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turing.pdf

Avatar for Phil Calçado Phil Calçado
November 03, 2011
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 turing.pdf

Avatar for Phil Calçado

Phil Calçado

November 03, 2011
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  1. A Brief, Incomplete, and Mostly Wrong Introduction to Alan Turing's

    Work Phil Calçado – SoundCloud @pcalcado http://philcalcado.com
  2. 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.)
  3. 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.
  4. What about the set of all sets that do not

    contain themselves? Does it contain itself?
  5. 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
  6. Yo, Russel, I'm gonna let you finish, but no formal

    system extending basic arithmetic can be used to prove its own consistency.
  7. “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.”
  8. “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.”
  9. Question: Is it possible to create a machine that examines

    another machine's configuration and input and verify if it halts?
  10. “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.”
  11. Now imagine a machine that can simulate other machines. By

    reading the desired configuration from the tape.
  12. “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.”