The Annotated Turing: A Guided Tour Through Alan Turing's Historic Paper on Computability and the Turing Machine [Englisch] [Taschenbuch]

Some books entertain, some inform; some confirm what you already knew, some make you change your mind about something. But then there are some books that just make you think "wow! I wish I'd written that".

For me, Charles Petzold's The Annotated Turing falls into that last category (as well, of course, as the informational category). It's a book worth reading not only for the topic itself but the way it's presented.

Petzold provides the necessary background before working through Turing's famous 1936 paper "On computable numbers, with an application to the Entscheidungsproblem" with rich annotations at every stage, including biographical details.

If you are interested in the foundation of mathematics, computability, Turing's work, or even just ways of explaining mathematics in a historical context, I highly recommend this book.

this is a fantastic book. It manages to explain simply and clearly the entirety of turing's landmark paper and providing a thorough grounding on the base mathematical knowledge. though I had taken some set theory in college, I am fairly confident that even a devoted highschooler with some experience in geometry proofs could understand and follow this book. Of course, I should also mention that this book is written extremely well such that at no point did I feel bored. when was the last time you found a math book completely riveting?

This is one of those books that you'll love if you're into mathematics or hard-core computer science, but you'll become somewhat of a skimmer if you don't have the chops to keep up with theory and proofs.. The Annotated Turing: A Guided Tour Through Alan Turing's Historic Paper on Computability and the Turing Machine by Charles Petzold. And in case you're wondering, I fall into the second category. :)

Contents:
Part 1 - Foundations
This Tomb Holds Diophantus
The Irrational and the Transcendental
Centuries of Progress
Part 2 - Computable Numbers
The Education of Alan Turing
Machines at Work
Addition and Multiplication
Also Known as Subroutines
Everything Is a Number
The Universal Machine
Computers and Computability
Of Machines and Men
Part 3 - Das Entscheidungsproblem
Logic and Computability
Computable Functions
The Major Proof
The Lambda Calculus
Conceiving the Continuum
Part 4 - And Beyond
Is Everything a Turning Machine?
The Long Sleep of Diophantus
Selected Bibliography
Index

In order to give the reader a better understanding of Turing's paper on computing machines, Petzold takes each section of the original paper and adds commentary and background. The parts of the actual Turing paper are set off in shaded areas with a different font, preserving the line breaks, formatting, and even the typos when possible. By the time you're done with the book, you have a complete copy of Turing's original work. Petzold does a very good job in laying the foundations for concepts and conclusions in the paper. For instance, he provides a concise explanation of rational, irrational, real, and transcendental numbers in a way that most people can follow. It's important to understand those ideas, as they quickly come into play when the dissection of the paper begins. He also provides historical background on Turing and his counterparts. This is important because you should understand that back in the 1930's, the idea and concepts of automated computing were still in their infancy. If you try and judge his work based on what we know today, you may not get the full implication of how radical this was back in his time.

So is this a book that everyone will enjoy? In a word, no. This book deals with some heavy math theory, and to get the most out of it you'd have to either have a solid background in math or be willing to spend a lot of time trying to understand it. I'll admit that most of the details were far over my head, and as such I missed a significant amount of the impact of this book. Having said that, I can also see how Petzold did a very good job in breaking down a complex subject and making it attainable to a reader that isn't at the same level of Turing. In fact, I'd venture to guess that without a book like this, many would not have the opportunity to dig into Turing's work with any degree of depth or success.