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John Napier

John Napier: Life, Logarithms, and Legacy

Julian Havil
Copyright Date: 2014
Pages: 300
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  • Book Info
    John Napier
    Book Description:

    John Napier (1550-1617) is celebrated today as the man who invented logarithms-an enormous intellectual achievement that would soon lead to the development of their mechanical equivalent in the slide rule: the two would serve humanity as the principal means of calculation until the mid-1970s. Yet, despite Napier's pioneering efforts, his life and work have not attracted detailed modern scrutiny.John Napieris the first contemporary biography to take an in-depth look at the multiple facets of Napier's story: his privileged position as the seventh Laird of Merchiston and the son of influential Scottish landowners; his reputation as a magician who dabbled in alchemy; his interest in agriculture; his involvement with a notorious outlaw; his staunch anti-Catholic beliefs; his interactions with such peers as Henry Briggs, Johannes Kepler, and Tycho Brahe; and, most notably, his estimable mathematical legacy.

    Julian Havil explores Napier's original development of logarithms, the motivations for his approach, and the reasons behind certain adjustments to them. Napier's inventive mathematical ideas also include formulas for solving spherical triangles, "Napier's Bones" (a more basic but extremely popular alternative device for calculation), and the use of decimal notation for fractions and binary arithmetic. Havil also considers Napier's study of the Book of Revelation, which led to his prediction of the Apocalypse in his first book,A Plaine Discovery of the Whole Revelation of St. John-the work for which Napier believed he would be most remembered.

    John Napierassesses one man's life and the lasting influence of his advancements on the mathematical sciences and beyond.

    eISBN: 978-1-4008-5218-5
    Subjects: Mathematics, History

Table of Contents

  1. Front Matter
    (pp. i-xii)
  2. Table of Contents
    (pp. xiii-xiv)
  3. Acknowledgments
    (pp. xv-xvi)
  4. Introduction
    (pp. 1-7)

    On 16 February 2012 the British prime minister, David Cameron, gave a speech in Scotland’s capital of Edinburgh on a theme that would have had resonance with John Napier:¹ Scottish independence. That is, independence from England, with whom there has long been martial and political conflict and most particularly since the Scots signed theAuld Alliancewith France in 1295 to the chagrin of the English king Edward I, theHammer of the Scots. The sword has been replaced by the pen, the speeches conciliatory and, in the year of this book’s publication, the decision regarding independence from the United...

  5. CHAPTER ONE Life and Lineage
    (pp. 8-34)

    In this first chapter we attempt to paint a picture of Napier’s life and of the world in which he lived it, necessarily using a broad historical brush concerning his life and, having consideration for balance and book length, a brush of even greater width with regard to his Scotland. He was born, lived and died in a tumultuous world of political and religious upheaval, one in which science and superstition, justice and brutality, religion and hatred, life and premature and perhaps violent death coexisted without demur. It defies credulity that someone with his inherited responsibilities and living so remote...

  6. CHAPTER TWO Revelation and Recognition
    (pp. 35-61)

    The Four Horsemen of the Apocalypse, the Scarlet Woman, the Seventh Seal, the Number of the Beast (666), Alpha and Omega, the Bottomless Pit, Wormwood, Armageddon – images that have inspired theologians, interpreters, mystics, artists, authors, poets and film directors over centuries and which have in common their appearance in the final Book of the New Testament: Revelation. Otherwise known as the Apocalypse, the form and content of its twenty-two chapters renders it the most obscure of the biblical texts and it is the only fully apocalyptic work in the Christian canon: apocalyptic not in the modern sense of catastrophic...

  7. CHAPTER THREE A New Tool for Calculation
    (pp. 62-95)

    By Napier’s time, calculative aids had developed from the Salamis tablet of ancient Greece through to the Roman calculi and hand abacus and on to the apices, coin-board and line-board of the Middle Ages: in chapter 5 we will see Napier’s own adaptation of these ideas in his “local arithmetic.” A new and sophisticated mechanism had recently appeared in the form ofProsthaphaeresis, which uses a pair of standard trigonometric identities to convert multiplication to addition and which we mention in appendix F. Napier’s world-changing contribution to calculative aid was to introduce another tool of incomparably greater sophistication, the principles...

