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Significant Scots
John Napier
By Jeremy Hodges in the Daily Mail, July 8, 2000

He was ‘the person to whom the title of great man is more justly due than to any other whom this country has produced’. In this simple pronouncement, the Scottish intellectual David Flume summed up his fellow countryman John Napier.

Yet most Scots know little or nothing about the 16th-century mathematician, philosopher and inventor who, from his secluded tower in Scotland, produced the vital tool needed by mankind to explore the globe and fathom the universe. Without Napier's invention of logarithms and the decimal notation for complex fractions, the discoveries of others such as Galileo, Kepler and Newton would have been hindered by years of long and complex calculations.

For decades Napier wrestled with mathematics in the privacy of his home, while his superstitious neighbours grew convinced he was involved in sorcery and witchcraft. Dressing in a long, black gown to match his thick, black beard, he did nothing to dispel their illusions. He achieved one of the greatest mathematical discoveries of all time while living through one of the most violent and turbulent periods in Scotland’s history with his home town of Edinburgh embroiled in civil war and ravaged by the plague.

For centuries his reputation remained almost as obscure as the location of his unmarked grave somewhere in the capital. But his name now lives on at Napier University in Edinburgh, this year celebrating the 450th anniversary of his birth in 1550.

Last month an honorary degree was conferred on Brigadier General John Hawkins Napier II, who travelled from his American home to receive the honour bestowed upon him thanks to his illustrious ancestor.

Now the university is setting its sights on education and encouraging the mathematical inquisitiveness which so characterised the esteemed man from whom it takes its name, as it prepares to launch John Napier’s Mathematical Challenge for Schools, to run over the coming months.

Best known in his lifetime as author of a Protestant theological work that probed the prophecies of the Apocalypse to prove the Pope was the Antichrist, Napier was far from the modern idea of a mathematician - he was a late-Renaissance man whose powers of lateral thinking took in everything from agricultural improvement to devising engines of war.

There was plenty of conflict brewing when he was born at Merchiston Castle outside Edinburgh, the son of Sir Archibald Napier, a Scottish judge and wealthy landowner.

Three years previously, Napier’s grandfather had been slain while fighting in the army of Mary Queen of Scots against the English at the Battle of Pinkie. John Napier would spend most of his life trying not to get involved in the sectarian strife that swept Scotland. He was not always successful — at 17 he was forced to study abroad, having left St Andrews University prematurely after his friendship with a Catholic student was thought inadvisable in such sensitive times.

Returning to Edinburgh in 1571, he found the capital plunged into civil war with constant skirmishes between the forces of Mary attempting a Catholic comeback, and those of her young son’s Regent, determined to maintain the Protestant Reformed church.

Napier returned to find his father imprisoned in Edinburgh Castle by the Queen’s party, while the family home at Merchiston was occupied by the forces of the Regent, then besieging Edinburgh. The following year, when Merchiston was bombarded by the guns of Edinburgh Castle, Napier sought refuge on one of the family estates at Gartness in Stirlingshire. There he met and fell in love with Elizabeth Stirling, daughter of a neighbouring landowner, and, in 1573, they married.

He built the family home on the banks of the River Endrick at Gartness. There, according to the Statistical Account of Scotland, ‘John Napier of Merchiston, Inventor of Logarithms, resided a great part of his time when he was making his calculations.

‘It is reported that the noise of the cascade, being constant, never gave him uneasiness; but that the clack of the mill, which was only occasional, greatly disturbed his thoughts. He was therefore, when in deep study, sometimes under the necessity of desiring the miller to stop the mill, that the train of his ideas might not be interrupted.’ In this haven of tranquility, Napier’s young wife bore him a son and a daughter but their happiness was shortlived - in 1579, Elizabeth died. A few years Later, Napler remarried.

Agnes Chisholm, of Cromlix, Perthshire. was to bear him five sons and five daughters - a large and noisy brood for a man who liked to spend long hours in silent contemplation, a lone, eccentric figure accompanied only by a pet black cockerel.

In his head Napier might be wrestling with theological or mathematical complexities but to onlookers his behaviour seemed sinister. Rumours spread that he was a warlock after he enlisted the help of the  cockeral to discover which if his servants had been stealing from him. Each servant was ordered to go into a darkened room and stroke the cockeral - the bird would crow, said Napier, when the guilty servant touched it.

