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.
Author(s): Paul J. Nahin
Publisher: Princeton University Press
Year: 2012
Language: English
Pages: 244
Cover......Page 1
Title......Page 4
Copyright......Page 5
Contents......Page 8
Preface......Page 12
1 What You Need to Know to Read This Book......Page 16
Notes and References......Page 20
2 Introduction......Page 21
Notes and References......Page 29
3.1 The Mathematician......Page 32
3.2 The Electrical Engineer......Page 43
Notes and References......Page 54
4.1 Boole's Early Interest in Symbolic Analysis......Page 58
4.2 Visualizing Sets......Page 59
4.3 Boole's Algebra of Sets......Page 60
4.4 Propositional Calculus......Page 63
4.5 Some Examples of Boolean Analysis......Page 67
4.6 Visualizing Boolean Functions......Page 74
Notes and References......Page 80
5.1 Digital Technology: Relays versus Electronics......Page 82
5.2 Switches and the Logical Connectives......Page 83
5.3 A Classic Switching Design Problem......Page 86
5.4 The Electromagnetic Relay and the Logical NOT......Page 88
5.5 The Ideal Diode and the Relay Logical AND and OR......Page 91
5.6 The Bi-Stable Relay Latch......Page 96
Notes and References......Page 99
6.1 A Common Mathematical Interest......Page 103
6.2 Some Fundamental Probability Concepts......Page 104
6.3 Boole and Conditional Probability......Page 111
6.4 Shannon, Conditional Probability, and Relay Reliability......Page 114
6.5 Majority Logic......Page 121
Notes and References......Page 125
7.1 Channel Capacity, Shannon's Theorem, and Error-Detection Theory......Page 129
7.2 The Exclusive-OR Gate (XOR)......Page 137
7.3 Error-Detection Logic......Page 142
7.4 Error-Correction Theory......Page 143
7.5 Error-Correction Logic......Page 147
Notes and References......Page 151
8.1 Two Sequential-State Problems......Page 154
8.2 The NOR Latch......Page 157
8.3 The Clocked RS Flip-Flop......Page 161
8.4 More Flip-Flops......Page 169
8.5 A Synchronous, Sequential-State Digital Machine Design Example......Page 173
Notes and References......Page 175
9 Turing Machines......Page 176
9.1 The First Modern Computer......Page 177
9.2 Two Turing Machines......Page 179
9.3 Numbers We Can't Compute......Page 183
Notes and References......Page 188
10.1 Computation and Fundamental Physics......Page 191
10.2 Energy and Information......Page 193
10.3 Logically Reversible Gates......Page 195
10.4 Thermodynamics of Logic......Page 199
10.5 A Peek into the Twilight Zone: Quantum Computers......Page 203
10.6 Quantum Logic—and Time Travel, Too!......Page 212
Notes and References......Page 220
Epilogue: For the Future: The Anti-Amphibological Machine......Page 225
Appendix: Fundamental Electric Circuit Concepts......Page 234
Acknowledgments......Page 238
E......Page 240
N......Page 241
U......Page 242
X......Page 243
