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The Logician and the Engineer

Book Description

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.

Table of Contents

  1. Cover
  2. Title
  3. Copyright
  4. Contents
  5. Preface
  6. 1 What You Need to Know to Read This Book
    1. Notes and References
  7. 2 Introduction
    1. Notes and References
  8. 3 George Boole and Claude Shannon: Two Mini-Biographies
    1. 3.1 The Mathematician
    2. 3.2 The Electrical Engineer
    3. Notes and References
  9. 4 Boolean Algebra
    1. 4.1 Boole’s Early Interest in Symbolic Analysis
    2. 4.2 Visualizing Sets
    3. 4.3 Boole’s Algebra of Sets
    4. 4.4 Propositional Calculus
    5. 4.5 Some Examples of Boolean Analysis
    6. 4.6 Visualizing Boolean Functions
    7. Notes and References
  10. 5 Logical Switching Circuits
    1. 5.1 Digital Technology: Relays Versus Electronics
    2. 5.2 Switches and the Logical Connectives
    3. 5.3 A Classic Switching Design Problem
    4. 5.4 The Electromagnetic Relay and the Logical NOT
    5. 5.5 The Ideal Diode and the Relay Logical AND and OR
    6. 5.6 The Bi-Stable Relay Latch
    7. Notes and References
  11. 6 Boole, Shannon, and Probability
    1. 6.1 A Common Mathematical Interest
    2. 6.2 Some Fundamental Probability Concep2ts
    3. 6.3 Boole and Conditional Probability
    4. 6.4 Shannon, Conditional Probability, and Relay Reliability
    5. 6.5 Majority Logic
    6. Notes and References
  12. 7 Some Combinatorial Logic Examples
    1. 7.1 Channel Capacity, Shannon’s Theorem, and Error-Detection Theory
    2. 7.2 The Exclusive-OR Gate (XOR)
    3. 7.3 Error-Detection Logic
    4. 7.4 Error-Correction Theory
    5. 7.5 Error-Correction Logic
    6. Notes and References
  13. 8 Sequential-State Digital Circuits
    1. 8.1 Two Sequential-State Problems
    2. 8.2 The NOR Latch
    3. 8.3 The Clocked RS Flip-Flop
    4. 8.4 More Flip-Flops
    5. 8.5 A Synchronous, Sequential-State Digital Machine Design Example
    6. Notes and References
  14. 9 Turing Machines
    1. 9.1 The First Modern Computer
    2. 9.2 Two Turing Machines
    3. 9.3 Numbers We Can’t Compute
    4. Notes and References
  15. 10 Beyond Boole and Shannon
    1. 10.1 Computation and Fundamental Physics
    2. 10.2 Energy and Information
    3. 10.3 Logically Reversible Gates
    4. 10.4 Thermodynamics of Logic
    5. 10.5 A Peek into the Twilight Zone: Quantum Computers
    6. 10.6 Quantum Logic—and Time Travel, Too!
    7. Notes and References
  16. Epilogue
    1. For the Future: The Anti-Amphibological Machine
  17. Appendix
    1. Fundamental Electric Circuit Concepts
  18. Acknowledgments
  19. Index