The bird remained silent but Napier stunned the household by immediately identifying the culprit. Surely this was sorcery. But all he had done was put soot on the cockerel's feathers - the innocent servants all had black on their hands, while the guilty one's were clean because he was afraid to touch the bird.

At Merchiston, when pigeons belonging to a neighbouring landowner had been eating Napier's grain, he threatened to restrain them. 'Do so, if you can catch them,' scoffed his neighbour. Next morning, Napier's servants could be seen stuffing hundreds of semi-conscious pigeons into sacks. Onlookers were convinced Napier had bewitched them - in fact he had simply scattered succulent peas soaked in wine to get the birds drunk and incapable.

He put this gift of original thought to good use in many fields, including the farmland around Gartness. He discovered that putting salt on the land would help kill weeds and fertilise the soil. He worked out the optimum quantities and published a book, The New Order of Gooding and Manuring all sorts of Field Land with Common Salt.

But he could do nothing to avert the plague that struck Edinburgh in the 1590's, when the city fathers expelled victims to plague houses which they erected without permission on Napier's land at Merchiston - he fought a long legal battle to have them removed.

To a modern mind, he also wasted much thought and ingenuity on obscure theology. But in 1593, when Napier published his Plan Discovery of the Whole Revelation of St. John, his book became an international best-seller in the Protestant world, running to nine editions in Huguenot France, four in Germany and three in Holland, as well as five in English.

At a time when Protestant countries regarded Catholicism as a threat to national security, any book proving the Pope was the Antichrist was bound to go down well. Less acceptable was Napier's interest in the occult - he dabbled in alchemy and witchcraft and passed on his knowledge to his son Robert, although when King James was burning witches at Edinburgh Castle it was as well to keep this interest secret.

Napier's reputation as a sorcerer led him into dubious association with the thuggish Robert Logan of Restalrig, who had been involved in the Gowrie Conspiracy to abduct the King and imprison him at Fastcastle, Logan's private fortress on the East Coast, where his family were in the habit of committing robbery with violence on any passer-by. For this Logan had been declared an outlaw, yet inexplicably Napier agreed to help him search for buried treasure at Fastcastle. Luckily none were ever found, since Logan would rather have committed murder than hand over Napier's share.

But while dabbling in the occult was a private folly, Scotland's religious differences were a public grief for Napier. Since 1588, when the Spanish Armada threatened Protestant Scotland, he had been a commissioner of the Church of Scotland.

After the Armada was wrecked, Scottish Catholic nobles continued to intrigue with the King of Spain. Among them was Napier's father-in-law, Sir James Chisholm. In 1593, Napier had the unpleasant task of sitting on the Kirk convention that Sir James excommunicated.

Yet Napier was a staunch supporter of the Protestant cause and, when Catholic Spain threatened another invasion in 1596, he turned his powers on invention to weapons of war.

In his Secrete Inventionis he published details of a giant mirror to burn enemy ships by focusing the sun's rays on them, a man-powered tank, a submarine, and a form of artillery which could clear a field of anything standing over a foot high. In the event none of these were needed.

Napier pressed on with invention and theology and in fact it was not until the age of 64 that he published his greatest discovery - logarithms - with the boast: "This new course of Logarithms doth clean take away all the difficulty that heretofore hath been in mathematical calculations.'

The impact of Napier's work was enormous. While explorers voyaged across the globe, they could not navigate accurately or map their discoveries because the calculations were too complicated to perform rapidly on board a ship. When a captain had a copy of Napier's log tables, all this changed.

Without an advance in mathematics to underpin the growth of science in understanding the universe, it had been impossible to chart the orbit of the planets around the sun - the necessary calculations were so complex that it would take decades to achieve. Napier's logarithms, for which he had devised the decimal point as a way of expressing complex fractions, enabled a breakthrough.

Johannes Kepler, who in 1609 first published his work on the laws of planetary motion, had taken four years to calculate the orbit of Mars alone.

It might have taken him longer than a lifetime to work out the rest, had he not obtained Napier's logarithms.

In 1619 he wrote to Napier to acknowledge his great debt - only to find the hitherto unknown Scottish mathematical genius had died two years previously.

But before his death Napier had left full details of how his logarithms had been calculated, and had left one final invention as a boon to the merchant classes. Napier's Rods, or Napier's Bones as they were called from the material they were made of, were in effect a powerful pocket calculator.

Each set of 11 rods, marked off in numbered squares, could be assembled in different ways to multiply or divide large numbers by reading down and across the columns of figures created.

