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.
Libraries & Culture, Winter 1997, pp. 81–93. (c) William Kneale, “Boole and the Revival of Logic,” Mind, April 1948, pp. 149–175. (d) T.A.A. Broadbent, “George Boole (1815-1864),” Mathematical Gazette, December 1964, pp. 373–378. (e) Rush Rhees, “George Boole As Student and Teacher by Some of His Friends and Pupils,” Proceedings of the Royal Irish Academy 57, 1954–1956, pp. 74–78. (f) R. H., “George Boole FRS,” British Quarterly Review, July 2, 1866, pp. 141–181. “R. H.” was Boole’s friend,
the blue chip. Since box C has the blue chip, then the red and white chips are in boxes A and B. In particular, one of those two boxes must have the red chip, but (a2) and (b2) deny that. Thus, Case 2 is also nonsense. Case 3: Take (c) as true, and (a) and (b) as false. Then, with reversals, we have (a3) box A does not contain the red chip; (b3) box B contains the red chip; (c3) box C does not contain the blue chip. This works. (b3) says B has the red chip. That leaves the blue and white
language. The only MATLAB functions that may need some explanation are zeros (which sets each of the 50 elements of the row vector tape equal to zero, initially), and sum (which adds the 50 elements of tape, giving the number of elements of tape equal to 1). Both operations can easily be implemented as for/end loops in other languages. The very last line of rado.m prints the final values of shift and the number of 1’s in tape. 4. See Minsky’s book (note 1), Chapter 7, pp. 132–145, and in
addition to being a “capital lion.” 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
Cambridge Mathematical Journal), with William Thomson in the editor’s chair (since 1845) as the permanent replacement to Gregory. In 1849 all of Boole’s hard work achieved for him what, as a teenager teaching dull boys simple math at an obscure boarding school in Doncaster, would have been just an outrageous day-dream fantasy. That year he applied for the position of professor of mathematics at the newly created Queen’s College (today’s University College) in Cork, Ireland. No matter his lack of