Forgotten genius still burns bright

WHEN John Napier was born in 1550 in the medieval tower house of Merchiston Castle near Edinburgh, his eyes opened on to an astonishing world.

Europe, having been set ablaze by the artists, architects, sculptors, inventors and writers of the Renaissance, had also pushed out to new frontiers in different fields.

Copernicus had just proved that the sun was the centre of the universe, Columbus had crossed the Atlantic, Vasco da Gama had sailed around the Cape of Good Hope, finding a sea route to India, and Magellan had set off, planning to circumnavigate the globe, a feat achieved by his surviving captain, Juan Sebastiano del Cano.

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Scotland, although on the geographical outskirts of this burgeoning Europe, was not left behind. She now had universities at St Andrews, Glasgow and Aberdeen, and her people were cosmopolitan.

As early as the 1040s Macbeth, King of Scots, had mounted his horse and ridden to Rome, and over the centuries the Scots had continued this great tradition of travelling, bringing back not only stories of what they had seen but French and Dutch tapestries, illuminated books, and sometimes even masons and craftsmen to build their new homes and chapels. Only a few miles from young John’s cradle at Merchiston Castle stood Rosslyn Chapel, which contains late Gothic carving in such elegance and profusion that it continues to bewilder the beholder today; and in the centre of Edinburgh, the new, graceful crown spire of the Kirk of St Giles, where the Napier family was buried, was a source of great pride .

In the world of 1550, however, all the masons’ measurements, all the merchants’ accounts, and all the navigators’ and astronomers’ calculations, were laboriously worked out by long division and multiplication sums, squares and cubical extractions. It was a tedious, expensive and time consuming process and as Napier was later to point out, "for the most part subject to many slippery errors".

IT was to be the destiny of John Napier to change all this. Watching his father, the Master of the Mint, dealing with the nation’s finances, and at the other end of the scale, seeing the shopkeepers in luckenbooths at St Giles struggling with their sums, Napier decided that somehow it should be possible to remove what he called "those hindrances" - the long divisions and multiplications.

With dogged tenacity, he worked away all his adult life at the problem until it was almost an obsession. His first invention was logarithms, tables of numbers, which, when read across, simplified multiplication and division, a version of which was used by every schoolchild as a shortcut in the mathematics classroom.

He also introduced the decimal point, which was less cumbersome than the decimal fractions that had been devised by the Flemish mathematician Simon Stevinus in 1585. Then came what was to be known universally as "Napier’s Bones", the Rabdologia, which was a method of calculation using small rods in a box.

Napier’s logarithms were to the Elizabethan and Jacobean world what the computer is to ours. The Bones were to the masons, the merchants and the farmers what the pocket calculator is to us. From the Rabdologia quickly developed the slide-rule, a version of which was used by NASA engineers in the 1960s .

Napier’s invention was a quantum leap in mathematics comparable to the discovery by Archimedes in the second century BC of formulae for the areas and volumes of spheres and cylinders, and comparable with the introduction of Hindu-Arabic numerals to Europe by Leonard Fibonacci in AD 1202.

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And the extraordinary thing about Napier was, first, that he had thought his most important contribution to mankind was not in the field of mathematics and science, but a publication on religious philosophy and second, that his great mathematical discovery was made in comparative isolation in a tower house in Scotland.

Napier plodded on with his ideas and his figures, quite alone.

On the Continent, Johannes Kepler, the German astronomer, first saw the enormous importance of Napier’s logarithms. Without using them it had taken Kepler four years to calculate the orbit of the planet Mars.

Yet Napier died in April 1617, before receiving the international acclaim his inventions deserved. His son Robert published his father’s Constructio, a description in Latin of how he had worked out his great invention of logarithms.

BY 1620 a logarithmetic scale had been invented by the Englishman Edmund Gunther, and William Oughtred began work on a rudimentary slide-rule. The first slide-rule to have a scale which moved inside a rule was produced in 1654 and used logarithms for multiplying and dividing .

Only a decade later, Sir Isaac Newton was sitting in a garden when an apple fell from the branch of a tree. From this simple occurrence he began working on his gravitation theories, and he used Kepler’s calculations to develop his work. These calculations were only available to him because Kepler in turn had Napier’s logarithms to assist him.

Today, the tables of logarithms have been replaced by the calculator. Clearly this is handier for mathematical working - but Napier’s logarithms did not depend on batteries to function.

Napier’s contribution to mathematics cannot be over-estimated. His fame was at its greatest in the decades immediately after his death. Then curiously for nearly two centuries he seemed to slip into oblivion.

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In 1787, however, a very scholarly and technical book, An Account of the Life, Writings and Inventions of John Napier of Merchiston, was published by the Earl of Buchan and Walter Minto.

Then in 1833, Napier had a boys’ boarding school named after his home when Merchiston Castle School was founded and housed in the building. The school later moved, but more recognition was to come for Napier now has a university in the city named after him.

These are only some of the terrestrial accolades. Napier is among a very select band of people who are honoured in space.

In 1922 the International Astronomical Union decided that there should be a systematic listing of lunar nomenclature - the resulting report listed a crater on the moon named after Napier, and spelt it in the oldest known way, and the way he himself frequently used, Neper Crater.

There he is, along with Plato, Archimedes, Copernicus, Kepler, Tycho, Schickhard and Aristotle, up among the stars.

John Napier by Lynne Gladstone-Millar is published by the National Museums of Scotland, priced 6.99