars than earlier. This development then led to the demarcation of a larger number of constellations; the so-called astrolabe divided thirty-six of these among the three circles of the gods Anu, Ellil, and Ea. Bicolumnar lists of stars showed in the usual indeterminate manner the arrangement of fixed stars and planets with respect to one another. The series MUL.APIN ("Plow-star") uses complete sentences and explanatory relative clauses, and makes substantially more concrete pronouncements. The sun, moon, planets, and fixed stars were even more carefully observed in the first millennium, and the high temples were often used in this endeavor as observatories. In Assyria, whose kings had bestowed upon astronomy a quite unique position after the ninth century, the royal residence-city Calah was the center of astronomical observations. The new capital cities Dur-Sharrukin and especially Nineveh, with their observatories, carne later. We know a great many astronomers by name from letters and from the numerous astronomic-astrological reports of the period after 700 Before Common Era. Drawings of noteworthy phenomena in the heavens were already being made at an early date; according to Ptolemy, lists of eclipses were kept after 747 Before Common Erawith absolute precision. An initial result of this practice was that lunar eclipses could be reckoned with approximate accuracy after 700 Before Common Era; previously these had been seen as signs of the wrath of the gods. The same was also true with the much rarer solar eclipses, as in the case of the total solar eclipse of June 15,763 (see above, V.l). Nevertheless, the astrological texts often mention "untimely" eclipses that took place before they were expected. Thales of Miletus, however, was able to predict accurately the momentous solar eclipse of May 28,585, on the basis of Babylonian series of observations. Otherwise, there were only sporadic astronomical calcu lations in the Assyrian period.
The beginnings of astronomical calculations in Babylonia, which could be tied to the great and as yet unquenched tradition of mathematics, may lie in the sixth century. Babylonian astronomy was comprehensively pursued until the Achaemenaean period, when Greek and Babylonian astronomers began to work together; it was developed further still in the Seleucid and Parthian periods. The Babylonians contributed to this process the series of observations, which extended in part centuries into the past, while the Greeks brought their ability for systematic thinking and the formulation of scientific and mathematica1 results as well as problems. Famous Babylonian astronomers even carne to bear Hellenized names. Thus, the man regarded as the creator of System A of Babylonian lunar ca1culations, Nabu-rimanni (about 500?) was a1so ca1led Naburianos; later one finds Kidinnu (Cidenas) and Belussur (Berossos; about 300 Before Common Era. Of course, the astronomical calculations were presented without any basic discussion, as typical in Babylonia. Therefore, ifhistorians of astronomy often speak of Late Babylonian lunar or planetary theories, they nowhere refer to formulated concepts which can be deduced from the highly complicated numerical series found in the texts, and which the Greeks could have formulated in terms of a theory. The mathematical methods of the later astronomers far surpass those which the Old Babylonian algebra had been able to achieve. Presented in the form of a graph, the figures for the size of lunar eclipses result in "peaked curves." The cooperation of the Babylonian astronomers, some of whom emigrated to Greek territory, with their Greek counterparts was a development whose significance for scientific progress can scarcely be overestimated. Great advances in the practica1 aspects of the calendar accrued as a by- product of these astronomica1 calculations. The fact that there was no connection between day, month, and year which could be expressed in terms of whole numbers created problems all over the world. For the most part these problems could be resolved fairly well by provisiona1 alterations in the nature of the calendar. For example, the Babylonians added an extra month, Vlb or, more frequently, XIlb, to the twelve months of the lunar year as often as necessary, with the aim of equalizing the lunar and solar years. For centuries this was done from time to time only by specia1 decree of the royal administration; corresponding directives are extant.
The astronomers knew approximately seven hundred intercalary periods for this kind of calendrical adjustment, which were never put into practice. After abut 380 Before common era, there was a 19 year period with 8 leap years which produced a tolerable approximation of reality. For the purpose of simplifying calculations, astronomers often worked with 12 monts of thirty days each. The names of the months from the Neo-Babylonian period were adopted at na early date by the Judeans, and later by the Syrians as well.
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