The Annotated Turing 1st Edition by Charles Petzold ISBN 0470229055 9780470229057

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ISBN 10: 0470229055 
ISBN 13: 9780470229057
Author: Charles Petzold

Programming Legend Charles Petzold unlocks the secrets of the extraordinary and prescient 1936 paper by Alan M. Turing

Mathematician 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-day computer programming.

The book expands Turing’s original 36-page paper with additional background chapters and extensive annotations; the author elaborates on and clarifies many of Turing’s statements, making the original difficult-to-read document accessible to present day programmers, computer science majors, math geeks, and others.

Interwoven into the narrative are the highlights of Turing’s own life: his years at Cambridge and Princeton, his secret work in cryptanalysis during World War II, his involvement in seminal computer projects, his speculations about artificial intelligence, his arrest and prosecution for the crime of “gross indecency,” and his early death by apparent suicide at the age of 41.

The Annotated Turing 1st Table of contents:

• Part I: Context and Precursors to Turing’s Paper

  • Chapter 1: The Foundations of Mathematics in Crisis
    • Hilbert’s Program: Formalism and the Entscheidungsproblem (Decision Problem)
    • Gödel’s Incompleteness Theorems: The First Cracks
    • The Search for a Formalization of “Computable”
  • Chapter 2: Early Attempts at Computability and Logic
    • Church’s Lambda Calculus
    • Herbrand-Gödel Recursion
    • Other Contemporary Ideas (e.g., Post’s Formulation)
    • The Need for a Definitive Model

• Part II: Alan Turing’s “On Computable Numbers, with an Application to the Entscheidungsproblem” (The Annotated Paper)

  • Chapter 3: Section 1: Computing Machines
    • Turing’s Conceptual Machine: The Tape, Head, States, and Table of Instructions
    • The Notion of a “Configuration”
    • Analysis and Elaboration of Turing’s Definitions
    • Connecting to Human “Computers” (Mathematicians)
  • Chapter 4: Section 2: Definitions
    • Computable Numbers, Computable Sequences
    • Circular and Circle-Free Machines
    • The Idea of a “Computable Function”
    • Detailed Breakdown of Turing’s Formalism
  • Chapter 5: Section 3: Examples of Computing Machines
    • Step-by-step walkthrough of Turing’s simple examples (e.g., sequences of 0s and 1s)
    • How these examples illustrate the machine’s operation
    • Understanding the “State” and “Symbol” tables
  • Chapter 6: Section 4: Universal Computing Machine
    • The Concept of a Machine that Can Simulate Any Other Machine
    • The Encoding of Machine Descriptions (Standard Description, SD)
    • The Construction and Operation of the Universal Machine (U)
    • The Profound Implications of Universality
  • Chapter 7: Section 5: Enumeration of Computable Sequences
    • Listing all possible computable numbers
    • The Countability of Turing Machines
    • The Limits of Enumeration
  • Chapter 8: Section 6: The Diagonal Process
    • Cantor’s Diagonalization Applied to Computability
    • Constructing a Number that No Machine Can Compute
    • The Existence of Non-Computable Numbers
  • Chapter 9: Section 7: Application to the Entscheidungsproblem
    • Relating Computability to Logic
    • Defining the “Stopping Problem” (Halting Problem)
    • Proof that the Halting Problem is Undecidable
    • The Direct Implication for Hilbert’s Decision Problem
  • Chapter 10: Section 8: The Solvability of Problems
    • Further Discussion of Undecidable Problems
    • The Limits of Formal Systems and Algorithms
  • Chapter 11: Appendix: The Computable Numbers are Enumerable
    • Turing’s Response to Church’s Thesis
    • Connecting his work to Lambda Calculus and recursive functions

• Part III: The Legacy and Impact of Turing’s Ideas

  • Chapter 12: The Church-Turing Thesis
    • The Enduring Significance of this Conjecture
    • Its Role in Computer Science and Logic
    • The Concept of “Algorithm” and “Computability”
  • Chapter 13: From Theory to Practice: The Stored-Program Computer
    • Turing’s Influence on Von Neumann Architecture
    • The ACE (Automatic Computing Engine) and Early Computers
    • The Practical Realization of the Universal Machine
  • Chapter 14: Beyond Computation: Turing’s Later Work
    • Codebreaking at Bletchley Park
    • Artificial Intelligence and the Turing Test
    • Mathematical Biology (Morphogenesis)
  • Chapter 15: Turing’s Enduring Relevance
    • The Foundations of Computer Science
    • The Limits of What Can Be Computed
    • The Philosophical Implications of Computability

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