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# The Annotated Turing: A Guided Tour Through Alan Turing's Historic Paper on Computability and the Turing Machine

Programming Legend Charles Petzold unlocks the secrets of the extraordinary and prescient 1936 paper by Alan M. TuringMathematician Alan Turing invented an imaginary computer known as the Turing Machine; in an age before computers, he explored the concept of what it meant to be "computable," creating the field of computability theory in the process, a foundation of present
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Paperback, 372 pages

Published
June 1st 2008
by John Wiley & Sons

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However, there's no way through it but to do it.

Well mathematicians and computer programmers have the same problem. British mathematician, Alan Turing, proved that there is no way a computer can be designed with the correct set of instructions (program) so as to be able to determine if any ...more

*finally*feel that I truly know the difference now, in a deep sense, of what makes a given transcendental number computable or not (there's unfortunately rather little detail on computable functions themselves, but that's an easy extension from computable numbers). Kudos to Petzold for his fine background material on Hilbert's

*erweiterte Funktionenkalkul*...more

Petzold demonstrates his knowledge of computing and mathematics and ...more

It seems that I am practi ...more

Along the way, in this pleasantly written book, the author places the paper in a historical setting, which in part extends back to the Greek mathematician Diophantus, and provides numerous insights into the development of ideas that led up to Turing's paper, as well as numerous anecdotes of Turing's brief career. Turing's ca ...more

Next, the author covers probably the part that most interest me: Turing machines. Turing shows how such machines can be used to perform computation and, in an impressive series of steps, shows how a Universal machine can be used to execute the operations of any Turing ...more

Indeed, his definition of "computable" applied to numbers is sort of the opposite: a computable number is a number that can be expressed as the output of a program that never stops printing digits (i.e. pi is computable because you can write a Turing number representing a program that prints 3.1415... etc to an arbitrary # degrees precision.) By this definition all real numbers are computable. ( ...more

Except for the penultimate chapter, "Is Everything A Turing Machine?" Petzold takes us through a tour of mathematical and philosophical history eventually conflat ...more

I'd recommend it to anyone who (like me) is interested in trying to program a Turing machine or (not like me) is VERY well-versed and interested in logic and computational analysis. Otherwise, this book will take you a year to rea ...more

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