Encyclopedia of Society and Culture in the Ancient World

advanced early civilizations. A signifi cant increase in sophis-

tication occurred sometime aft er 500 b.c.e. By then, however,

the great epochs of hieroglyphic Egyptian civilization had

ended.

Around 525 b.c.e. Persia conquered Egypt. Th e Persian

Empire’s intellectual capital, Babylon, lay outside Egypt. In

332 b.c.e. Alexander of Macedonia followed the Persians into

Egypt and put a permanent end to the pharaonic dynasties. A

Greek presence had been in Egypt since the seventh century

b.c.e., but with the coming of Alexander began the Greek

Ptolemaic Dynasty, which ruled Egypt until the Romans ar-

rived in the fi rst century b.c.e. Alexander’s general Ptolemy

made his capital at Alexandria, a city founded by Alexander,

who kept a company of philosophers and scientists with him

for the purpose of spreading Greek learning and civilization

to the barbarous parts of the world he conquered. Ptolemy

built the greatest library of the ancient world at Alexandria,

which fl ourished as a center of learning. Th e Museum, or

Temple of the Muses, which housed the library, was a precur-

sor to the modern university, with lecture halls, laboratories,

experimental gardens for the study of botany, a zoological col-

lection, and departments of medicine, astronomy, literature,

and mathematics. For several centuries Alexandria and its

Museum attracted the most brilliant astronomers and math-

ematicians of the ancient world. Th e work of the Alexandrian

scientists remained dominant even aft er the fall of the Roman

Empire in the fi ft h century and until new systems of thought

were developed in the 17th century by Galileo, Copernicus,

and Isaac Newton.

Th e activity at Alexandria is Egyptian, even if research

was conducted in Greek. Claudius Ptolemy, antiquity’s great-

est astronomer (second century c.e.), was an Egyptian who

wrote in Greek and had a Latin-Macedonian name. Egyptian

developments in science and medicine, therefore, were not

minor but were made obscure by the medium of hieroglyphic

writing. For much of the period in which the hieroglyphic

script was dominant, Egyptian learning did not signifi cantly

lag behind that of any other nation.

THE MIDDLE EAST

BY MICHAEL J. O’NEAL

Th e Sumerians, Akkadians, Assyrians, and Babylonians did

not think in terms of scientifi c laws, and nothing like the

modern scientifi c method of inquiry existed, with its empha-

sis on formulating hypotheses and testing them to arrive at

general principles about the physical world. Th ey did, how-

ever, develop mathematical reasoning to a high level of so-

phistication, enabling them to calculate everything from the

area of a fi eld to the amount of seed required to be sown in or-

der to achieve a predicted yield. Mathematics in turn fed into

architectural design, astronomical reckoning, time keeping,

and all manner of economic control over seed, yields, rations,

and productivity. Th ere was no self-conscious discussion of

science per se, but it is clear that the ancient Mesopotamians

were fully capable of thinking and calculating in a rigorous,

predictable, and, above all, accurate manner.

MATHEMATICS

Th e ancient Mesopotamians developed a sophisticated sys-

tem of mathematics. Early on they learned that they needed

a precise system of measurement. Arable land had to be mea-

sured accurately so that the requisite amount of seed and ir-

rigation water could be calculated to make the land deliver a

high yield. Irregularly shaped plots of land were divided into

triangles and rectangles, and area was calculated by sum-

ming the areas of the parts. Volumetric calculations were also

necessary. In constructing a wall or digging a pit, the need to

calculate volumes of earth, the numbers of bricks required,

and the amount of labor to be hired and for how long were all

important to the planning of a project. Th e amount of food

rations (barley, beer, salt, oil, fi sh, and so forth) had to be cal-

culated as well. Th e best surviving records come from what

historians call the Old Babylonian Period, dating roughly

from about 2000 to 1600 b.c.e.

Th e mathematical system of the Babylonians (and the

Sumerians before them) was a sexagesimal system, mean-

ing that it was based on the number 60 rather than on the

number 10. Any metrological system contains within it units

of measure with fi xed conversion factors. Th us, for example,

a foot consists of 12 inches, a mile of 5,280 feet, and so on.

Th e sexagesimal system of the Sumerians and Babylonians

evolved out of their conversion factors. In the late third mil-

lennium b.c.e. a fi nal step took place, that of place holding.

In the modern numerical system, the value of the digit 3 var-

ies depending on its place. By itself it stands for 3, but in the

numeral 30 it represents three 10s, in 300 it represents three

100, and so on. Th e Babylonians developed a similar system.

Now they needed only two symbols, one for the digit and one

for its place. A vertical wedge was the “base unit.” A corner

wedge, derived from the small circle, had a value of 10 ver-

tical wedges. A further vertical wedge was worth six corner

wedges, and so on. Th ese symbols could be repeated as of-

ten as necessary to arrive at such fi gures as 1, 60, 360, 3,600,

and the like. From there it is easy to see the roots of many

peculiarities of modern measurement systems. Th ere are 360

degrees in a circle, 12 inches in a foot (for 12 is a factor of 60),

three feet in a yard (for three is also a factor of 60), and the

like.

Several hundred clay tablets exist in two forms: table

tablets and problem texts. Th e table tablets could be consid-

ered an extension of the interest in listing discussed earlier.

Th e tablets have a simple structure and show the two-sym-

bol system of counting, along with the place-holding system.

Th ere are no subtraction or addition tables, but there are nu-

merous tables for multiplication. Th ese tables list multiples

of one number, called the principal number (p). Th us, there

were calculations for 1p, 2 p, and so on. Th e tables calculate

up to 20p and then skip to 30p, 40 p, and 50p. For a num-

ber such as 53, for example, the results for 50p and 3p were

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