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

Boolean algebra, also called Boolean logic, is at the heart of the electronic circuitry in everything we use--from our computers and cars, to our kitchen gadgets and 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, best-selling popular math writer 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 (1815-1864) and electrical engineer and pioneering information theorist Claude Shannon (1916-2001)--advanced Boolean logic and became founding fathers of the electronic communications age.

Presenting the dual biographies of Boole and Shannon, Nahin examines the history of Boole's innovative ideas, and considers how they led to Shannon's groundbreaking work on electrical relay circuits and information theory. Along the way, Nahin presents logic problems for readers to solve and talks about the contributions of such key players as Georg Cantor, Tibor Rado, and Marvin Minsky--as well as the crucial role of Alan Turing's "Turing machine"--in the development of mathematical logic and data transmission. Nahin takes readers from fundamental concepts to a deeper and more sophisticated understanding of how a modern digital machine such as the computer is constructed. Nahin also delves into the newest ideas in quantum mechanics and thermodynamics in order to explore computing's possible limitations in the twenty-first century and beyond.

The Logician and the Engineer shows how a form of mathematical logic and the innovations of two men paved the way for the digital technology of the modern world.

"From electromechanical relays to quantum computing, Nahin takes us on a delightful exploration of Boolean logic and the careers of George Boole and Claude Shannon. This is a superb book for anyone who wants to understand how that gigahertz chip in their favorite electronic doohickey really works."--Lawrence Weinstein, author of Guesstimation 2.0: Solving Today's Problems on the Back of a Napkin

"Written with the skill and ability that we have come to expect from Paul Nahin, 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

Presenting the dual biographies of Boole and Shannon, Nahin examines the history of Boole's innovative ideas, and considers how they led to Shannon's groundbreaking work on electrical relay circuits and information theory. Along the way, Nahin presents logic problems for readers to solve and talks about the contributions of such key players as Georg Cantor, Tibor Rado, and Marvin Minsky--as well as the crucial role of Alan Turing's "Turing machine"--in the development of mathematical logic and data transmission. Nahin takes readers from fundamental concepts to a deeper and more sophisticated understanding of how a modern digital machine such as the computer is constructed. Nahin also delves into the newest ideas in quantum mechanics and thermodynamics in order to explore computing's possible limitations in the twenty-first century and beyond.

The Logician and the Engineer shows how a form of mathematical logic and the innovations of two men paved the way for the digital technology of the modern world.

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