John Napier

John Napier of Merchiston, also called Johannes Neper or Nepair (/ˈneɪpɪər/ Edinburgh, February 1, 1550-ibidem, April 4, 1617), was a Scottish mathematician and inventor, recognized for being the first to define logarithms. He also made common the use of the decimal point in arithmetic operations.

Biography

Castle of Merchiston

Napier's father was Sir Archibald Napier of Merchiston Castle and his mother was Janet Bothwell (daughter of politician and judge Francis Bothwell, Lord of Session and sister of Adam Bothwell, who would become Bishop of Orkney).

The Castle of Merchiston, according to an engraving of 1834

At the age of 13 he began attending the University of Saint Andrews, in Fife. He stayed there less than a year. His mother died during this period of time. His uncle Adam Bothwell recommended in a letter to John's father that he send him to Europe for an education: Sir, I beg you to send John to the school in France or the school in Flanders because he can't learn anything good at home. It is thought likely that the advice was followed and that Napier traveled the Netherlands, France and Italy to train.

Back in Merchiston in 1571, he married Elizabeth Stirling the following year, with whom he had two children. They lived in a castle in Gartland (Stirling). She died in 1579. Napier soon after married Agnes Chisholm, with whom he had ten children.

When his father died in 1608, John went to live at Merchiston Castle. He died nine years later, on April 4, due to natural causes.

Contributions in mathematics

In his lifetime, Napier showed great interest in finding techniques to simplify computational tasks. Already in the 1570s he wrote his first treatise on it, in which he shows various efficient methods of calculation, describes simpler notations, and investigates the imaginary roots of equations. The work was not published until 1838, when these ideas had already been superseded by other mathematicians.

Without a doubt, his greatest contribution to the field of mathematics was the concept of logarithm. Napier studied about them between 1590 and 1617. The first work he published in this regard was Mirifici Logarithmorum Canonis Descriptio (Description of an admirable table of logarithms) in 1614. There he describes how to use logarithms to solve problems with triangles and give a table of logarithms. In 1619 his son Robert posthumously published Mirifici logarithmorum canonis constructio (Construction of an admirable table of logarithms), which explains how the table of logarithms is constructed.

Although in the beginning he called logarithms «artificial numbers», he himself would later create the name by which they are known today, by combining the Greek words «logos» (proportion) and «arithmos» (number).

Napier's discovery was an immediate success, both in mathematics and astronomy. Some of the pioneers in following his work were Henry Briggs and John Speidell. Johannes Kepler dedicated a 1620 publication to Napier, stating that logarithms were the central idea in discovering the third law of motion of the planets.

A quote from Pierre-Simon Laplace honors Napier's discovery and application of logarithms:

With the reduction of the work of several months of calculation within a few days, the invention of logarithms seems to have doubled the lives of astronomers.

Pierre-Simon Laplace

Another contribution, albeit laterally, by Napier is the use of the current decimal notation. Thanks to the spread of his work Mirifici logarithmorum canonis constructio throughout Europe, in which the comma was used to separate the integer part of a decimal in a number, this notation became popular. Although he was not the one who created it, he was responsible for making it popular.

Napier designed three devices to facilitate calculations, described in his 1617 work Rabdologiae. Although the most famous is his Neperian abacus, his promptuario can be considered as one of the first calculating machines in history.

Theology

All his life he dedicated himself to fighting for his religious ideas, being a passionate Protestant.

From his earliest years Napier was interested in the study of Revelation. In 1594 he published Plaine Discovery of the Whole Revelation of Saint John, a very influential work at the time, being translated into French and German and republished on several occasions. There, among other things, he affirms that the Pope he is the Antichrist and urges the king of Scotland to expel all papists and atheists from his court. Furthermore, he predicts the end of the world.

Interest in the occult

In addition to his mathematical and religious interests, Napier was often perceived as a magician, and is believed to have engaged in alchemy and necromancy. It was said that he would travel with a black spider in a small box, and that his black rooster was his familiar spirit.

