added. Some of these tables also provide the square of the
principal number.
Th e Babylonians had no division tables, but they did
make extensive use of reciprocal tables. (A reciprocal is sim-
ply 1 divided by the number in question, so that the recipro-
cal of 60 is 1/60.) Th us, instead of dividing, they multiplied by
a reciprocal. To aid them in this task, they created extensive
reciprocal tables. Th ere are hundreds of these tables, along
with tables for squares, square roots, and cubes, many of
them compiled by students. Finally, there are coeffi cient lists,
which list conversion factors used in geometry (for example,
the ratio of a diagonal to a square’s side) and weights and
measures problems.
In addition to these tables are so-called problem texts,
that is, exercises used in schools. Some of the tablets that re-
cord these texts contain a number of problems on a single
topic; others contain problems related to diff erent topics. Th ey
have given historians insight into the kinds of problems ex-
amined in schools. Nearly all of the problems ask students to
come up with a number, never with any kind of proof. Th us,
they are “algebraic” problems, in contrast to the “geometric”
problems that ancient Greek students studied. (In algebra
the goal is to arrive at a correct answer, expressed as a num-
ber; in geometry the goal is oft en to prove, for example, that
the angles of a triangle add up to 360 degrees). Interestingly,
modern mathematicians have taken a more extensive interest
in Babylonian mathematics because of its emphasis on algo-
rithms, or following a process to arrive at an answer.
Most such problems were what modern students know
as “story problems,” that is, problems couched in everyday
terms by calling for calculations of things in the real world:
the length of a canal or broken reeds, the weight of a quantity
of stones, or the number of bricks used in a building. Many of
the problems are complex, requiring students to use not just
single equations but more complex linear and quadratic equa-
tions. Some of the texts record the procedures students would
follow to solve the problem, but none state general principles.
Instead, the emphasis seems to have been on working prob-
lems as examples oft en enough so that the student could then
work a new problem with diff erent values. In many cases, all
the problems in a group have the same answer, suggesting
that the group of exercises was designed to teach a process of
computation rather than to arrive at a correct answer.
Although the Babylonians did not have an organized
system of geometry—they did not compute angles, for in-
stance—many of the problems have geometric implications,
and many contain drawings of squares, rectangles, circles,
and triangles. Some problems required the student to com-
pute such quantities as lengths of diagonals or sides or to cal-
culate volume or area. Bricks and calculating a quantity of
bricks seem to have been a preoccupation with Babylonian
math teachers.
For reasons that historians do not fully understand, the
mathematical record of the Old Babylonians comes to an
abrupt halt aft er about 1600 b.c.e. What follows is a thou-sand-year gap in the record. Aft er this millennium the record
resumes, and historians have records of continued interest in
mathematics in the Mesopotamian region.ASTRONOMY
During the fi rst millennium b.c.e. the Babylonians compiled
columnar lists of stars, with the columns listing the stars and
their positions in relation to the positions of other stars. So
great became the interest in observation of the stars that tem-
ples became astronomical observatories. It should be noted
that at the same time, the Assyrians of the Near East also gave
great importance to astronomy, and Assyria’s capital, Kalhu
(modern Nimrud), was a center of astronomical observation
and study. In both Babylon and Assyria, lists of such events
as eclipses were meticulously kept aft er about 800 b.c.e.—so
accurately that future eclipses could be and were predicted.
Again, the Babylonians lacked a system, an underly-
ing theory to explain and systematize the phenomena they
observed in the heavens. Only aft er about the sixth century
b.c.e. did they begin to organize their knowledge into a sys-
tem. Th ey did so only because they began working alongside
Greek astronomers, who seemed, in common with the an-
cient Greeks, generally to have been better equipped to think
systematically. Many of the famous Babylonian astronomers
from this period even took Greek names. Naburimanni, who
lived around 500 b.c.e., became called Naburianos, and the
later astronomers Kidinnu and Belussur became, respec-
tively, Cidenas and Berossus.
Babylonian astronomical observation was not, however,
a “scientifi c” endeavor in the sense of an activity intended to
develop an understanding of the atmosphere or the planets
and the stars. Rather, the purpose of astronomical observa-
tion was completely diff erent than it is today. It was employed
in divination, akin to modern and medieval astrology. Celes-
tial divination was used to foretell the fate not of individuals
but of kings and the state. Th e decision to launch a military
campaign, like almost all major decisions, was almost always
preceded by celestial or some other form of divination.MEDICINE
Much of the interest in the natural sciences among the ancient
Mesopotamians focused on medicine and healing, an early
eff ort to exert some human control over inexplicable forces.
In the ancient Akkadian language, the word for doctor is lit-
erally translated as “fl uids expert.” Over millennia doctors in
the region accumulated a vast store of information having to
do with drugs, salves, and other medicines either taken orally
or applied to the body. Most of these drugs consisted either of
minerals or plant extracts, including spices.
Th e practice of medicine was closely interwoven with
magic and the science of omens. Th e application of drugs
was typically accompanied by prayers and incantations. Th e
goal was to strengthen the patient’s will to recover. Interest-
ingly, modern medicine has come to recognize that a patient’s
frame of mind can play an important role in recovery; mod-930 science: The Middle East0895-1194_Soc&Culturev4(s-z).i930 930 10/10/07 2:30:28 PM