The Logician and the Engineer: How George Boole and Claude Shannon Created the Information Age

by Paul Nahin

Overview

How two pioneers of math and technology ushered in the computer revolution

Boolean algebra, also called Boolean logic, is at the heart of the electronic circuitry in everything we use—from our computers and cars, to home appliances. How did a system of mathematics established in the Victorian era become the basis for such incredible technological achievements a century later? In The Logician and the Engineer, Paul Nahin combines engaging problems and a colorful historical narrative to tell the remarkable story of how two men in different eras—mathematician and philosopher George Boole and electrical engineer and pioneering information theorist Claude Shannon—advanced Boolean logic and became founding fathers of the electronic communications age. Nahin takes readers from fundamental concepts to a deeper and more sophisticated understanding of modern digital machines, in order to explore computing and its possible limitations in the twenty-first century and beyond.

Product Details

ISBN-13:	9781400844654
Publisher:	Princeton University Press
Publication date:	10/28/2012
Sold by:	Barnes & Noble
Format:	eBook
Pages:	248
Sales rank:	243,606
File size:	5 MB

About the Author

Paul J. Nahin is the author of many bestselling popular math books, including Mrs. Perkins's Electric Quilt, In Praise of Simple Physics, and An Imaginary Tale (all Princeton). He is professor emeritus of electrical engineering at the University of New Hampshire.

Table of Contents

Preface xi

1 What You Need to Know to Read This Book 1
Notes and References 5

2 Introduction 6
Notes and References 14

3 George Boole and Claude Shannon: Two Mini-Biographies 17

• 3.1 The Mathematician 17
• 3.2 The Electrical Engineer 28
• Notes and References 39

4 Boolean Algebra 43

• 4.1 Boole's Early Interest in Symbolic Analysis 43
• 4.2 Visualizing Sets 44
• 4.3 Boole's Algebra of Sets 45
• 4.4 Propositional Calculus 48
• 4.5 Some Examples of Boolean Analysis 52
• 4.6 Visualizing Boolean Functions 59
• Notes and References 65

5 Logical Switching Circuits 67

• 5.1 Digital Technology: Relays versus Electronics 67
• 5.2 Switches and the Logical Connectives 68
• 5.3 A Classic Switching Design Problem 71
• 5.4 The Electromagnetic Relay and the Logical NOT 73
• 5.5 The Ideal Diode and the Relay Logical AND and OR 76
• 5.6 The Bi-Stable Relay Latch 81
• Notes and References 84

6 Boole, Shannon, and Probability 88

• 6.1 A Common Mathematical Interest 88
• 6.2 Some Fundamental Probability Concepts 89
• 6.3 Boole and Conditional Probability 96
• 6.4 Shannon, Conditional Probability, and Relay Reliability 99
• 6.5 Majority Logic 106
• Notes and References 110

7 Some Combinatorial Logic Examples 114

• 7.1 Channel Capacity, Shannon's Theorem, and Error-Detection Theory 114
• 7.2 The Exclusive-OR Gate (XOR) 122
• 7.3 Error-Detection Logic 127
• 7.4 Error-Correction Theory 128
• 7.5 Error-Correction Logic 132
• Notes and References 137

8 Sequential-State Digital Circuits 139

• 8.1 Two Sequential-State Problems 139
• 8.2 The NOR Latch 142
• 8.3 The Clocked RS Flip-Flop 146
• 8.4 More Flip-Flops 154
• 8.5 A Synchronous, Sequential-State Digital Machine Design Example 158
• Notes and References 160

9 Turing Machines 161

• 9.1 The First Modern Computer 162
• 9.2 Two Turing Machines 164
• 9.3 Numbers We Can't Compute 168
• Notes and References 173

10 Beyond Boole and Shannon 176

• 10.1 Computation and Fundamental Physics 176
• 10.2 Energy and Information 178
• 10.3 Logically Reversible Gates 180
• 10.4 Thermodynamics of Logic 184
• 10.5 A Peek into the Twilight Zone: Quantum Computers 188
• 10.6 Quantum Logic--and Time Travel, Too! 197

Notes and References 205

Epilogue
For the Future: The Anti-Amphibological Machine 210

Appendix
Fundamental Electric Circuit Concepts 219

Acknowledgments 223
Index 225

Editorial Reviews

Most valuable to this reviewer, and likely to many potential readers, is the closing chapter, aptly titled Beyond Boole and Shannon. Here is provided an introduction to quantum computing and its logic, possibly portending the future of computers, yet unmistakably bearing the footprints of the two early pioneers. It is an unexpected yet fitting conclusion to this thoroughly enjoyable read.

Mathematical Reviews Clippings - Ronald E. Prather

A short but fairly detailed exploration of the genesis of Boolean logic and Shannon's information theory. . . . [G]ood background reading for anyone studying electronics or computer science.

Engineering & Technology - Christine Evans-Pughe

Although the book is technical, it is always easily understandable for anyone (for those who need it, some basic rules for electrical circuits are collected in a short appendix). It is not only understandable but also pleasantly bantering and at occasions even facetious.

European Mathematical Society - A. Bultheel

The reader is taken on a journey from the development of some abstract mathematical ideas through a nearly ubiquitous application of those ideas within the modern world with so many embedded digital computers. . . . I enjoyed the discussion of Claude Shannon. In the history of the computer and development of the internet and World Wide Web, his ideas and contributions are too often overlooked. He is one of my heroes and I believe that everyone that reads this book will come to the same conclusion.

