The Logician and the Engineer

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

PAUL J. NAHIN
Copyright Date: 2013
Pages: 248
https://www.jstor.org/stable/j.cttq957s
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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? InThe 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 Engineershows how a form of mathematical logic and the innovations of two men paved the way for the digital technology of the modern world.

    eISBN: 978-1-4008-4465-4
    Subjects: Mathematics, Technology, History

Table of Contents

  1. Front Matter
    (pp. i-vi)
  2. Table of Contents
    (pp. vii-x)
  3. Preface
    (pp. xi-xiv)
  4. 1 What You Need To Know to Read This Book
    (pp. 1-5)

    To read this book you don’t have to be an electronics genius, a computer geek, or a quantum mechanics whiz. But that doesn’t mean I’m assuming you are a high school dropout, either. I will, in fact, be assuming some knowledge of mathematics and electrical physics and an appreciation for the value of analytical reasoning—but no more than a technically minded college-prep high school junior or senior would have. In particular, the math level is that of algebra including knowing how matrices multiply. The electrical background is simple: knowing (1) that electricity comes in two polarities (positive and negative)...

  5. 2 Introduction
    (pp. 6-16)

    In 1859 the English naturalist Charles Darwin (1809–1882) published hisOn the Origin of Species, a book that revolutionized how humans view their place in the world. Just five years earlier a fellow countryman, the mathematician George Boole (1815–1864), had published hisAn Investigation of the Laws of Thought, a book that would have an equally huge impact on humanity. Even earlier, in fact, Boole had published hisMathematical Analysis of Logic(1847), which was, in essence, a first draft ofLaws of Thought. The importance of Boole’s work was not as much appreciated at the time as...

  6. 3 George Boole and Claude Shannon: Two Mini-Biographies
    (pp. 17-42)

    George Boole was born in Lincoln, a town in the north of England, on November 2, 1815. The first of four children born to John (1777–1848) and Mary Ann Boole (1780–1854)—his siblings, a sister and two brothers, all outlived him by decades, with his youngest brother surviving until 1902—he was particularly lucky with his father. While a simple tradesman (a cobbler), he was also a kind, generous, religious man who had a strong interest in both mathematics and the construction of optical instruments. He provided emotional stability and intellectual stimulation, if not wealth, to his family,...

  7. 4 Boolean Algebra
    (pp. 43-66)

    As the above quotation shows, Boole was interested in symbolic analysis years before he wrote hisLaws of Thought. As mentioned in the previous chapter, before even theMathematical Analysis of Logichad appeared he had published a paper on how to apply the symbolic manipulation of the differentiation and difference operators to the solution of differential and difference equations. The solution in that way of such equations, while of immense importance in mathematical physics, is both outside the scope and beyond the technical level of this book and I won’t pursue that mathematics here. My point is simply that...

  8. 5 Logic Switching Circuits
    (pp. 67-87)

    Today’s digital circuitry is built with electronic technology that the telephone engineers of the 1930s and the pioneer computer designers of the 1940s would have thought to be magic. And I mean that literally: to quote science fiction writer Arthur C. Clarke’s famous third law: “Any sufficiently advanced technology is indistinguishable from magic.”¹ An example of this is the ordinary radio, which while commonplace to us (modern kids probably find AM radio just a bit boring!) would have been magic to the greatest of the Victorian scientists, including James Clerk Maxwell, himself who first wrote the equations that give life...

  9. 6 Boole, Shannon, and Probability
    (pp. 88-113)

    Boole and Shannon shared a deep interest in the mathematics of probability. Boole’s interest was, of course, not related to the theory of computation—he was a century too early for that—while Shannon’s mathematical theory of communication and information processing is replete with probabilistic analyses. There is, nevertheless, an important intersection between what the two men did, and that’s what I’ll show you in this chapter. I will not go very deeply at all into what either man did with the subject of probability, but rather my intent here is to simply give you a flavor of how they...

  10. 7 Some Combinatorial Logic Examples
    (pp. 114-138)

    The entire point of Shannon’s 1948 “A Mathematical Theory of Communication” was to study the theoretical limits on the transmission of information from point A (thesource) to point B (thereceiver) through an intervening medium (thechannel). The information (for example, a human voice signal from a microphone or the output signals from the buttons of a keyboard) is imagined first to be encoded in some manner before being sent through the channel. In “Mathematical Theory’’ Shannon considers two distinct types of channels: the socalledcontinuous channelthat would carry, for example, a continuous signal like the human voice,...

  11. 8 Sequential-State Digital Circuits
    (pp. 139-160)

    What is asequential-stateproblem? This is a question that is most directly answered by giving some specific examples. Onecan, I should admit, formulate a theoretical, mathematical definition, but examples are both more illuminating and, even more importantly, I think, morefun. My first example will drive home the point made by the opening quotation, that the concept of a physical system changing state with time predates Shannon and Boole by centuries. In fact, you’ll see how the state concept predatesNewtonby even more centuries. This first example of the state concept comes from a late ninth century...

  12. 9 Turing Machines
    (pp. 161-175)

    ATuring machineis the combination of a sequential, finite-state machine plus an external read/write memory storage medium called thetape(think of a ribbon of magnetic tape). The tape is a linear sequence of squares, with each square holding one of several possible symbols. Most generally, a Turing machine can have any number of different symbols it can recognize, but I’ll assume here that we are discussing the 2-symbol case (0 or 1). In 1956, Shannon showed that this in no way limits the power of what a Turing machine can do.

    The tape is arbitrarily long in at...

  13. 10 Beyond Boole and Shannon
    (pp. 176-209)

    In a previous book, I opened the first section (“The Limits of Computation”) of the final chapter with these words:

    The speed of any computer is fundamentally limited by how fast its various component parts can send and receive signals among themselves—that is, by the speed of light and by how far those signals have to travel. We can’t do anything about the speed of light, but one way to increase the speed of a computer is simply to make it smaller. That means the computer’s volume decreases. Suppose, just to be specific, a computer has the shape of...

  14. Epilogue For the Future: The Anti-Amphibological Machine
    (pp. 210-218)

    To end this book on a math-free note, what follows is a personal vision of the sort of logical problem that may soon be one that even a quantum computer would find a struggle to deal with—the decipherment of entangled legalese, the sort of monstrous gobbledegook one finds, for example, in the increasingly convoluted IRS tax code (without TurboTax®, your author would long ago have gone quietly insane trying to file a Federal 1040 that didn’t have at least 73 “errors” in it). In the form of a short story, that vision is “The Language Clarifier,” which first appeared...

  15. Appendix Fundamental Electric Circuit Concepts
    (pp. 219-222)
  16. Acknowledgments
    (pp. 223-224)
  17. Index
    (pp. 225-228)
  18. Back Matter
    (pp. 229-229)