A Brief, Incomplete, and Mostly Wrong Introduction to Alan Turing's Work
-
Upload
phil-calcado -
Category
Technology
-
view
1.269 -
download
0
Transcript of A Brief, Incomplete, and Mostly Wrong Introduction to Alan Turing's Work
![Page 1: A Brief, Incomplete, and Mostly Wrong Introduction to Alan Turing's Work](https://reader033.fdocuments.in/reader033/viewer/2022052823/5556836fd8b42a182f8b48d2/html5/thumbnails/1.jpg)
A Brief, Incomplete, and Mostly Wrong
Introduction to Alan Turing's Work
Phil Calçado – SoundCloud@pcalcado
http://philcalcado.com
![Page 2: A Brief, Incomplete, and Mostly Wrong Introduction to Alan Turing's Work](https://reader033.fdocuments.in/reader033/viewer/2022052823/5556836fd8b42a182f8b48d2/html5/thumbnails/2.jpg)
Sets are weird.
![Page 3: A Brief, Incomplete, and Mostly Wrong Introduction to Alan Turing's Work](https://reader033.fdocuments.in/reader033/viewer/2022052823/5556836fd8b42a182f8b48d2/html5/thumbnails/3.jpg)
How many numbers are there between
1 and 3?
![Page 4: A Brief, Incomplete, and Mostly Wrong Introduction to Alan Turing's Work](https://reader033.fdocuments.in/reader033/viewer/2022052823/5556836fd8b42a182f8b48d2/html5/thumbnails/4.jpg)
Georg Cantor
![Page 5: A Brief, Incomplete, and Mostly Wrong Introduction to Alan Turing's Work](https://reader033.fdocuments.in/reader033/viewer/2022052823/5556836fd8b42a182f8b48d2/html5/thumbnails/5.jpg)
How many numbers are there between
4.4 and 4.5?
![Page 6: A Brief, Incomplete, and Mostly Wrong Introduction to Alan Turing's Work](https://reader033.fdocuments.in/reader033/viewer/2022052823/5556836fd8b42a182f8b48d2/html5/thumbnails/6.jpg)
4.4...00014.4...0002
...
4.49...0001...
![Page 7: A Brief, Incomplete, and Mostly Wrong Introduction to Alan Turing's Work](https://reader033.fdocuments.in/reader033/viewer/2022052823/5556836fd8b42a182f8b48d2/html5/thumbnails/7.jpg)
Now that's some crazy
shit.
![Page 8: A Brief, Incomplete, and Mostly Wrong Introduction to Alan Turing's Work](https://reader033.fdocuments.in/reader033/viewer/2022052823/5556836fd8b42a182f8b48d2/html5/thumbnails/8.jpg)
Barbie
![Page 9: A Brief, Incomplete, and Mostly Wrong Introduction to Alan Turing's Work](https://reader033.fdocuments.in/reader033/viewer/2022052823/5556836fd8b42a182f8b48d2/html5/thumbnails/9.jpg)
Math is hard, let's go shopping!
![Page 10: A Brief, Incomplete, and Mostly Wrong Introduction to Alan Turing's Work](https://reader033.fdocuments.in/reader033/viewer/2022052823/5556836fd8b42a182f8b48d2/html5/thumbnails/10.jpg)
David Hilbert
![Page 11: A Brief, Incomplete, and Mostly Wrong Introduction to Alan Turing's Work](https://reader033.fdocuments.in/reader033/viewer/2022052823/5556836fd8b42a182f8b48d2/html5/thumbnails/11.jpg)
For the mathematician there is no Ignorabimus.
![Page 12: A Brief, Incomplete, and Mostly Wrong Introduction to Alan Turing's Work](https://reader033.fdocuments.in/reader033/viewer/2022052823/5556836fd8b42a182f8b48d2/html5/thumbnails/12.jpg)
You lazy bastards
![Page 13: A Brief, Incomplete, and Mostly Wrong Introduction to Alan Turing's Work](https://reader033.fdocuments.in/reader033/viewer/2022052823/5556836fd8b42a182f8b48d2/html5/thumbnails/13.jpg)
„Wir müssen wissen, und wir werden wissen”
![Page 14: A Brief, Incomplete, and Mostly Wrong Introduction to Alan Turing's Work](https://reader033.fdocuments.in/reader033/viewer/2022052823/5556836fd8b42a182f8b48d2/html5/thumbnails/14.jpg)
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.)
