By Paul J. Nahin
Boolean algebra, often known as Boolean common sense, is on the middle of the digital circuitry in every little thing we use--from our desktops and autos, to our kitchen instruments and residential home equipment. How did a approach of arithmetic tested within the Victorian period develop into the root for such remarkable technological achievements a century later? In The philosopher and the Engineer, best-selling renowned math author Paul Nahin combines attractive difficulties and a colourful ancient narrative to inform the notable tale of ways males in several eras--mathematician and thinker George Boole (1815-1864) and electric engineer and pioneering details theorist Claude Shannon (1916-2001)--advanced Boolean good judgment and have become founding fathers of the digital communications age.
Presenting the twin biographies of Boole and Shannon, Nahin examines the heritage of Boole's cutting edge principles, and considers how they ended in Shannon's groundbreaking paintings on electric relay circuits and data thought. alongside the way in which, Nahin provides common sense difficulties for readers to resolve and talks in regards to the contributions of such key gamers as Georg Cantor, Tibor Rado, and Marvin Minsky--as good because the the most important position of Alan Turing's "Turing machine"--in the improvement of mathematical common sense and information transmission. Nahin takes readers from basic thoughts to a deeper and extra subtle knowing of the way a latest electronic computing device similar to the pc is developed. Nahin additionally delves into the latest rules in quantum mechanics and thermodynamics so that it will discover computing's attainable boundaries within the twenty-first century and past.
The philosopher and the Engineer indicates how a kind of mathematical good judgment and the recommendations of 2 males cleared the path for the electronic expertise of the fashionable international.
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Extra resources for The Logician and the Engineer: How George Boole and Claude Shannon Created the Information Age
Sample text
Every element of B is an element of A. 2 VISUALIZING SETS To understand the essence of what Boole did to cast logic into algebraic form, it is very helpful to use the language of sets. I’ll discuss what Boole did in the next section but, first, to lay the groundwork for that I’ll say just a bit here on set terminology. A set is simply a collection of things (the elements of the set), either physical or conceptual. For example, we could talk of the set of all rocks (I’ll call that set A) and we could talk of the set of all small rocks (I’ll call that set B).
4. Green’s name is famous in mathematical physics, and is attached to such things as Green’s functions and Green’s theorem. You can find more on his somewhat mysterious life in D. M. Cannell, George Green, Mathematician and Physicist, 1793–1841: The Background to His Life and Work, SIAM, 2001. 5. A very nice discussion of symbolic algebra, and of the relationship between Boole and Gregory, is in Patricia R. Allaire and Robert E. Bradley, “Symbolical Algebra as a Foundation for Calculus: D. F. Gregory’s Contribution,’’ Historia Mathematica, November 2002, pp.
M. Cannell, George Green, Mathematician and Physicist, 1793–1841: The Background to His Life and Work, SIAM, 2001. 5. A very nice discussion of symbolic algebra, and of the relationship between Boole and Gregory, is in Patricia R. Allaire and Robert E. Bradley, “Symbolical Algebra as a Foundation for Calculus: D. F. Gregory’s Contribution,’’ Historia Mathematica, November 2002, pp. 395–426. Another very nice discussion, both technically and historically, of Boole’s symbolic manipulation of the differentiation operator Dx (= ddx ) is in Michael A.