A Brief, Incomplete, and Mostly Wrong Introduction to Alan Turing's Work
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This document provides a brief and incomplete introduction to the work of Alan Turing. It discusses ideas from set theory by Cantor and Russell. It mentions Turing's proof that there is no general algorithm to determine if a computing machine will halt on all inputs. The document notes Turing conceived of a universal computing machine that could simulate any other machine by reading its configuration from an infinite tape, and highlights the coincidence that the same logical principles apply to both mathematical problem solving and department store operations.
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A Brief, Incomplete, and Mostly Wrong Introduction to Alan Turing's Work
- 1. A Brief, Incomplete, and Mostly Wrong Introduction to Alan Turing's Work Phil Calçado – SoundCloud @pcalcado http://philcalcado.com
- 3. How many numbers are there between 1 and 3?
- 4. Georg Cantor
- 5. How many numbers are there between 4.4 and 4.5?
- 8. Barbie
- 9. Math is hard, let's go shopping!
- 10. David Hilbert
- 11. For the mathematician there is no Ignorabimus.
- 13. „Wir müssen wissen, und wir werden wissen”
- 14. Given a diophantine equation with any number of unknown quantities and with rational integral numerical coefficients: To devise a process according to which it can be determined by a finite number of operations whether the equation is solvable in rational integers. 10. Determination of the Solvability of a Diophantine Equation (Entscheidung der Losbarkeit einer diophantischen Gleichung.)
- 15. 10. Determination of the Solvability of a Diophantine Equation (Entscheidung der Losbarkeit einer diophantischen Gleichung.) Given a diophantine equation with any number of unknown quantities and with rational integral numerical coefficients: To devise a process according to which it can be determined by a finite number of operations whether the equation is solvable in rational integers.
- 16. Bertrand Russel
- 19. What about the set of all sets that do not contain themselves? Does it contain itself?
- 22. Types of sets: ● Type 1: Sets of stuff that are not sets ● Type 2: Sets of Type 1 sets ● Type 3: Sets of Type 2 sets
- 24. Kurt Gödel
- 25. Yo, Russel, I'm gonna let you finish, but no formal system extending basic arithmetic can be used to prove its own consistency.
- 27. Whatever.
- 28. “The end the work was finished, but my intellect never quite recovered from the strain. I have been ever since definitely less capable of dealing with difficult abstractions than I was before. This is part, though by no means the whole, of the reason for the change in the nature of my work.”
- 29. Alan Turing
- 30. “It is of fundamental importance for the character of this problem that only mechanical calculations according to given instructions [...] are admitted as tools for the proof.”
- 33. It reads and writes from and to an infinite paper tape.
- 34. The tape is the machine's memory.
- 35. It writes to the tape accordingly to some simple rules defined by configuration.
- 36. Now imagine a machine that can simulate other machines.
- 37. By reading the desired configuration from the tape.
- 38. Question: Is it possible to create a machine that examines another machine's configuration and input and verify if it halts?
- 39. “There's no general process for determining whether the machine might scan a character it's not expecting, or gets into an infinite loop printing blanks, whether it crashes, burns, goes belly up, or ascends to the great bit bucket in the sky.”
- 41. Now imagine a machine that can simulate other machines. By reading the desired configuration from the tape.
- 43. Howard H. Aiken
- 44. “If the basic logics of a machine designed for solution of equations coincide with the logics of a machine for a department store, I'd regard this as the most amazing coincidence I've ever encountered.”