Prelude: Computing from Ancient Times to the Modern Era - The Technical and Social History of Software Engineering - page 6

computers and software. This required sophisticated knowledge of the previous
topics, combined with fairly accurate measurements and intellectual curiosity in
minds that have a bent for mathematical reasoning. These probably originated
with people who had been educated in mathematical concepts and were inventive
enough to extend earlier mathematical concepts in new directions.
One of the earliest cities, Mohenjo-Daro, which was built in Northern India
about 3,700 years ago, shows signs of sophisticated mathematics. In fact, balance
scales and weights have been excavated from Mohenjo-Daro.
This city may have held a population of 35,000 at its peak. The streets are laid
out in a careful grid pattern; bricks and construction showed signs of standard di-
mensions and reusable pieces. These things require measurements.
Both Mohenjo-Daro and another city in Northern India, Harappa, show signs
of some kind of central authority because they are built in similar styles. Both cit-
ies produced large numbers of clay seals incised both with images of animals and
with symbols thought to be writing, although these remain undeciphered. Some of
these clay seals date as far back as 3,300 BCE .
Other ancient civilizations also developed counting, arithmetic, measures of
length, and weights and scales. Egypt and Babylonia had arithmetic from before
2,000 BCE .
As cities became settled and larger, increased leisure time permitted occupa-
tions to begin that were not concerned with physical labor or hunting. These occu-
pations did not depend on physical effort and no doubt included priests and sham-
ans. With time freed from survival and food gathering, additional forms of math-
ematical understanding began to appear.
Keeping track of the positions of the stars over long periods, measuring longer
distances such as property boundaries and distances between villages, and meas-
uring the headings and distances traveled by boats required more complex forms
of mathematics and also precise measurements of angles and time periods. The
advent of boat building also required an increase in mathematical knowledge.
Boat hulls are of necessity curved, so straight dimensional measurements were not
enough.
Rowing or sailing a boat in fresh water or within sight of land can be done with
little or no mathematical knowledge. But once boats began to venture onto the
oceans, it became necessary to understand the positions of the stars to keep from
getting lost.