A Brief, Incomplete, and Mostly Wrong Introduction to Alan Turing's Work
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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.”