Monday, July 11, 2016 0

John Napier was born in Scotland in 1550 and died in 1617. Although he doesn’t appear to have received much formal education, he made a very significant contribution to the development of mathematics with the invention of logarithms.

As the world became increasingly complex, there was a pressing need to find quicker methods of multiplying and dividing numbers: for trade, engineering, navigation, astronomy and so on. In 1614, Napier published Mirifici Logarithmorum Canonis Descriptio (A Description of the Wonderful World of Logarithms). A logarithm is really just a power; for example, the base 10 logarithm of 1000 is 3 because . Napier realised that any number could be written as a power of 10, and then multiplying two numbers simply became a matter of adding their powers, or logarithms*. For example:

(because )

So

*(In fact, he didn’t use base 10, but I’m simplifying things for clarity).

All that was required was to draw up tables of logarithms for all numbers (in practice, for numbers from 1 to 10, the rest could be easily derived from these), and tables of powers of 10 for the answers – these were called “anti-logarithms.” Turning multiplications into additions, and divisions into subtractions, was brilliantly simple, and Napier’s logarithms were quickly, and universally, adopted. Believe it or not, apart from increasing the accuracy of the tables, no better methods were invented and logarithms were still in use right up to the development of cheap electronic calculators in the 1980s. Every schoolchild had to master logarithm tables and methods of calculation.

Napier also improved on Fibonnaci’s “lattice” method of calculation by the invention knows as “Napier’s Bones” (because the rods of numbers were originally made from ivory, which looked like bone). See here for a good description of how the method works. The slide rule was another invention which used two sliding logarithmic scales to do direct calculations of multiplications and divisions – although, as with any ruler, it had limited accuracy. Slide rules were also in use in schools until calculators superseded them. They were invented a few years after Napier published Mirifici by William Oughtred, who also invented the multiplication symbol!

What else did Napier do? He produced some excellent theorems regarding spherical trigonometry; he invented the decimal point (decimals themselves had only been invented a little earlier) which he prophesised, correctly, would revolutionise mathematics. But his invention of logarithms ensured that the work of great scientists such as Kepler and Newton would not be held up by the labour of tedious calculation.

Napier: interesting facts
1.   Edinburgh Napier University is named after him,  part of the campus being built on his land.
2.   He occasionally signed himself “Neper”, and the Neper crater on the moon is named after him.
3.   Napier had an interest in alchemy, but never turned anything to gold!
4.   He was born to a noble family, and eventually became a significant landowner and the laird of Merchiston Castle.

Merchiston Castle, now part of Merchiston Castle School