John Napier: A Man of Invention. Marisela Guerrero. El Paso Community College

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1 John Napier: A Man of Invention John Napier: A Man of Invention Marisela Guerrero El Paso Community College Author Note This paper was prepared for Math 1342, Honors Program

2 Guerrero 2 John Napier: A Man of Invention When you hear the names of Pythagoras or Plato, what comes into mind? Math should be the obvious concept associated with these two great mathematicians, but there were other experts in the field of mathematics, such as John Napier, who greatly contributed to the math we know today. John Napier, born in 1550, was from an early age interested in devising a method to facilitate computation and ultimately succeeded with his introduction of logarithms. Napier s family pushed for him to excel, as shown in a letter from his uncle, the Bishop of Orkney, to his father, Archibald Napier, written when John was eleven years old: I pray you, sir, to send your son John to school; over to France or Flanders; for he cannot learn well at home nor get profit in this most perilous world - that he may be saved in it; - that he may seek honour and profit as I do not doubt that he will... (John Napier). A year after returning to Scotland from studying abroad, Napier married his first wife Elizabeth Stirling in 1572, who he fathered two children with. During this time Napier expressed his passion and interest in religious and political matters, being a faithful Protestant practitioner. John Napier's commitment to the Protestant church may be overlooked due to his notable contributions in mathematics. Yet he considered his work regarding the church, A Plaine Discovery of the Whole Revelation of St. John, to be his greatest achievement. He believed that if he was ever going to be known for something, this would be it. (John Napier Logarithm Inventor Put Religion First). In A Plaine Discovery of the Whole Revelation of St. John, John heavily opposed the Catholic Church and went as far as accusing Pope Clement VIII of being the Antichrist and predicting the end of the world to be either 1688 or His passion was shown in his dedication of attempting to decipher the true intentions of the Catholic religion.

3 Guerrero 3 One of John Napier's most important works was a religious one: "A Plaine discovery of the Whole Revelation of St John", completed in 1593 (or 1594 under the Gregorian calendar). Protestant Reformation had exploded in Europe in 1517 when a devout German Augustinian monk Martin Luther took exception to the sale of "Indulgences" by a wandering Dominican and printed a series of theses condemning such activities by the Catholic Church. "Indulgences" were certificates that absolved the purchaser from sin and guaranteed them a place in heaven for a price (The Works of John Napier). This statement gives an insight as to why John opposed the Church, with his stance being that the only reason the Church grants Indulgences was to make money. A Plaine discovery of the Whole Revelation of St. John earned Napier some fame and his recognition grew when his work was translated into Dutch, French and German. A few years into his marriage with Elizabeth, she died and John was remarried to Agnes, daughter of Sir James Chisholm of Cromlix. Aside from his work in religion, John s fascination with simplicity led him to the creation on his best known work, the logarithm. Logarithms were meant to shorten calculations, especially multiplication, such as those needed in astronomy. (John Napier: Scottish Mathematician). John was thought to have worked alone on this project, which greatly aided astronomers and mathematicians alike. The invention of logarithms was hugely significant in that it made multiplication, division and root extraction far less laborious, particularly for very large numbers. Astronomers, navigators, mathematicians and other scientists were excited by the invention. Calculations were made using Napier's tables and the logarithm identities (The Works of John Napier). His creation of logarithms allowed other scientists, observers and intellectuals alike, to get through difficulties in mathematics much faster. It was also the fact that Napier had a great interest in astronomy, which led to his contribution to mathematics. John was not just a star gazer; he was involved in research that required lengthy

4 Guerrero 4 and time consuming calculations of very large numbers. Once the idea came to him that there might be a better and simpler way to perform large number calculations, Napier focused on the issue and spent twenty years perfecting his idea (John Napier). Napier presented a mechanical means of simplifying calculations in his Rabdologiae published in He described a method of multiplication using "numbering rods" with numbers marked off on them. The reason for publishing the work is given by Napier in the dedication, where he says that so many of his friends, to whom he had shown the numbering rods, were so pleased with them that they were already becoming widely used, even beginning to be used in foreign countries. Napier's numbering rods were made of ivory, so that they looked like bones which explains why they are now known as Napier's bones (John Napier). To multiply numbers the bones were placed side by side and the appropriate products read off. Glaisher described how to use Napier's bones in an article he wrote for Encyclopedia Britannica and this description is quoted in [9]. Napier's bones are also described in [5], [14] and [17] (John Napier). Seeing how Napier s bones worked, one might assume logarithms were the same concept. This is actually not the case, as Napier's bones are used for simple multiplication and division problems (made simpler by addition and subtraction), they could not be used to calculate large problems like logarithms can (John Napier Logarithm Inventor Put Religion First). Napier was a mathematician who as a family man, grew on his religion and interests in mathematics. He aspired to be great, even if it meant working alone, creating something which would shape the way calculations were made, even after his death. Napier left his mark in the world of religion with his most prominent book, A Plaine discovery of the Whole Revelation of St. John, as well as in the arithmetic world, credited with his conception of the logarithm and bones.

5 Guerrero 5 Works Cited "John Napier". Encyclopedia Britannica. Encyclopedia Britannica Online. Encyclopedia Britannica Inc., Web. 24 Mar Retrieved From < John Napier. Thocp. Retrieved From: Havil, Julian. John Napier: Life, Logarithms, and Legacy. Princeton, NJ: Princeton U, Print. Mangiola, Sarah. "John Napier Logarithm Inventor Put Religion First." Electronic Design (2013): Academic Search Complete. Web. 25 Mar