
John
Napier
(15501617)
Discoverer
of logarithms
Napier was a man of great intellect, persistence and will, leading
a solitary lifestyle; his interests in subjects like divination
acquired him a reputation as a necromancer. But his true genius
lay in mathematics: he developed theories of logarithms, computing
them and constructing tables He was the first to devise the
use of the decimal point. He also invented the world’s
first mechanical computing device in the form of a series of
rods which were nicknamed ‘Napier’s Bones’. Napier
was also an enthusiastic religious controversialist who wasted
much time and talent inventing war machines to fend off his
particular Spanish Catholic bogeyman.
More About John Napier. Genius is a reasonable word to apply to John Napier, the laird of Merchiston; and a lot of enthusiasm went with it. He was born in 1550, when life was lacking a lot of the conveniences we take for granted today.
Napier's prime passion was to have Roman Catholics abolished, especially Roman Catholic lairds, for the twin sins of being Papists and being rich. Well, everybody needs a hobby. On the side, he published in several languages. He invented advanced war machines. He tried his hand at astrology and divination. He was a vigorous and hard working intellectual. Almost in passing, he invented logarithms. Nowadays, we don't need them much, because the pocket calculator is so common. Logarithms were the calculators of their time, and they don't need batteries and screwdrivers, so we probably should hang on to them. They help us to do difficult sums without taxing our brains.
This, very briefly, is what logarithms are all about: powers. In mathematics, a power indicates the number of times a number is to be multiplied by itself. Two to the power of one is two; two to the power of two is four; to the power of three, eight. Ten to two is 100.
John Napier's logarithms were an aid to many generations struggling to work out their complicated sums. The power is usually written as a small number above and to the right of the number being raised. When we write 10 , we are actually writing one plus
nine noughts. The power number is also called the index or the exponent. Non mathematicians should read slowly now. Ten is easypeasy. If we have something like
241, it is headache time. But what Napier realised is that any number can be expressed as the index of another number. Any number can be seen as the index of 10. And if some dogged scholar, such as Napier, can be bothered to work out the sums for every number, and print them in a table, we can look them up.
When we are faced with some awkward number to multiply by another awkward number, we look up the logarithms of both numbers and just add them. Then we look up the answer to the simple addition in an antilogarithm table, and lo and behold there it is. It is a staggering advance.
For instance, what number has to be multiplied by itself 13 times to produce the answer 1,594,323? Look up the log tables. It's three. You might find that difficult to do on a pocket calculator.