But in such success lay his ultimate downfall.

In his calculations and methodologies he made possible the very modern technology which was to supersede him and render him until now, Scotland's greatest and most forgotten man.

Sir John Napier, eighth Laird of Merchiston was born in 1550 at Merchiston Tower, which was then just outside the boundary of the city of Edinburgh, capital of Scotland, and was known as the 'Marvellous Merchiston', a title which was well-deserved, for his genius and imaginative vision encompassed a number of fields.

Another account

John NapierNAPIER, JOHN, of Merchiston, near Edinburgh, the celebrated inventor of the logarithms, was born in the year 1550. He was descended from an ancient race of land proprietors in Stirlingshire and Dumbartonshire. His father, Sir Alexander Napier of Edinbellie, in the former county, and Merchiston, in the county of Edinburgh, was master of the mint to James VI., and was only sixteen years of age when the subject of this memoir was born. The mother of the inventor of the logarithms was Janet, only daughter of Sir Francis Bothwell, a lord of session, and sister of Adam, bishop of Orkney. There is a prevalent notion that the inventor of the logarithms was a nobleman: this has arisen from his styling himself, in one of his title pages, Baro Merchistonii; in reality, this implied baron in the sense of a superior of a barony, or what in England would be called lord of a manor. Napier was simply Laird of Merchiston—a class who in Scotland sat in parliament under the denomination of the lesser barons.

Napier was educated at St Salvator’s college, in the university of St Andrews which he entered in 1562. He afterwards travelled on the continent, probably to improve himself by intercourse with learned and scientific men. Nothing further is ascertained respecting him, till after he had reached the fortieth year of his age. He is then found settled at the family seats of Merchiston, near Edinburgh, and Gartness, in Stirlingshire, where he seems to have practiced the life of a recluse student, without the least desire to mingle actively in political affairs. That his mind was alive, however, to the civil and religious interests of his country, is proved by his publishing, in 1593, an exposition of the Revelations, in the dedication of which, to the king, he urged his majesty, in very plain language, to attend better than he did to the enforcement of the laws, and the protection of religion, beginning reformation in his own "house, family, and court." From this it appears that Napier belonged to the strict order of Presbyterians in Scotland; for such are exactly the sentiments chiefly found prevalent among that class of men at this period of our history.

In the scantiness of authenticated materials for the biography of Napier, some traditionary traits become interesting. It is said that, in his more secluded residence at Gartness, he had both a waterfall and a mill in his immediate neighbourhood, which considerably interrupted his studies. He was, however, a great deal more tolerant of the waterfall than of the mill; for while the one produced an incessant and equable sound, the other was attended with an irregular clack-clack, which marred the processes of his mind, and sometimes even rendered it necessary for him, when engaged in an unusually abstruse calculation, to desire the miller to stop work. He often walked abroad in the evening, in a long mantle, and attended by a large dog; and these circumstances working upon minds totally unable to appreciate the real nature of his researches, raised a popular rumour of his being addicted to the black art. It is certain that, no more than other great men of his age, was he exempt from a belief in several sciences now fully proved to have been full of imposture. The practice of forming theories only from facts, however reasonable and unavoidable it may appear, was enforced only for the first time by a contemporary of Napier—the celebrated Bacon; and, as yet, the bounds between true and false knowledge were hardly known. Napier, therefore, practiced an art which seems nearly akin to divination, as is proved by a contract entered into, in 1594, between him and Logan of Fastcastle—afterwards so celebrated for his supposed concern in the Gowry conspiracy. This document states it to have been agreed upon, that, as there were old reports and appearances that a sum of money was hid within Logan’s house of Fastcastle, John Napier should do his utmost diligence to search and seek out, and by all craft and ingine (a phrase for mental power) to find out the same, or make it sure that no such thing has been there. For his reward he was to have the exact third of all that was found, and to be safely guarded by Logan back to Edinburgh; and in case he should find nothing, after all trial and diligence taken, he was content to refer the satisfaction of his travels and pains to the discretion of Logan. What was the result of the attempt, or if the attempt itself was ever made, has not been ascertained.

