Turing's Toy - The Story of a Mathematical Idea That Changed the World

Explore the groundbreaking story of Alan Turing's 1936 paper that introduced the concept of the Turing machine, a pivotal moment in computer science history. Delve into the historical context, implications, and intricate details of Turing's fictional machine that accidentally changed the course of history. Learn about the Hilbert Program, Principia Mathematica, the Decision Problem, and how Turing's work relates to Kurt Gödel's contributions. Discover the inner workings of the Turing machine, including its first iteration, number production, and the concept of the Universal Machine. Examine the philosophical implications of Turing's work, the development of circular and circle-free machines, and the construction of the "H" machine. Gain insights into Turing's conclusions, the parallel development of Alonzo Church's Lambda Calculus, and Turing's subsequent work. Conclude with a reflection on David Hilbert's legacy and the impact of these mathematical ideas on the world.

Intro
The "Hilbert Program"
Principia Mathematica
The Decision Problem Remains...
Kurt Gödel
Alan Turing
The Turing Machine is Born
The First Machine
Producing a Number
Computing 0.001011011101111...
The Standardized Table
Table in Standard Format
Serializing a Table
The Universal Machine
Description Numbers
Philosophy and the Turing Machine
Circular and Circle-Free Machines
Building the Machine "H"
Pseudo Code for "H"
Turing's Conclusion
Alonzo Church and Lambda Calculus
Turing After the Paper
David Hilbert and the Nazis
Hilbert's Tombstone in Göttingen