Leibniz on Binary: The Invention of Computer Arithmetic

by Lloyd Strickland, Harry R. Lewis

Overview

The first collection of Leibniz’s key writings on the binary system, newly translated, with many previously unpublished in any language.

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of Leibniz’s most important writings on the binary system, all newly translated by the authors with many previously unpublished in any language.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.

Product Details

ISBN-13:	9780262544344
Publisher:	MIT Press
Publication date:	11/15/2022
Pages:	248
Product dimensions:	6.90(w) x 9.90(h) x 0.70(d)

About the Author

Lloyd Strickland is Professor of Philosophy and Intellectual History at Manchester Metropolitan University, UK. He is the author of Leibniz and the Two Sophies, Leibniz’s Monadology, and various other books.

Harry Lewis is Gordon McKay Research Professor of Computer Science at Harvard University. He is the coauthor of Blown to Bits: Your Life, Liberty, and Happiness after the Digital Explosion, coeditor of What Is College For?, and editor of Ideas That Created the Future (MIT Press).

Table of Contents

List of Figures ix

Abbreviations x

Preface xi

Acknowledgments xiii

Introduction 1

1 Notes on Algebra, Arithmetic, and Geometric Series (October 1674) 27

2 The Series of All Numbers, and on Binary Progression (before 15/25 March 1679) 31

3 Binary Progression (before 15/25 March 1679) 35

4 Geometric Progressions and Positional Notation (before 15/25 March 1679) 41

5 Binary Arithmetic Machine (before 15/25 March 1679) 45

6 On the Binary Progression (15/25 March 1679) 47

7 Attempted Expression of the Circle in Binary Progression (c. 1679) 61

8 Sedecimal Progression (1679) 63

9 Binary Progression Is for Theory, Sedecimal for Practice (c. 1679) 69

10 On the Organon or Great Art of Thinking (first half [?] of 1679) 71

11 Binary Ancestral Calculations (early 1680s [?]) 75

12 Sedecimal on an Envelope (c. 1682-1685) 77

13 Remarks on Weigel (1694-mid-March 1695) 79

14 Leibniz to Duke Rudolph August (7/17-8/18 May 1696) 87

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) 89

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) 93

17 Leibniz to Duke Rudolph August (2/12 January 1697) 99

18 Duke Rudolph August to Johann Urban Muller (5/15 January 1697) 105

19 Leibniz to Claudio Filippo Grimaldi (mid-January-early February 1697) 107

20 Periods (May 1698-first half of January 1701) 117

21 Leibniz to Philippe Naudé (15 January 1701) 121

22 Leibniz to Joachim Bouvet (15 February 1701) 125

23 Essay on a New Science of Numbers (26 February 1701) 135

24 Binary Addition (spring-summer 1701 [?]) 145

25 Periods in Binary (spring-fall 1701) 149

26 Periods and Powers (mid-to-late June 1701 [?]) 151

27 Demonstration That Columns of Sequences Exhibiting Powers of Arithmetic Progressions, or Numbers Composed from These, Are Periodic (November 1701) 157

28 Joachim Bouvet to Leibniz (4 November 1701) 161

29 Leibniz to Bouvet (early April [?] 1703) 177

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) 189

31 Leibniz to César Caze (23 June 1705) 199

32 On Binary (late June 1705) 205

Bibliography 213

Index 225

What People are Saying About This

From the Publisher

"A wonderful book that explains both the significance and scope of Leibniz’ binary arithmetic using original sources. The authors' clear exposition makes the genesis of binary arithmetic accessible to everyone."
—Bharath Sriraman, Professor of Mathematics, University of Montana - Missoula; Editor of The Handbook of the Mathematics of the Arts and Sciences, Springer Nature

"Strickland and Lewis present Leibniz’s development of binary through lovingly typeset translations of his papers, notes and letters, together with a contextual narrative that is both well-researched and quite enjoyable.”
—Simson Garfinkel, co-author of The Computer Book: From the Abacus to Artificial Intelligence, 250 Milestones in the History of Computing

“Leibniz on Binary enhances our understanding of how binary arithmetic was developed and sheds light on the intellectual workings of one of the inventors of the modern age.”
—Jim Waldo, Gordon McKay Professor of the Practice of Computer Science and CTO, John A. Paulson School of Engineering and Applied Sciences, Harvard University
 
“A fascinating read for anyone interested in how rationality combined with religious passion. This eminently readable translation highlights bold connections of newly invented binary algorithms with mechanization of thought, Chinese hexagrams, and creation out of nothing.​”
—Slava Gerovitch, MIT, author of From Newspeak to Cyberspeak: A History of Soviet Cybernetics

“This book is a model of how the history of computer science and mathematics should be written. Leibniz pointed out the importance of putting ourselves into the place of others, and here we get to put ourselves into the shoes of Leibniz himself, as we're treated to dozens of his private notes, carefully translated into idiomatic English and thoroughly explained.”
—Don Knuth, Professor Emeritus of The Art of Computer Programming, Stanford University