MAA Reviews - Charles Ashbacher

Paul J. Nahin really knows how to tell a good story. The Logician and the Engineer in part is the biography of two very important persons in computer history, George Boole and Claude Shannon, but there's more; this book encompasses a wide range of computer history and computer design, and there are logic puzzles and brainteasers throughout. George Boole, a pure mathematician, and Claude Shannon, a practical electrical engineer, never met as they were born a hundred years apart. . . . The Logician and the Engineer will be enjoyed by budding computer scientists, engineers and more experienced readers. The Logician and the Engineer is truly a gem.
— Robert Schaefer

New York Journal of Books

The reader is taken on a journey from the development of some abstract mathematical ideas through a nearly ubiquitous application of those ideas within the modern world with so many embedded digital computers. . . . I enjoyed the discussion of Claude Shannon. In the history of the computer and development of the internet and World Wide Web, his ideas and contributions are too often overlooked. He is one of my heroes and I believe that everyone that reads this book will come to the same conclusion.
— Charles Ashbacher

MAA Reviews

Paul J. Nahin really knows how to tell a good story. The Logician and the Engineer in part is the biography of two very important persons in computer history, George Boole and Claude Shannon, but there's more; this book encompasses a wide range of computer history and computer design, and there are logic puzzles and brainteasers throughout. George Boole, a pure mathematician, and Claude Shannon, a practical electrical engineer, never met as they were born a hundred years apart. . . . The Logician and the Engineer will be enjoyed by budding computer scientists, engineers and more experienced readers. The Logician and the Engineer is truly a gem.

New York Journal of Books - Robert Schaefer

Meshing logic problems with the stories of two extraordinary men—Victorian philosopher-mathematician George Boole and twentieth-century information theorist Claude Shannon—Paul Nahin fashions a tale of innovation and discovery. . . . Alongside a gripping account of how Shannon built on Boole's work, Nahin explores others key to the technological revolution, from Georg Cantor to Alan Turing.

Nature

"Meshing logic problems with the stories of two extraordinary men . . . Paul Nahin fashions a tale of innovation and discovery. Alongside a gripping account of how Shannon built on Boole's work, Nahin explores others key to the technological revolution, from Georg Cantor to Alan Turing."—Nature

"Engaging. . . . Nahin assumes some rudimentary knowledge but expertly explains concepts such as relay circuits, Turing machines, and quantum computing. Reasoning through the problems and diagrams will give persistent readers genuine aha moments and an understanding of the two revolutionaries who helped to lay the foundation of our digital world."—Scientific American

"Part biography, part history, and part a review of basic information theory, this book does an excellent job of fitting these interlocking elements together."—Library Journal

"The reader is taken on a journey from the development of some abstract mathematical ideas through a nearly ubiquitous application of those ideas within the modern world with so many embedded digital computers. . . . I enjoyed the discussion of Claude Shannon. In the history of the computer and development of the internet and World Wide Web, his ideas and contributions are too often overlooked. He is one of my heroes and I believe that everyone that reads this book will come to the same conclusion."—Charles Ashbacher, MAA Reviews

"Paul J. Nahin really knows how to tell a good story. . . . The Logician and the Engineer is truly a gem."—New York Journal of Books

"A short but fairly detailed exploration of the genesis of Boolean logic and Shannon's information theory. . . . [G]ood background reading for anyone studying electronics or computer science."—Christine Evans-Pughe, Engineering & Technology

"Although the book is technical, it is always easily understandable for anyone (for those who need it, some basic rules for electrical circuits are collected in a short appendix). It is not only understandable but also pleasantly bantering and at occasions even facetious."—A. Bultheel, European Mathematical Society

"Most valuable to this reviewer, and likely to many potential readers, is the closing chapter, aptly titled Beyond Boole and Shannon. Here is provided an introduction to quantum computing and its logic, possibly portending the future of computers, yet unmistakably bearing the footprints of the two early pioneers. It is an unexpected yet fitting conclusion to this thoroughly enjoyable read."—Ronald E. Prather,Mathematical Reviews Clippings

"Nahin has had the very good idea of connecting the very different worlds and times of Boole, Shannon, and others to demonstrate that a little Victorian algebra can turn out to be very useful."—SIAM Review

"The exposition is clear and does not assume any prior knowledge except elementary mathematics and a few basic facts from physics. I recommend this well-written book to all readers interested in the history of computer science, as well as those who are curious about the fundamental principles of digital computing."—Antonín Slavík, Zentralblatt MATH

"[T]his is a useful and often interesting introduction to the life and work of two intellectual giants who are largely unknown to the general public."—Gareth and Mary Jones, London Mathematical Society Newsletter

"The problems are varied and indeed intriguing, and the solutions are delightful."—Mathematics Magazine

"This book is not light reading. It would be excellent for advanced high school juniors or seniors with a strong interest in computer science as well as mathematics."—Tom Ottinger, Mathematics Teacher

"Nahin leavens the math and engineering with humor and an infectious intellectual curiosity, and the parallels between Boole and Shannon are convincingly drawn. . . . [The Logician and the Engineer] will give your brain a workout, but an enjoyable one."—San Francisco Book Review

From the Publisher