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Table of Contents
Part I: How Do We Compute? What Can We Prove?
1. Alan Mathison Turing
2. On Computable Numbers, with an Application to the Entscheidungsproblem
3. On Computable Numbers, with an Application to the Entscheidungsproblem
correction
4. Review of Turing 1936-7
5. Computability and ¿-definability
6. The p-function in ¿-K-conversion
7. Systems of Logic based on Ordinals
8. A Formal Theorem in Church's Theory of Types
9. The Use of Dots as Brackets in Church's System
10. Practical Forms of Type Theory
11. The Reform of Mathematical Notation
Part II: Hiding and Unhiding Information: Cryptology, Complexity and Number Theory. 1. On the Gaussian Error Function
2. A Method for the Calculation of the Zeta-function
3. Some Calculations of the Riemann Zeta-function
4. On a Theorem of Littlewood
5. The Word Problem in Semi-groups with Cancellation
6. Solvable and Unsolvable Problems
7. The Word Problem in Compact Groups
8. On Permutation Groups
9. Rounding-off Errors in Matrix Processes
10. A Note on Normal Numbers
11. Turing's treatise on the Enigma (Prof's Book); Report by Turing on U.S. Navy cryptanalytic work and their machinery, November 1942; Speech System 'Delilah'
report on progress, 6 June 1944; Checking a Large Routine; An early program proof by Alan Turing; Programmers' Handbook for the Manchester electronic computer; Local Programming Methods and Conventions
Part III: Building a Brain: Intelligent Machines, Practice and Theory. 1. Lecture to the London Mathematical Society
2. Intelligent Machinery
3. Computing Machinery and Intelligence
4. Chess; Solvable and Unsolvable Problems
5. Intelligent Machinery: A heretical theory; Can digital computers think?; Can automatic calculating machines be said to think?
6. Some Remarks on the Undecidability Results
Part IV: The Mathematics of Emergence: The Mysteries of Morphogenesis. 1. The Chemical Basis of Morphogenesis
2. A Diffusion Reaction Theory of Morphogenesis in Plants
3. Morphogen Theory of Phyllotaxis; Geometrical and Descriptive Phyllotaxis; Chemical Theory of Morphogenesis; A Solution of the Morphogenetical Equations for the Case of Spherical Symmetry
4. Outline of the Development of the Daisy.
1. Alan Mathison Turing
2. On Computable Numbers, with an Application to the Entscheidungsproblem
3. On Computable Numbers, with an Application to the Entscheidungsproblem
correction
4. Review of Turing 1936-7
5. Computability and ¿-definability
6. The p-function in ¿-K-conversion
7. Systems of Logic based on Ordinals
8. A Formal Theorem in Church's Theory of Types
9. The Use of Dots as Brackets in Church's System
10. Practical Forms of Type Theory
11. The Reform of Mathematical Notation
Part II: Hiding and Unhiding Information: Cryptology, Complexity and Number Theory. 1. On the Gaussian Error Function
2. A Method for the Calculation of the Zeta-function
3. Some Calculations of the Riemann Zeta-function
4. On a Theorem of Littlewood
5. The Word Problem in Semi-groups with Cancellation
6. Solvable and Unsolvable Problems
7. The Word Problem in Compact Groups
8. On Permutation Groups
9. Rounding-off Errors in Matrix Processes
10. A Note on Normal Numbers
11. Turing's treatise on the Enigma (Prof's Book); Report by Turing on U.S. Navy cryptanalytic work and their machinery, November 1942; Speech System 'Delilah'
report on progress, 6 June 1944; Checking a Large Routine; An early program proof by Alan Turing; Programmers' Handbook for the Manchester electronic computer; Local Programming Methods and Conventions
Part III: Building a Brain: Intelligent Machines, Practice and Theory. 1. Lecture to the London Mathematical Society
2. Intelligent Machinery
3. Computing Machinery and Intelligence
4. Chess; Solvable and Unsolvable Problems
5. Intelligent Machinery: A heretical theory; Can digital computers think?; Can automatic calculating machines be said to think?
6. Some Remarks on the Undecidability Results
Part IV: The Mathematics of Emergence: The Mysteries of Morphogenesis. 1. The Chemical Basis of Morphogenesis
2. A Diffusion Reaction Theory of Morphogenesis in Plants
3. Morphogen Theory of Phyllotaxis; Geometrical and Descriptive Phyllotaxis; Chemical Theory of Morphogenesis; A Solution of the Morphogenetical Equations for the Case of Spherical Symmetry
4. Outline of the Development of the Daisy.