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# The Logician and the Engineer

How George Boole and Claude Shannon Created the Information Age

**Paul J. Nahin **

- Hardcover2012Hardcover24.9519.95ISBN9780691151007248 pp.6 x 9 1/42 halftones. 41 line illus. 25 tables.Live
- Paperback2017Paperback17.9514.95ISBN9780691176000248 pp.6 x 9 1/42 halftones. 41 line illus. 25 tables.Live

- E-bookISBN9781400844654

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.

*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.

## Reviews

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*Nature***--**

*Scientific American***--**

*Library Journal***--Charles Ashbacher,**

*MAA Reviews**Logician and the Engineer*is truly a gem."

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*New York Journal of Books***--Christine Evans-Pughe,**

*Engineering & Technology***--A. Bultheel,**

*European Mathematical Society**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***--**

*SIAM Review***--Antonín Slavík,**

*Zentralblatt MATH***--Gareth and Mary Jones,**

*London Mathematical Society Newsletter***--**

*Mathematics Magazine***--Tom Ottinger,**

*Mathematics Teacher**The Logician and the Engineer*] will give your brain a workout, but an enjoyable one."

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*San Francisco Book Review*## Endorsements

**--Andrew Hodges, author of**

*Alan Turing: The Enigma***--Lawrence Weinstein, author of**

*Guesstimation 2.0: Solving Today's Problems on the Back of a Napkin**The Logician and the Engineer*is an interesting and informative account of the history of formal logic, the lives of its two great investigators, and the applications of Boolean algebra in electronic computation."

**--Chuck Adler, St. Mary's College**

## 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

**Epilogue**

For the Future: The Anti-Amphibological Machine 210

**Appendix**

Fundamental Electric Circuit Concepts 219

*Acknowledgments*223

*Index*225

## Other Books Written by this Author(s)

- Paul J. Nahin

## Series

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