Leibniz on Binary

The Invention of Computer Arithmetic

Lloyd Strickland, Harry R. Lewis

• Publisher: The MIT Press
• Year: 2022
• eBook ISBN: 9780262372121
• Edition: 0
• Topic: Mathematics
• Subtopic: Computer Science General
• Index: Mathematics

The polymath Gottfried Wilhelm Leibniz (1646–1716) is known for his independent invention of the calculus in 1675. Another major—although less studied—mathematical contribution by Leibniz is his invention of binary arithmetic, the representational basis for today's digital computing. This book offers the first collection of Leibniz's most important writings on the binary system, all newly translated by the authors with many previously unpublished in any language. Taken together, these thirty-two texts tell the story of binary as Leibniz conceived it, from his first youthful writings on the subject to the mature development and publication of the binary system.

As befits a scholarly edition, Strickland and Lewis have not only returned to Leibniz's original manuscripts in preparing their translations, but also provided full critical apparatus. In addition to extensive annotations, each text is accompanied by a detailed introductory "headnote" that explains the context and content. Additional mathematical commentaries offer readers deep dives into Leibniz's mathematical thinking. The texts are prefaced by a lengthy and detailed introductory essay, in which Strickland and Lewis trace Leibniz's development of binary, place it in its historical context, and chart its posthumous influence, most notably on shaping our own computer age.

Table of contents

• Cover
• Title Page
• Copyright Page
• Dedication
• Epigraph
• Table of Contents
• List of Figures
• Abbreviations
• Preface
• Acknowledgments
• Introduction
• 1. Notes on Algebra, Arithmetic, and Geometric Series (October 1674)
• 2. The Series of All Numbers, and on Binary Progression (before 15/25 March 1679)
• 3. Binary Progression (before 15/25 March 1679)
• 4. Geometric Progressions and Positional Notation (before 15/25 March 1679)
• 5. Binary Arithmetic Machine (before 15/25 March 1679)
• 6. On the Binary Progression (15/25 March 1679)
• 7. Attempted Expression of the Circle in Binary Progression (c. 1679)
• 8. Sedecimal Progression (1679)
• 9. Binary Progression Is for Theory, Sedecimal for Practice (c. 1679)
• 10. On the Organon or Great Art of Thinking (first half [?] of 1679)
• 11. Binary Ancestral Calculations (early 1680s [?])
• 12. Sedecimal on an Envelope (c. 1682–1685)
• 13. Remarks on Weigel (1694–mid-March 1695)
• 14. Leibniz to Duke Rudolph August (7/17–8/18 May 1696)
• 15. A Wonderful Expression of All Numbers by 1 and 0 Representing the Origin of Things from God and Nothing, or the Mystery of Creation (7/17 May 1696)
• 16. Wonderful Origin of All Numbers from 1 and 0, Which Serves as a Beautiful Representation of the Mystery of Creation, since Everything Arises from God and Nothing Else (8/18 May 1696)
• 17. Leibniz to Duke Rudolph August (2/12 January 1697)
• 18. Duke Rudolph August to Johann Urban Müller (5/15 January 1697)
• 19. Leibniz to Claudio Filippo Grimaldi (mid-January–early February 1697)
• 20. Periods (May 1698–first half of January 1701)
• 21. Leibniz to Philippe Naudé (15 January 1701)
• 22. Leibniz to Joachim Bouvet (15 February 1701)
• 23. Essay on a New Science of Numbers (26 February 1701)
• 24. Binary Addition (spring–summer 1701 [?])
• 25. Periods in Binary (spring–fall 1701)
• 26. Periods and Powers (mid-to-late June 1701 [?])
• 27. Demonstration That Columns of Sequences Exhibiting Powers of Arithmetic Progressions, or Numbers Composed from These, Are Periodic (November 1701)
• 28. Joachim Bouvet to Leibniz (4 November 1701)
• 29. Leibniz to Bouvet (early April [?] 1703)
• 30. Explanation of Binary Arithmetic, Which Uses Only the Digits 0 and 1, with Some Remarks on Its Usefulness, and on the Light It Throws on the Ancient Chinese Figures of Fuxi (7 April 1703)
• 31. Leibniz to César Caze (23 June 1705)
• 32. On Binary (late June 1705)
• Bibliography
• Index