John Napier, mathematician, physicist, and astronomer, died on the 4th of April, 1617.
You might not recognise the name of Jhone Neper, which doesn’t sound so very Scottish, but in his day, he was famous all over the European Continent. His surname appeared in a variety of different spellings throughout his lifetime and during the centuries since the 17th in which he lived. The forms Neper, Naper, Nepeir, Napeir, Nepair, Napare, and Naipper are all to be seen, however, the only form of Jhone Neper that would not have been used in his lifetime is the present day, modern spelling of John Napier. He is inarguably most famous for what we now call logarithms. The straightforward addition of exponents, which we use today to simplify the operations of multiplication and division, stemmed from his interest in astronomy. Like others, such as Copernicus, Galileo, Tycho Brahe, and Kepler, John Napier was involved in astronomical research that required lengthy and time consuming calculations. He figured there had to be a simpler way.
We can claim logarithms to have been invented by Napier, but like many an invention, their emergence and nowadays mainstream usage wasn’t solely down to the work of a solitary individual. That’s something we shouldn’t be too surprised at, even if a little disappointed when our ‘heroes’ are diminished somewhat by the thought. A form of logarithms had allegedly been invented by the Swiss mathematician, Jost (Jobst) Bürgi, perhaps as early as 1588, however, his method is distinct from Napier’s and wasn’t published until 1620. In the meantime, Napier spent twenty years, from 1594, perfecting his own concept. Whether or not Tycho Brahe knew of the Swiss clockmaker’s method, he was certainly very much aware of Napier’s ideas, because he spent much of the intervening period impatiently awaiting the outcome. As an astronomer, he had very practical uses for Napier’s logarithms.
Napier published his first set of logarithmic tables in 1614, in his book called, ‘A Description of the Admirable Table of Logarithms’ (Mirifici logarithmorum canonis descriptio). Without doubt, these tables were a stroke of genius and proved to be a big hit with astronomers and scientists, particularly the aforementioned Brahe and a certain Johannes Kepler. It’s also said that the English mathematician, Henry Briggs, was so influenced by the tables that he traveled to Scotland just to meet Napier. His visit led to them cooperating on the development of ‘Base 10’ logarithms, which is what is used in the ‘logs’ we know today.
Napier wrote in his ‘log book’ that, “Seeing there is nothing that is so troublesome to mathematical practice.... than the multiplications, divisions, square and cubical extractions of great numbers, which besides the tedious expense of time are... subject to many slippery errors, I began therefore to consider [how] I might remove those hindrances”. Laplace, 200 year later, agreed, saying that logarithms, “...by shortening the labours, doubled the life of the astronomer.” And the 18th Century Scots philosopher, David Hume, wrote that Napier was a “person to whom the title of a great man is more justly due than to any other whom his country ever produced.” Tribute indeed!
John Napier was born in Merchiston Castle, in Edinburgh, in 1550, we know not when, but we can be sure he had a birthday to celebrate. Napier’s father, who became Sir Archibald Napier and a Master of the Mint in Scotland, was only sixteen when John was born, which fact may be striking today, but not so uncommon in the 16th Century. As was the practice for nobility, Napier did not enter school until he was thirteen, in which year he went to St Salvator’s College at the University of St. Andrews, albeit only for a short time. Thereafter, as is believed, he travelled in Europe to continue his studies. Enigmatically, little is known about those years and where or when he may have studied. Perhaps he visited Bürgi in Switzerland or went to see Brahe in the Netherlands.
In any event, in 1571, Napier turned twenty-one and returned to Scotland. On the death of Sir Archibald, in 1608, Napier became the 7th Laird and moved into Merchiston Castle, where he lived for the rest of his life. Because of his inherited wealth and a religious zeal inherited from his father, Napier was involved with the political and spiritual controversies of his time. Napier was fervently anti-Catholic and one of his ‘claims to fame’ – the one he thought he should be famous for, rather than mere logarithms – was his 1593 book entitled, ‘A Plaine Discovery of the Whole Revelation of St. John’. In that fantasy, he claimed his calculations, based on the Book of Revelations, pointed to Pope Clement VIII being the ‘Antichrist’. He also predicted that the world would come to an end in either 1688 or 1700. In the preface to the book, he stated that it’s purpose was “... for preventing the apparent danger of Papistry arising within this Island… .”
Despite the craziness, Napier was a man of many talents and high intelligence, who was known around Edinburgh as ‘Marvelous Merchiston’, for the many ingenious mechanisms he built to improve his crops and beasts. He experimented with fertilizers, invented an apparatus to remove water from flooded coal pits, and built devices to better survey and measure the land. In addition, he had plans, never completed, for elaborate devices to deflect any Spanish invasion and other military projects, similar to today’s submarine, machine gun, and battle tank. Don’t forget his incentive – the Spaniards were Catholics. Napier’s other mathematical contributions included a mnemonic for formulae used in solving spherical triangles, two formulae known as ‘Napier’s analogies’ as used in solving spherical triangles and the invention known as ‘Napier’s rods’ or ‘Napier’s bones’, which were basically multiplication tables, inscribed on sticks of ivory. In addition to multiplication, the rods were also used in taking square roots and cube roots. Napier also found exponential expressions for trigonometric functions and, last but by no means least, he was the ‘inventor’ of the decimal point.
John Napier died on the 4th of April, 1617, in Edinburgh, probably from complications arising from gout. It is said that the whereabouts of his remains are uncertain, but Wikipedia states they were buried in St Cuthbert’s Church, in Edinburgh.