Information Technology Reference
In-Depth Information
own digits. The tablet, the abacus, and mathematical tables are three important aids to
manual calculating [9].
Simply having a tablet to write down the numbers being manipulated is a great
help. In ancient times, erasable clay and wax tablets served this purpose. By the late
Middle Ages, Europeans often used erasable slates. Paper tablets became common in
the nineteenth century, and they are still popular today.
An
abacus
is a computing aid in which a person performs arithmetic operations by
sliding counters along rods, wires, or lines. The first abacus was probably developed in
the Middle East more than two thousand years ago. In a Chinese, Japanese, or Russian
abacus, counters move along rods or wires held in a rectangular frame. Beginning in
medieval Europe, merchants performed their calculations by sliding wooden or metal
counters along lines drawn in a wooden counting board (Figure 1.3). Eventually the
word “counter” came to mean not only the disk being manipulated but also the place
in a store where transactions take place [9].
Mathematical tables have been another important aid to manual computing for
about two thousand years. A great breakthrough occurred in the early seventeenth cen-
tury, when John Napier and Johannes Kepler published tables of logarithms. These tables
were tremendous time savers to anyone doing complicated math because they allowed
them to multiply two numbers by simply adding their logarithms. Many other useful
tables were created as well. For example, businesspeople consulted tables to compute in-
terest and convert between currencies. Today, people who compute their income taxes
“by hand” make use of tax tables to determine how much they owe.
Even with tablets, abacuses, and mathematical tables, manual calculating is slow, te-
dious, and error-prone. To make matters worse, mathematical tables prepared centuries
ago usually contained errors. That's because somebody had to compute each table entry
and somebody had to typeset each entry, and errors could occur in either of these steps.
Advances in science, engineering, and business in the post-Renaissance period moti-
vated European inventors to create new devices to make calculations faster and more
reliable and to automate the printing of mathematical tables.
Blaise Pascal had a weak physique but a powerful mind. When he got tired of summing
by hand long columns of numbers given him by his father, a French tax collector,
he constructed a mechanical calculator to speed the chore. Pascal's calculator, built
in 1640, was capable of adding whole numbers containing up to six digits. Inspired
by Pascal's invention, the German Gottfried Leibniz constructed a more sophisticated
calculator that could add, subtract, multiply, and divide whole numbers. The hand-
cranked machine, which he called the Step Reckoner, performed multiplications and
divisions through repeated additions and subtractions, respectively. The calculators of
Pascal and Leibniz were not reliable, however, and did not enjoy commercial success.
In the nineteenth century, advances in machine tools and mass-production meth-
ods, combined with larger markets, made possible the creation of practical calculating
machines. Frenchman Charles Thomas de Colmar utilized the stepped drum gear mech-