Some of Napier's neighbors accused him of being a witch and consorting with the devil, believing that all the time he spent in his studio was used to learn black art. These rumors were fueled when Napier used his black cock to catch a thief. Napier told his servants to go into a dark room and pet the rooster, stating that the bird would crow if they were the ones stealing his property. Unbeknownst to the servants, Napier had covered the rooster in soot. As the servants left the room, Napier examined his hands to find what he had been too afraid to touch the cock with.

Another act that Napier did, which might seem mystical to its inhabitants, was when Napier drove the pigeons from his farm, as they were eating his grain. Napier caught the pigeons by spreading alcohol-laced grain all over the field, then catching the pigeons once they were too drunk to fly.

There is still a contract for a treasure hunt, made between Napier and Robert Logan of Restalrig. Napier had to search the Fast Castle to find a treasure supposedly hidden there, where it is stated that Napier should 'use his utmost diligence to search and search, and with all trades and wits to find out the same, or make sure that there would be none of that. he's been there." This contract was never honored by Napier, and no gold was found when the Edinburgh Archaeological Field Society excavated the castle between 1971 and 1986.

Influence

Among Napier's early followers were instrument makers Edmund Gunter and John Speidell. The development of logarithms is credited as the most important factor in the general adoption of decimal arithmetic. The Trissotetras (1645) by Thomas Urquhart is based on Napier's work on trigonometry.

Henry Briggs was an early adopter of the Napierian logarithm. He later calculated a new table of logarithms in base 10, accurate to 14 decimal places.

Eponyms

An alternative unit to the decibel used in electrical engineering, the neper carries the name of Napier, just like the Universitat Napier d'Edinburgh in Edinburgh, Scotland.

The crater Neper a la Lluna bears its name.

In French and Portuguese, the natural logarithm bears its name (respectively, Logarithme Népérien and Logarithmos Neperianos). In Italy, the mathematical constant i carries its name in Italy (Numero di Nepero).

Family

In 1572, Napier is going to marry Elizabeth, aged 16, daughter of James Stirling, the fourth Laird of Keir i de Cadder. They will have two fills. Elizabeth will die in 1579, and Napier is going to marry his children to Agnes Chisholm, with whom he will have two more fills.

Napier's successor, Sir James Chisholm of Cromlix, will be one of the many excommunicated by the General Assembly of the presbyterian party following the Spanish en blanc plot. Napier is going to assure the General Assembly that he is going to excommunicate the conspirators and is going to sue King James VI and that he is going to comply with the punishment of the conspirators, but finally he will be ignored, because the king believed that the ministers were acting in a cruel way and I was in favor of following more appeasement policies.

The seu mig germà (through the new casament of his father) was Alexander Napier, Lord Laurieston.

Other inventions

The bones of Napier, also known as rods or sticks of Napier, is an abacus to perform simple mathematical operations.

Napier was also an inventor in various branches:

• He invented two abacos of simple operations that are known with the names of Napier and Promptu Bones.
• In agriculture, he investigated the use of salts to fertilize the soil and kill the weeds. The method was effective and published in the book The new order of gooding and manuring all sorts of field land with common salt.
• He built a hydraulic screw, improving a previous idea of Archimedes.
• In 1596 he distributed a brief manuscript entitled Secrete inventionis in which he described his designs for four machines with possible military applications: an assault car, a submarine, a firearm and a mirror to focus the sun's rays on enemy ships to set them on fire (idea inspired by Archimedes). Napier himself destroyed his drawings of these machines shortly before his death.

Acknowledgments

• The moon crater Neper carries this name in his memory.
• The asteroid (5558) Johnnapier also commemorates its name.
• An alternative measurement unit to the decibellium used in electrical engineering and carries the name of Napier: the Neper or Neperio (Np).
• A university has its name: the Napier University of Edinburgh, Scotland.

Published Books

• (1593) A Plaine Discovery of the Whole Revelation of St. John.
• (1614) Mirifici logarithmorum canonis descriptio [1]
• (1617) Rabdologiæ seu Numerationis per Virgulas libri duo [2][3]
• (1619) Mirifici logarithmorum canonis constructio [4]
• (1839) Logistic art [5]