![Page 15: A Brief, Incomplete, and Mostly Wrong Introduction to Alan Turing's Work](https://reader033.fdocuments.in/reader033/viewer/2022052823/5556836fd8b42a182f8b48d2/html5/thumbnails/15.jpg)
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.
![Page 16: A Brief, Incomplete, and Mostly Wrong Introduction to Alan Turing's Work](https://reader033.fdocuments.in/reader033/viewer/2022052823/5556836fd8b42a182f8b48d2/html5/thumbnails/16.jpg)
Bertrand Russel
![Page 17: A Brief, Incomplete, and Mostly Wrong Introduction to Alan Turing's Work](https://reader033.fdocuments.in/reader033/viewer/2022052823/5556836fd8b42a182f8b48d2/html5/thumbnails/17.jpg)
Sets can contain sets.
![Page 18: A Brief, Incomplete, and Mostly Wrong Introduction to Alan Turing's Work](https://reader033.fdocuments.in/reader033/viewer/2022052823/5556836fd8b42a182f8b48d2/html5/thumbnails/18.jpg)
Sets can contain
themselves.
![Page 19: A Brief, Incomplete, and Mostly Wrong Introduction to Alan Turing's Work](https://reader033.fdocuments.in/reader033/viewer/2022052823/5556836fd8b42a182f8b48d2/html5/thumbnails/19.jpg)
What about the set of all sets that do not contain themselves? Does it contain itself?
![Page 20: A Brief, Incomplete, and Mostly Wrong Introduction to Alan Turing's Work](https://reader033.fdocuments.in/reader033/viewer/2022052823/5556836fd8b42a182f8b48d2/html5/thumbnails/20.jpg)
![Page 21: A Brief, Incomplete, and Mostly Wrong Introduction to Alan Turing's Work](https://reader033.fdocuments.in/reader033/viewer/2022052823/5556836fd8b42a182f8b48d2/html5/thumbnails/21.jpg)
![Page 22: A Brief, Incomplete, and Mostly Wrong Introduction to Alan Turing's Work](https://reader033.fdocuments.in/reader033/viewer/2022052823/5556836fd8b42a182f8b48d2/html5/thumbnails/22.jpg)
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
![Page 23: A Brief, Incomplete, and Mostly Wrong Introduction to Alan Turing's Work](https://reader033.fdocuments.in/reader033/viewer/2022052823/5556836fd8b42a182f8b48d2/html5/thumbnails/23.jpg)
It's not technically cheating...
![Page 24: A Brief, Incomplete, and Mostly Wrong Introduction to Alan Turing's Work](https://reader033.fdocuments.in/reader033/viewer/2022052823/5556836fd8b42a182f8b48d2/html5/thumbnails/24.jpg)
Kurt Gödel
![Page 25: A Brief, Incomplete, and Mostly Wrong Introduction to Alan Turing's Work](https://reader033.fdocuments.in/reader033/viewer/2022052823/5556836fd8b42a182f8b48d2/html5/thumbnails/25.jpg)
Yo, Russel, I'm gonna let you finish, but no formal system extending basic arithmetic can be used to prove
its own consistency.
![Page 26: A Brief, Incomplete, and Mostly Wrong Introduction to Alan Turing's Work](https://reader033.fdocuments.in/reader033/viewer/2022052823/5556836fd8b42a182f8b48d2/html5/thumbnails/26.jpg)
![Page 27: A Brief, Incomplete, and Mostly Wrong Introduction to Alan Turing's Work](https://reader033.fdocuments.in/reader033/viewer/2022052823/5556836fd8b42a182f8b48d2/html5/thumbnails/27.jpg)
Whatever.
![Page 28: A Brief, Incomplete, and Mostly Wrong Introduction to Alan Turing's Work](https://reader033.fdocuments.in/reader033/viewer/2022052823/5556836fd8b42a182f8b48d2/html5/thumbnails/28.jpg)
“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.”