  8. CHAPTER FOUR Constructing the Canon
    (pp. 96-130)

    With the publication of theDescriptioNapier had provided the world with its first set of tables of logarithms, instructions for their use and examples of their usefulness; he had also made a promise:

    I may have it in mind to add to the tables the method of their construction.

    Yet he was gravely ill; indeed, in the 1616 English translation, his dedication to Charles, Prince of Wales, mentioned that he was “almost spent with sickness,” presaging his death in early 1617. There was to be a fitting return to scholarly Latin, though, with the 1619 posthumous publication that was...

  9. CHAPTER FIVE Analogue and Digital Computers
    (pp. 131-154)

    Through Napier’s inspiration and the continued work of himself and Briggs, logarithms had provided the scientist with a new tool of massive utility; and through his adaptation of an old one, Napier had also provided users of elementary arithmetic with another. We move back two years to his third and final publication: the 1617Rabdologia seu Numerationis per Virgulas libri duo;Rabdologia, or the Calculation with Rods in Two Books. His fondness for portmanteau words has the Greek wordsρ̀ὰβδoζandλoγὶα, r(h)abdos and logia, rod and study, conjoined to formRabdologia; the study of rods, then, in terms of...

  10. CHAPTER SIX Logistics: The Art of Computing Well
    (pp. 155-178)

    John Napier’s second son of his second marriage, Robert, was the literary executor to his late father’s estate. We have mentioned his involvement in the publication of theConstructio, thereby ensuring that the methods underlying the construction of logarithms were brought to the greater scientific world, but his further intervention also caused the final fragments of Napier’s mathematical output to be preserved, if inadvertently. Soon after his father’s death, Robert had trawled the unpublished mathematical papers to produce his own hand-written collation, the title of which clearly indicated its purpose:

    The Baron of Merchiston his booke of Arithmeticke and Algebra....

  11. CHAPTER SEVEN Legacy
    (pp. 179-206)

    John Napier departed our world having contributed to it as an influential landowner, politician, theologian, mathematician and inventor of calculating devices. His theology was rooted in the context of his time with the Plaine Revelation serving as a yardstick by which the modern theological historian can measure the state and development of human spirituality in the tumultuous time of the Reformation. According to him,¹ humankind should have ceased to exist long ago; according to him, his musings on that most opaque book of the Bible foretold the world’s imminent end. Yet posterity should not judge the man, but the era...

  12. Epilogue
    (pp. 207-208)

    Our book about John Napier and his work is at an end. Mark Napier finished his biography with a transcript of the letter from Kepler to Napier, to which we allude on page 269, and just before that we have him writing:

    Yet is he scarcely remembered, for his genius reposes afar off, amid the wilderness of science, like a solitary lake unexplored by those who enjoy its waters in the valley.

    Is he resolved to dust,

    And have his country’s marbles nought to say?

    Could not her quarries furnish forth one bust?

    Did he not to her breast his...

  13. APPENDIX A Napier’s Works
    (pp. 209-209)
  14. APPENDIX B The Scottish Science Hall of Fame
    (pp. 210-210)
  15. APPENDIX C Scotland and Conflict
    (pp. 211-215)
  16. APPENDIX D Scotland and Reformation
    (pp. 216-219)
  17. APPENDIX E A Stroll Down Memory Lane
    (pp. 220-228)
  18. APPENDIX F Methods of Multiplying
    (pp. 229-231)
  19. APPENDIX G Amending Napier’s Kinematic Model
    (pp. 232-232)
  20. APPENDIX H Napier’s Inequalities
    (pp. 233-235)
  21. APPENDIX I Hos Ego Versiculos Feci
    (pp. 236-237)
  22. APPENDIX J The Rule of Three
    (pp. 238-249)
  23. APPENDIX K Mercator’s Map
    (pp. 250-263)
  24. APPENDIX L The Swiss Claimant
    (pp. 264-269)
  25. References
    (pp. 270-274)
  26. Index
    (pp. 275-280)