A Brief, Incomplete,
and Mostly Wrong
Introduction to Alan
Turing's Work
Phil Calçado – SoundCloud
@pcalcado
http://philca...
Sets are weird.
How many numbers are there between
1 and 3?
Georg Cantor
How many numbers are there between
4.4 and 4.5?
4.4...0001
4.4...0002
...
4.49...0001
...
Now that's
some crazy
shit.
Barbie
Math is hard,
let's go
shopping!
David Hilbert
For the
mathematician
there is no
Ignorabimus.
You lazy
bastards
„Wir müssen
wissen, und wir
werden wissen”
Given a diophantine equation with any number of
unknown quantities and with rational integral
numerical coefficients: To d...
10. Determination of the Solvability
of a Diophantine Equation
(Entscheidung der Losbarkeit einer
diophantischen Gleichung...
Bertrand Russel
Sets can
contain sets.
Sets can
contain
themselves.
What about the
set of all
sets that do
not contain
themselves?
Does it
contain
itself?
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
It's not
technically
cheating...
Kurt Gödel
Yo, Russel, I'm
gonna let you
finish, but no
formal system
extending basic
arithmetic can
be used to prove
its own
consist...
Whatever.
“The end the work was
finished, but my intellect
never quite recovered from the
strain. I have been ever since
definitely ...
Alan Turing
“It is of fundamental
importance for the character
of this problem that only
mechanical calculations
according to given
in...
Imagine a
machine.
It reads and writes from
and to an infinite paper
tape.
The tape is the machine's
memory.
It writes to the tape
accordingly to some
simple rules defined by
configuration.
Now imagine a machine
that can simulate other
machines.
By reading the desired
configuration from the
tape.
Question: Is it possible to
create a machine that
examines another machine's
configuration and input and
verify if it halt...
“There's no general process
for determining whether the
machine might scan a character
it's not expecting, or gets
into an...
tl;dr: No,
sorry.
Now imagine a machine
that can simulate other
machines.
By reading the desired
configuration from the
tape.
i.e.
Imagine a
general-purpose
computer.
Howard H. Aiken
“If the basic
logics of a
machine designed
for solution of
equations coincide
with the logics of
a machine for a
departmen...
http://amzn.to/s7mx97
http://amzn.to/sLiy1Y
http://amzn.to/rFpXVk
http://bit.ly/s643dS
http://soundcloud.com/jobs
A Brief, Incomplete, and Mostly Wrong Introduction to Alan Turing's Work
A Brief, Incomplete, and Mostly Wrong Introduction to Alan Turing's Work
A Brief, Incomplete, and Mostly Wrong Introduction to Alan Turing's Work
A Brief, Incomplete, and Mostly Wrong Introduction to Alan Turing's Work
A Brief, Incomplete, and Mostly Wrong Introduction to Alan Turing's Work
A Brief, Incomplete, and Mostly Wrong Introduction to Alan Turing's Work
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. 1. A Brief, Incomplete, and Mostly Wrong Introduction to Alan Turing's Work Phil Calçado – SoundCloud @pcalcado http://philcalcado.com
  2. 2. Sets are weird.
  3. 3. How many numbers are there between 1 and 3?
  4. 4. Georg Cantor
  5. 5. How many numbers are there between 4.4 and 4.5?
  6. 6. 4.4...0001 4.4...0002 ... 4.49...0001 ...
  7. 7. Now that's some crazy shit.
  8. 8. Barbie
  9. 9. Math is hard, let's go shopping!
  10. 10. David Hilbert
  11. 11. For the mathematician there is no Ignorabimus.
  12. 12. You lazy bastards
  13. 13. „Wir müssen wissen, und wir werden wissen”
  14. 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. 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. 16. Bertrand Russel
  17. 17. Sets can contain sets.
  18. 18. Sets can contain themselves.
  19. 19. What about the set of all sets that do not contain themselves? Does it contain itself?
  20. 20. 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
  21. 21. It's not technically cheating...
  22. 22. Kurt Gödel
  23. 23. Yo, Russel, I'm gonna let you finish, but no formal system extending basic arithmetic can be used to prove its own consistency.
  24. 24. Whatever.
  25. 25. “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.”
  26. 26. Alan Turing
  27. 27. “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.”
  28. 28. Imagine a machine.
  29. 29. It reads and writes from and to an infinite paper tape.
  30. 30. The tape is the machine's memory.
  31. 31. It writes to the tape accordingly to some simple rules defined by configuration.
  32. 32. Now imagine a machine that can simulate other machines.
  33. 33. By reading the desired configuration from the tape.
  34. 34. Question: Is it possible to create a machine that examines another machine's configuration and input and verify if it halts?
  35. 35. “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.”
  36. 36. tl;dr: No, sorry.
  37. 37. Now imagine a machine that can simulate other machines. By reading the desired configuration from the tape.
  38. 38. i.e. Imagine a general-purpose computer.
  39. 39. Howard H. Aiken
  40. 40. “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.”
  41. 41. http://amzn.to/s7mx97
  42. 42. http://amzn.to/sLiy1Y
  43. 43. http://amzn.to/rFpXVk
  44. 44. http://bit.ly/s643dS
  45. 45. http://soundcloud.com/jobs

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