The Logician and the Engineer (ebook)

Argumento de The Logician and the Engineer (ebook)

"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

"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

"Part biography, part history, and part a review of basic information theory, the book does an excellent job of fitting these interlocking elements together. Nahin's work is best suited to students and faculty in electrical engineering, mathematics, and information science. It is also recommended for anyone with an interest in the history of information technology."--William Baer, Library Journal

"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

"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

"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 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

"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

"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

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

"In this book, Nahin brings to life the immense practical outcomes of deep theoretical ideas. Too often, technological advances are seen as isolated inventions and the underlying mathematical and scientific infrastructure goes unappreciated. By following the story of George Boole and Claude Shannon with a lively historical style, and a futuristic extension to quantum computing, Nahin makes the connection of theory and practice into something vivid and compelling."--Andrew Hodges, author of Alan Turing: The Enigma

"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

"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. Readers will also learn about Turing machines, quantum computing, and other more futuristic topics."--Robert E. O'Malley, Jr., SIAM Review0Preface 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