The Logician and the Engineer: How George Boole and Claude Shannon Created the Information Age
Paul J. Nahin
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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.
unchanged, however, as again we simply evaluate the left-hand side and then the right-hand side of the claimed identity for all possible values of A and B, to get and we see that the column for A + AB does indeed match the column for A. Of course, we could also easily prove this identity by simply writing A + AB = A(1 + B) or (because 1 + B = 1) = A · 1 = A. A B A + AB 0 0 0 0 1 0 1 0 1 1 1 1 This sort of table is called a truth table, and it is a common tool for proving identities that
book. 8. Shannon analyzed several other interconnection schemes of crummy relay switches in his 1956 paper, and you can find some further discussion in my book Duelling Idiots and Other Probability Puzzlers. Princeton University Press, 2000 (corrected paperback, 2002), pp. 22–23. 9. Automata Studies (edited by C. E. Shannon and J. McCarthy,) Princeton University Press, 1956, pp. 329–378. 10. What might happen when a neural net becomes really large has sparked the imaginations of science
general n-symbol case that Shannon discusses: The formal resemblance of (7.1.2) to the entropy function in statistical mechanics (thermodynamics) is why Shannon called H, measured in bits, the information entropy function. Now, to the central point here. In (7.1.1) if p = 1 (all 0s) or if p = 0 (all 1s), then H = 0, just as Shannon argued on intuitive grounds. The maximum H in (7.1.1) occurs if , which also makes intuitive sense: maximum information occurs when maximum uncertainty exists.
boy?” “Look, Sam, I’m desperate, and I’ve had a lot of things on my mind besides the weather. I need your help, and I need it fast. Janet’s going to rake my behind over the coals, but good, if I don’t get someone to tell me what the divorce settlement she’s serving on me means!” “Willard, you want to see Professor Shyster over in the Law School. I deal in physical facts, mathematical validity, in cosmic truth, not the mental hash–mish-mash of lawyers!” “No, Sam, another fathead lawyer isn’t
old Shyster going to do with them, anyway?” “Actually, Willard, you’ve got it backward. Shyster is writing a law book, and he’s found that his early drafts weren’t really up to par as far as the publisher is concerned. Not scholarly-sounding enough, or something like that. So the Clarifier is just what he needed.” “I don’t get it, Sam,” said Willard, with a puzzled look on his face. “If Shyster’s book isn’t impressively complex enough, how’s the Clarifier going to help?” Sam leaned back in his