Besides dabbling in sciences which had no foundation in nature, Napier addicted himself to certain speculations which have always been considered as just hovering between the possible and the impossible, a number of which he disclosed, in 1596, to Anthony Bacon, the brother of the more celebrated philosopher of that name. One of these schemes was for a burning mirror, similar to that of Archimedes, for setting fire to ships; another was for a mirror to produce the same effects by a material fire; a third for an engine which should send forth such quantities of shot in all directions as to clear everything in its neighbourhood; and so forth. In fact, Napier’s seems to have been one of those active and excursive minds, which are sometimes found to spend a whole life in projects and speculations without producing a single article of real utility, and in other instances hit upon one or two things, perhaps, of the highest order of usefulness. As he advanced in years, he seems to have gradually forsaken wild and hopeless projects, and applied himself more and more to the useful sciences. In 1596, he is found suggesting the use of salt in improving land; an idea probably passed over in his own time as chimerical, but revived in the present age with good effect. No more is heard of him till, in 1614, he astonished the world by the publication of his book of logarithms. He is understood to have devoted the intermediate time to the study of astronomy, a science then reviving to a new life, under the auspices of Kepler and Galileo, the former of whom dedicated his Ephemerides to Napier, considering him as the greatest man of his age in the particular department to which he applied his abilities.

"The demonstrations, problems, and calculations of astronomy, most commonly involve some one or more of the cases of trigonometry, or that branch of mathematics, which, from certain parts, whether sides or angles, of a triangle being given, teaches how to find the others which are unknown. On this account, trigonometry, both plane and spherical, engaged much of Napier’s thoughts; and he spent a great deal of his time in endeavouring to contrive some methods by which the operations in both might be facilitated. Now, these operations, the reader, who may be ignorant of mathematics, will observe, always proceed by geometrical ratios, or proportions. Thus, if certain lines be described in or about a triangle, one of these lines will bear the same geometrical proportion to another, as a certain side of the triangle does to a certain other side. Of the four particulars thus arranged, three must be known, and then the fourth will be found by multiplying together certain two of those known, and dividing the product by the other. This rule is derived from the very nature of geometrical proportion, but it is not necessary that we should stop to demonstrate here how it is deduced. It will be perceived, however, that it must give occasion, in solving the problems of trigonometry, to a great deal of multiplying and dividing—operations which, as everybody knows, become very tedious whenever the numbers concerned are large; and they are generally so in astronomical calculations. Hence such calculations used to exact immense time and labour, and it became most important to discover, if possible, a way of shortening them. Napier, as we have said, applied himself assiduously to this object; and he was, probably, not the only person of that age whose attention it occupied. He was, however, undoubtedly the first who succeeded in it, which he did most completely by the admirable contrivance which we are now about to explain.

"When we say that 1 bears a certain proportion, ratio, or relation to 2, we may mean any one of two things; either that 1 is the half of 2, or that it is less than 2 by 1. If the former be what we mean, we may say that the relation in question is the same as that of 2 to 4, or of 4 to 8; if the latter, we may say that it is the same as that of 2 to 3, or of 3 to 4. Now, in the former case, we should be exemplifying what is called a geometrical, in the latter, what is called an arithmetical proportion: the former being that which regards the number of times, or parts of times, the one quantity is contained in the other; the latter regarding only the difference between the two quantities. We have already stated that the property of four quantities arranged in geometrical proportion, is, that the product of the second and third, divided by the first, gives the fourth. But when four quantities are in arithmetical proportion, the sum of the second and third, diminished by the subtraction of the first, gives the fourth. Thus, in the geometrical proportion, 1 is to 2 as 2 is to 4; if 2 be multiplied by 2 it gives 4; which divided by 1 still remains 4; while, in the arithmetical proportion, 1 is to 2 as 2 is to 3; if 2 be added to 2 it gives 4; from which if 1 be subtracted, there remains the fourth term 3. It is plain, therefore, that, especially where large numbers are concerned, operations by arithmetical must be much more easily performed than operations by geometrical proportion; for, in the one case you have only to add and subtract, while in the other you have to go through the greatly more laborious processes of multiplication and division.

