145951
Author: Chris Bernhardt
File Type: pdf
In 1936, when he was just twenty-four years old, Alan Turing wrote a remarkable paper in which he outlined the theory of computation, laying out the ideas that underlie all modern computers. This groundbreaking and powerful theory now forms the basis of computer science. In Turings Vision, Chris Bernhardt explains the theory, Turings most important contribution, for the general reader. Bernhardt argues that the strength of Turings theory is its simplicity, and that, explained in a straightforward manner, it is eminently understandable by the nonspecialist. As Marvin Minsky writes, The sheer simplicity of the theorys foundation and extraordinary short path from this foundation to its logical and surprising conclusions give the theory a mathematical beauty that alone guarantees it a permanent place in computer theory. Bernhardt begins with the foundation and systematically builds to the surprising conclusions. He also views Turings theory in the context of mathematical history, other views of computation (including those of Alonzo Church), Turings later work, and the birth of the modern computer. In the paper, On Computable Numbers, with an Application to the Entscheidungsproblem, Turing thinks carefully about how humans perform computation, breaking it down into a sequence of steps, and then constructs theoretical machines capable of performing each step. Turing wanted to show that there were problems that were beyond any computers ability to solve in particular, he wanted to find a decision problem that he could prove was undecidable. To explain Turings ideas, Bernhardt examines three well-known decision problems to explore the concept of undecidability investigates theoretical computing machines, including Turing machines explains universal machines and proves that certain problems are undecidable, including Turings problem concerning computable numbers. **Review A fascinating account of Alan Turings epic research paper, which kicked off the entire computer revolution. Im particularly impressed by the amount of detail the author includes while keeping everything simple, transparent, and a pleasure to read. (Ian Stewart, author of In Pursuit of the Unknown 17 Equations That Changed the World) This is a delightful introduction for the lay reader to the ideas surrounding Alan Turings great paper of 1936. (Scott Aaronson, Associate Professor of Electrical Engineering and Computer Science, MIT) Over the past several decades, Alan Turing, known as the father of computer science, has become an intellectual and cultural icon. Chris Bernhardt has written a very clear and accessible book that explains Turings work, showing how his ideas have developed into some of the most important ideas in computer science today. (Noson S. Yanofsky, author of The Outer Limits of Reason What Science, Mathematics, and Logic Cannot Tell Us) The dazzling array of computer applications, from desktop to cell phone, has obscured the play of ideas that first set our modern era in motion. In this account, Bernhardt reveals the crucial contribution to these developments made by Alan Turing and other early computer scientists. A marvelous book. (A. K. Dewdney, Professor Emeritus, Department of Computer Science, University of Western Ontario) About the Author Chris Bernhardt is Professor of Mathematics at Fairfield University. In 1936, when he was just twenty-four years old, Alan Turing wrote a remarkable paper in which he outlined the theory of computation, laying out the ideas that underlie all modern computers. This groundbreaking and powerful theory now forms the basis of computer science. In Turings Vision, Chris Bernhardt explains the theory, Turings most important contribution, for the general reader. Bernhardt argues that the strength of Turings theory is its simplicity, and that, explained in a straightforward manner, it is eminently understandable by the nonspecialist. As Marvin Minsky writes, The sheer simplicity of the theorys foundation and extraordinary short path from this foundation to its logical and surprising conclusions give the theory a mathematical beauty that alone guarantees it a permanent place in computer theory. Bernhardt begins with the foundation and systematically builds to the surprising conclusions. He also views Turings theory in the context of mathematical history, other views of computation (including those of Alonzo Church), Turings later work, and the birth of the modern computer.In the paper, On Computable Numbers, with an Application to the Entscheidungsproblem, Turing thinks carefully about how humans perform computation, breaking it down into a sequence of steps, and then constructs theoretical machines capable of performing each step. Turing wanted to show that there were problems that were beyond any computers ability to solve in particular, he wanted to find a decision problem that he could prove was undecidable. To explain Turings ideas, Bernhardt examines three well-known decision problems to explore the concept of undecidability investigates theoretical computing machines, including Turing machines explains universal machines and proves that certain problems are undecidable, including Turings problem concerning computable numbers. **
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