John Napier

1550 - 1617
by David F. Coppedge

Who was the first prominent scientist from the British Isles? Who, in the early 17th century, stands in the line of pioneers of calculating machines? Who doubled the productivity of early scientists? Who according to David Hume was one of the greatest men Scotland ever produced, yet would have argued against Hume’s skepticism? A man who studied the Bible seriously, and fervently defended Biblical Christianity against error. A man whose most famous discovery would have profound impact on the sciences, yet considered his Christian faith primary and his mathematics secondary. A man most students never heard of, John Napier.

Portrait of John Napier, 1550 – 1617

John Napier (the most common, but probably inaccurate, spelling of his name) was born of a wealthy landowner in Scotland. The year he entered St. Andrew’s University at age 13, his mother died. At the university, and later in studies in Europe, he learned higher mathematics and classical literature, but he first became passionately interested in theology at St. Andrews. After his marriage in 1572, he and his bride moved into a castle on the Merchiston estate when it was completed in 1574. His cleverness as an inventor became apparent as he managed his estates. He found ways to increase productivity of the soil using scientific approaches to fertilization. His wife died in their seventh anniversary year; a few years later he remarried. He had two sons, one from each marriage.

Napier was born the year when the Scottish Reformation commenced, 1550. During Napier’s lifetime, disputes between Protestants and Catholics threatened to split the country in two. The controversy was not merely intellectual, because the Catholic Church had made an alliance with the Spanish in 1593 to invade Britain with the goal of conquest. Napier, fiercely committed to Scriptural authority, determined to defend Scotland from the errors of the papistry. On three occasions he accompanied deputations to make their case before the king. On his own initiative, he also wrote a commentary on Revelation called A Plaine Discourse on the Whole Revelation of St. John in which he interpreted the harlot that sits on seven hills (Rev. 17:9) as Rome, the seat of the Catholic pope. A sense of his zeal can be gained from his preface, where he explains his response to a sermon on the Apocalypse:

… I was so mooved in admiration, against the blindnes of Papists, that could not most evidently see their seven hilled citie Rome, painted out there so lively by Saint John, as the mother of all spiritual whoredome, that not onely bursted I out in continual reasoning against my said familiar, but also from thenceforth, I determined with my selfe (by the assistance of Gods spirit) to employ my studie and diligence to search out the remanent mysteries of that holy Book: as to this houre (praised be the Lorde) I have bin doing at al such times as conveniently I might have occasion.

He wrote humbly as one who did not feel adequate to convey such important truths, yet was compelled by the urgency to “prevent the rising againe of Antichristian darknes within this Iland, then to prolong the time in painting of language.” His commentary, which took years of study, was widely published in the British Isles and on the continent, and has been called, for Scotland, “the first published original work relating to theological interpretation, and is quite without a predecessor in its own field.”

What Are You Beating on that Log, a rithm?

Napier is best known as the inventor of logarithms in 1614. His discovery has been called second only to Newton’s Principia in importance to the foundational history of British science. Logarithms (a term coined by Napier) provided a shortcut to calculation, replacing tedious multiplications and divisions with simpler additions and subtractions. It was not an accidental discovery. Napier set his mind to find a way to make the mathematician’s life easier, because the effort required for long calculations made the work tedious and error prone. His work was original and detailed, without precedent or anticipation by previous writers. The publication consisted of a 57 page treatise in Latin, with 90 additional pages of tables. His first approach was not to any base, but this was later improved with the help of an admiring mathematician from London, Henry Briggs, who made the four-day journey with the express purpose of meeting the esteemed Scot. Briggs understood the potential value of Napier’s discovery. Together, they improved upon the concept, setting logarithms to the familiar base 10, the “common logs” as still used today, although “natural logarithms” are often set to the base e in the sciences (see Euler). By convention, “log” is the abbreviation for common logs to base 10, and “ln” is the abbreviation for natural logs to base e.

Logarithms are related to exponents. Logarithmic functions are the inverse of exponential functions. When graphed, the asymptotic curves appear as mirror images of each other reflected against the line y = x.

Logarithmic functions are an essential part of scientific calculators.

Logarithms were to become extremely valuable for the advance of planetary science by Kepler and later astronomers. Laplace said that “by shortening the labors, they doubled the life of the astronomer.” Kepler’s biographer Max Caspar claims that another mathematician on the continent, Jost Burgi, a friend to Kepler, could have scooped the fame for this invention in Germany but published six years too late, so the rightful priority goes to Napier, who had independently developed the method out of his own gifted mind. One encyclopedia remarks, “The more one considers the condition of science at the time, and the state of the country in which the discovery took place, the more wonderful does the invention of logarithms appear.” Napier lived in an era of tumult and superstition, but appears to have been a man of good sense and reason. The same encyclopedia elaborates, “Considering the time in which he lived, Napier is singularly free from superstition: his [Plaine Discourse] relates to a method of interpretation to a later age … and none of his writings contain allusions to astrology or magic.” Although he probably accepted some aspects of astrology (as did practically everyone in his era) some biographies suggest Napier did practical jokes playing upon the superstitions of his neighbors, hinting of his disdain for pseudoscience.

Logic in His Bones

A modern implementation of Napier’s calculating tool

Three years after the publication of his logarithms, Napier invented another aid to calculation that puts him in the timeline of calculating machines and computers. He constructed rods of ivory with integers on them, constructed in such an ingenious way that, laid side by side, one could quickly adduce sums, quotients, products, and square and cube roots. Later dubbed “Napier’s Bones” by others, these devices again revealed the creative mind that preferred theology as his first love and mathematics just a sidelight. Other achievements in mathematics included decimal notation for fractions and the concept of negative numbers. But this inventor also put his ingenuity to practical matters of warfare, for the defense of his homeland in light of the perilous times. He conceived of a shielded chariot that would protect its drivers while allowing artillery to be fired in all directions, a mirror that could burn a ship from a distance, and a device that could sail underwater. So it could be claimed that Napier was the visionary father of the tank, the death ray, and the submarine.

John Napier was the first major contributor to science from the British Isles. The encyclopedia states, “There is no British author of the time except Napier whose name can be placed in the same rank as those of Copernicus, Tycho Brahe, Kepler, Galileo, or Stevinus,” all from the continent. The story of the inventor of logarithms reminds us again that Christian faith, and zealous commitment to the defense of the Word of God, is no impediment to scientific progress. On the contrary, science was born, grew and flourished among Christian stalwarts like John Napier.

The scientific uses of logarithms are everywhere. Here, the Mandelbrot Set is applied to a logarithmic spiral, often found in nature – such as in the conch shell, hurricanes, spiral galaxies and other instantiations of the Fibonacci Series.



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