"Now, it occurred to Napier, reflecting upon this important distinction, that a method of abbreviating the calculation of a geometrical proportion might perhaps be found, by substituting, upon certain fixed principles, for its known terms, others in arithmetical proportion, and then finding, in the quantity which should result from the addition and subtraction of these last, an indication of that which should have resulted from the multiplication and division of the original figures. It had been remarked before this, by more than one writer, that if the series of numbers 1, 2, 4, 8, &c., that proceed in geometrical progression, that is, by a continuation of geometrical ratios, were placed under or along side of the series 0, 1, 2, 3, &c., which are in arithmetical progression, the addition of any two terms of the latter series would give a sum, which would stand opposite to a number in the former series indicating the product of the two terms in that series, which corresponded in place to the two in the arithmetical series first taken. Thus, in the two lines,

1, 2, 4, 8, 16, 32, 64, 128, 256,

0, 1, 2, 3, 4, 5, 6, 7, 8,

the first of which consists of numbers in geometrical, and the second of numbers in arithmetical progression, if any two terms, such as 2 and 4, be taken from the latter, their sum 6, in the same line, will stand opposite to 64 in the other, which is the product of 4 multiplied by 16, the two terms of the geometrical series which stand opposite to the 2 and 4 of the arithmetical. It is also true, and follows directly from this, that if any three terms, as, for instance, 2, 4, 6, be taken in the arithmetical series, the sums of the second and third, diminished by the subtraction of the first, which makes 8, will stand opposite to a number (256) in the geometrical series which is equal to the product of 16 and 64 (the opposites of 4 and 6), divided by 4 (the opposite of 2).

"Here, then, is, to a certain extent, exactly such an arrangement or table as Napier wanted. Having any geometrical proportion to calculate, the known terms of which were to be found in the first line or its continuation, he could substitute for them at once, by reference to such a table, the terms of an arithmetical proportion, which, wrought in the usual simple manner, would give him a result that would point out or indicate the unknown term of the geometrical proportion. But, unfortunately, there were many numbers which did not occur in the upper line at all, as it here appears. Thus, there were not to be found in it either 3, or 5, or 6, or 7, or 9, or 10, or any other numbers, indeed, except the few that happen to result from the multiplication of any of its terms by two. Between 128 and 256, for example, there were 127 numbers wanting, and between 256 and the next term (512) there would be 255 not to be found.

"We cannot here attempt to explain the methods by which Napier’s ingenuity succeeded in filling up these chasms, but must refer the reader, for full information upon this subject, to the professedly scientific works which treat of the history and construction of logarithms. Suffice it to say, that he devised a mode by which he could calculate the proper number to be placed in the table over against any number whatever, whether integral or fractional. The new numerical expressions thus found, he called Logarithms, a term of Greek etymology, which signifies the ratios or proportions of numbers. He afterwards fixed upon the progression, 1, 10, 100, 1000, &c., or that which results from continued multiplication by 10, and which is the same according to which the present tables are constructed. This improvement, which possesses many advantages, had suggested itself about the same time to the learned Henry Briggs, then professor of geometry in Gresham college, one of the persons who had the merit of first appreciating the value of Napier’s invention, and who certainly did more than any other to spread the knowledge of it, and also to contribute to its perfection." [The above account of logarithms, which has the advantage of being very simple and intelligible, is extracted from the Library of Entertaining Knowledge.]

The invention was very soon known over all Europe, and was everywhere hailed with admiration by men of science. Napier followed it up, in 1617, by publishing a small treatise, giving an account of a method of performing the operations of multiplication and division, by means of a number of small rods. These materials for calculation have maintained their place in science, and are known by the appellation of Napier’s Bones.

In 1608, Napier succeeded his father, when he had a contest with his brothers and sisters, on account of some settlements made to his prejudice by his father, in breach of a promise made in 1586, in presence of some friends of the family, not to sell, wadset, or dispose, from his son John, the lands of Over Merchiston, or any part thereof. The family disputes were probably accommodated before June 9, 1613, on which day John Napier was served and returned heir of his father in the lands of Over Merchiston.

This illustrious man did not long enjoy the inheritance which had fallen to him so unusually late in life. He died, April 3, 1617, at Merchiston castle, and was buried in the church of St Giles, on the eastern side of its southern entrance, where is still to be seen a stone tablet, exposed to the street, and bearing the following inscription:—"Sep. familiae Naperoru. interius hic situm est."

Napier was twice married; first, in 1571, to Elizabeth, daughter of Sir James Stirling of Keir, by whom he had a son and a daughter; secondly, to Agnes, daughter of James Chisholm of Cromlix, by whom he had ten children. His eldest son, Archibald, who succeeded him, was raised to the rank of a baron by Charles I., in 1627, under the title of lord Napier, which is still borne by his descendants. A very elaborate life of him was published in 1835, (Blackwood, Edinburgh).

Memoirs of John Napier of Merchiston, Lineage, Life, and Times
With a History of the Invention of Logarithms by Mark Napier (1834)

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