Mathematics

In Mesopotamia, right from the third millennium BC texts concerning the size of fields and the dividing and surveying of plots testify to mathematical thinking. The Old Babylonian period (first half of the second millennium) saw schools of scribes spread throughout the cuneiform-using Near East, and these centers of learning have turned up many tablets of mathematical exercises.

One of the particularities of cuneiform mathematics was the use of a positional base-sixty system. In a few cases, the texts are purely mathematical, devoid of explanation, while in other cases they present a “set of problems” with long, detailed explication. The vast majority, however, are lists of problems that have been solved.

It is now generally admitted that solving second-degree problems in Mesopotamia and Elam was governed by geometric reasoning related to the method of completing a square, the very one that would subsequently be developed in Greek and, later, Arabic. Often the problems were presented in a realistic context alluding to the social activities of the day. The favored subjects were surveying, building with bricks, excavating foundations, digging canals, dividing labor and wages among workers, rates of interests, and problems of inheritance. And yet despite the often contrived nature of the setting, these problems do not appear to have been designed to solve concrete problems of everyday life.

Few texts from the first millennium BC have been discovered to date. Those that have survived are less interesting in terms of mathematical theory. A tablet found in Babylon from the Seleucid period, however, sets an algebraic problem similar to the mathematical problems of the second millennium, although the method of solving it differs. This table indicates a new way of envisaging the teaching of algebra and geometry in school at the end of the first millennium BC. Another Seleucid table displays significant features probably corresponding to important innovations in the field of mathematics in the middle of the first millennium BC. Noteworthy is the use of a special sign to indicate zero, which resembles the double wedge-mark separating two parts of a sentence. Zeroes appeared on older documents, for example on tablets from Susa dating from the second millennium BC, but they were rare. The use of a special sign for zero became more systematic from 500 BC onward. Another part of this same table indicates the dimensions of a triangle, a figure that had never been attested in mathematical documents from Babylonia of the second millennium BC.


Astronomy/astrology

These sciences emerged prior to Hammurabi’s day. Around the middle of the first millennium BC, Babylonian astronomers began to depict or map the movements of stars and planets in a much more precise way, not only in relation to one another but also in relation to the sun and moon. Accurate predictions thus became possible. Calculating celestial phenomena therefore assumed increasing importance and liberated mathematics—born of the need to measure land—from the field of algebraic geometry.

The main contribution of Babylonian astronomy to scientific progress was the production of tables with the computations necessary to predict celestial phenomena. This new kind of astronomical knowledge supplied exact predictions on the new and full moon, on eclipses, and on the periodical appearance of the planets. It was at roughly this time that the zodiac, later adopted by Greek astronomers and astrologers, was devised.


Cartography

The Mappa Mundi or map of the Babylonian world was discovered at Sippar in southern Iraq, although the map and accompanying texts were probably produced in Babylon. The map takes up the lower two-thirds of the front of the tablet; it deals with distant lands, mythological events and creatures, and the world located beyond the everyday one—this clay-impressed vision of the world is therefore a schematic one.

The dominant feature of the map is a large circular ring inscribed marratu, “salt sea.” The Babylonians apparently shared with certain Greek cartographers the idea that the inhabited world was surrounded by an ocean. Within the circle, geographical places and features within Mesopotamia were represented by the use of various circles, rectangles, and curves (usually labeled).

The eleven fragmentary lines of text that precede the map are fairly enigmatic. They clearly refer to the creation of the world as recounted in the epic Enuma Elish, that is to say the victory of the god Marduk over Tiamat, the primordial ocean. It mentions “annihilated gods” known to have been engendered by Tiamat, and also refers to a bridge that allowed Marduk to cross the waters that were home to, among others, the viper and the mušhuššu dragon (seen on brick panels in Babylon).


Divination

In Babylon, the study of omens was one of the most important parts of the school curriculum. The concept of divination, or prophetic analysis, was based on a belief in a cause-and-effect relationship between two successive events. Thus the entrails of a sheep that displayed certain features were related to some major contemporary event, and the two phenomena were thought to be necessarily correlated. This logical error nevertheless had an impact on scientific thinking in so far as ancient scholars who practiced divination compiled many lists of data concerning everything considered to be an omen (the position of heavenly bodies, the flight of birds, the behavior of oil in water, smoke, abnormal births, etc.) Although we might think that divination wandered down the wrong path given its desired goal, its methods of handling data and the idea of drawing conclusions from a mass of information might nevertheless be perceived as forerunners of modern scientific methods.

The Babylonians thought that the position of constellations, planets, sun, and moon (eclipses, for example) had an impact on events on earth. The science of observation of heavenly bodies, in fact, would swiftly be applied to divination, thus giving birth to a secondary field of learning, astrology, that combined the observable movements of the night sky to events that occurred on earth. During the Persian and Hellenistic periods, astrology yielded horoscopes that would influence Greek thought.


Medicine and magic

Babylonian healers were keen observers who scrupulously noted the symptoms of their patients. They left a long list of symptoms, known as the “Diagnostic Treatise.” The text offers only poor insight into the classification of illnesses, because symptoms were not linked to the ailments that caused them but to the part of the human body where they occurred. The “Diagnostic Treatise”—for which no Egyptian equivalent has been found—was based on gathering and analyzing data, even if the initial postulate did not conform to our idea of diagnosis.

Therapeutic texts began by describing a symptom, then listed the remedies and treatments liable to remove the symptom but not necessarily cure the illness—curing was probably a domain reserved for the gods. Magical incantations and practices were done by an exorcist, whereas the role of doctor entailed treating symptoms. Therapeutic texts often mention the weight or quantity of each substance used in preparations, indications that probably reflect the proportions to be respected. Nothing similar appears in texts of incantations or the accompanying rituals. The combination of several substances in a preparation perhaps suggests that the effects of each ingredient were known, so that the side effects of one substance might be countered by the addition of another. One of the important features of Babylonian pharmacology, later found in Greek and Arabic medicine, was the use of single substances as well as preparations that could contain up to ninety different active substances.

Most incantations were supposed to conjure away sickness, indeed death, but magic focused on the supernatural causes of illness, such as the vengeance of an angry god, an act of witchcraft, or the patient’s non-respect of ancient taboos, the upshot of which would be the loss of divine protection against demons and sickness. The teaching of magic texts was a major part of Babylon’s school curriculum, and Babylonian libraries contained a range of magical texts, most of them poetic. Although magic was conceived as a way of altering the effects of supernatural forces, these texts were designed to alter the patient’s psychological state by reducing anxiety and neurotic fears.