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John Napier's calculating tools
Undoubtedly one of the most influential mathematicians ever, John Napier's
(1550-1617) contributions to the field were both theoretical and practical.
Along with his discovery of the method of logarithms, he left his mark by
devising ways to ease the labour of calculation.
Life and work
Born into a family of wealthy landowners in Scotland, Napier enrolled at the
University of St. Andrews, where he cultivated an interest in theology. Study
in Europe gave the young Napier a taste of mathematics, which occupied his
attention when not engaging in Scottish politics or tending to his estate as
Baron of Murchiston.
After years of experimenting with calculation, he was able to determine a
general formula for the number of times a 'base' had to be multiplied by
itself to reach another value. While this notion of a logarithm appears simple
now, his use of complex proportions rather than integers (hence the word
'logarithm', which roughly means 'ratio number') led him to a way of using
addition and subtraction as substitutes for multiplication and division.
Napier published this work in 1614 as a Description of the Wonderful Rule of
Logarithms.
Napier's bones
Napier spent much of his time inventing practical ways to simplify large
arithmetic problems. Three of these methods were published after his death in
1617 as a treatise, Rabdology (Image 1), a word which was a portmanteau of the
Greek words for 'rod' and 'calculation'.
The most popular of these methods involved a series of numbered columns that
could be laid side by side to simplify large multiplications. This was adapted
from an ancient Indian method known as gelosia, so called in Renaissance Italy
due to its resemblance to a kind of window design of the same name.
A tool for teaching
Because Napier's bones, also called 'speaking rods', largely eliminated the
mental arithmetic required by large calculations, they became a popular tool
in a society where few were educated enough to perform complex arithmetic.
The linguist and royal Master of the Ceremonies to Charles I and II, Sir
Charles Cotterell (1612?-1702) designed a device combining Napier's bones with
a simple abacus arranged as a portable compendium . It came along
with a text which advertised itself as
"So easy a way, to learn and use that Art,/That even those who can
neither write nor/Read, have been thereby taught all the general/Parts of
it."
Meant as a didactic tool, the book also catered to "skilful Artists" who
wished to use the very same rods to calculate square and cube roots. Even into
the 20th century, Napier's bones were an educational resource shown to
students to help them think about breaking big calculations into smaller parts.
The first adding machine?
A popular way of arranging Napier's bones as rolling rods may have inspired
the very first calculating machine. In 1617, the astronomer Johannes Kepler
(1571-1630) discussed Napier's discoveries with his Tübingen colleague Wilhelm
Schickard (1592-1635). A few years later, in 1623, Schickard wrote to Kepler
describing a machine he had devised using rods and a set of gears that could
mechanically carry or borrow numbers during addition and subtraction.
Unfortunately, the machine Schickard commissioned to be built for Kepler was
destroyed in a fire, and Schickard's own has never been found, so only
drawings and descriptions can tell us about this device. Whether Schickard
deserves credit as the inventor of the first mechanical calculator, or whether
that credit should go to Blaise Pascal, who invented a working machine in
1642, is a debate that still continues.
73, Scott KF5JRV
Pmail: KF5JRV @ KF5JRV.#NWAR.AR.USA.NA
Email: KF5JRV@GMAIL.com
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