a. For a long time, our distant fore-bearers managed without keeping records.
However, as society grew more structured and people organized into tribes, daily life
grew too complex to function without records. When people began to collect animals,
and engage in commerce, when families entered into social relations with one another,
they began using the ten fingers and then stones, sticks, scratches on a rock, or knots
in a string. These manual devices made it easier to account for sheep in a flock, days
between cycles of the moon, or the number of successful hunts.
Figure 1-2. Knots on a string used to keep track of day-to-day affairs.
b. By about 4,000 years ago, early civilizations had developed sophisticated
numbering systems to keep track of commercial transactions. At the Ashmolean
Museum in Oxford, England, there is a royal Egyptian staff dating back to the year 3400
BC. Indentations in the wood make record of 120,000 prisoners taken, a booty of
400,000 oxen and 1,422,000 goats.
Figure 1-3. Ancient numbering systems used the additive method. The number "216"
is shown in the corner insets, as written in cuneiform and hieroglyphics.