![Page 29: A Brief, Incomplete, and Mostly Wrong Introduction to Alan Turing's Work](https://reader033.fdocuments.in/reader033/viewer/2022052823/5556836fd8b42a182f8b48d2/html5/thumbnails/29.jpg)
Alan Turing
![Page 30: A Brief, Incomplete, and Mostly Wrong Introduction to Alan Turing's Work](https://reader033.fdocuments.in/reader033/viewer/2022052823/5556836fd8b42a182f8b48d2/html5/thumbnails/30.jpg)
“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.”
![Page 31: A Brief, Incomplete, and Mostly Wrong Introduction to Alan Turing's Work](https://reader033.fdocuments.in/reader033/viewer/2022052823/5556836fd8b42a182f8b48d2/html5/thumbnails/31.jpg)
![Page 32: A Brief, Incomplete, and Mostly Wrong Introduction to Alan Turing's Work](https://reader033.fdocuments.in/reader033/viewer/2022052823/5556836fd8b42a182f8b48d2/html5/thumbnails/32.jpg)
Imagine a machine.
![Page 33: A Brief, Incomplete, and Mostly Wrong Introduction to Alan Turing's Work](https://reader033.fdocuments.in/reader033/viewer/2022052823/5556836fd8b42a182f8b48d2/html5/thumbnails/33.jpg)
It reads and writes from and to an infinite paper
tape.
![Page 34: A Brief, Incomplete, and Mostly Wrong Introduction to Alan Turing's Work](https://reader033.fdocuments.in/reader033/viewer/2022052823/5556836fd8b42a182f8b48d2/html5/thumbnails/34.jpg)
The tape is the machine's memory.
![Page 35: A Brief, Incomplete, and Mostly Wrong Introduction to Alan Turing's Work](https://reader033.fdocuments.in/reader033/viewer/2022052823/5556836fd8b42a182f8b48d2/html5/thumbnails/35.jpg)
It writes to the tape accordingly to some
simple rules defined by configuration.
![Page 36: A Brief, Incomplete, and Mostly Wrong Introduction to Alan Turing's Work](https://reader033.fdocuments.in/reader033/viewer/2022052823/5556836fd8b42a182f8b48d2/html5/thumbnails/36.jpg)
Now imagine a machine that can simulate other
machines.
![Page 37: A Brief, Incomplete, and Mostly Wrong Introduction to Alan Turing's Work](https://reader033.fdocuments.in/reader033/viewer/2022052823/5556836fd8b42a182f8b48d2/html5/thumbnails/37.jpg)
By reading the desired configuration from the
tape.
![Page 38: A Brief, Incomplete, and Mostly Wrong Introduction to Alan Turing's Work](https://reader033.fdocuments.in/reader033/viewer/2022052823/5556836fd8b42a182f8b48d2/html5/thumbnails/38.jpg)
Question: Is it possible to create a machine that
examines another machine's configuration and input and
verify if it halts?
![Page 39: A Brief, Incomplete, and Mostly Wrong Introduction to Alan Turing's Work](https://reader033.fdocuments.in/reader033/viewer/2022052823/5556836fd8b42a182f8b48d2/html5/thumbnails/39.jpg)
“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.”
![Page 40: A Brief, Incomplete, and Mostly Wrong Introduction to Alan Turing's Work](https://reader033.fdocuments.in/reader033/viewer/2022052823/5556836fd8b42a182f8b48d2/html5/thumbnails/40.jpg)
tl;dr: No, sorry.
![Page 41: A Brief, Incomplete, and Mostly Wrong Introduction to Alan Turing's Work](https://reader033.fdocuments.in/reader033/viewer/2022052823/5556836fd8b42a182f8b48d2/html5/thumbnails/41.jpg)
Now imagine a machine that can simulate other
machines.
By reading the desired configuration from the
tape.
![Page 42: A Brief, Incomplete, and Mostly Wrong Introduction to Alan Turing's Work](https://reader033.fdocuments.in/reader033/viewer/2022052823/5556836fd8b42a182f8b48d2/html5/thumbnails/42.jpg)
i.e.
Imagine a general-purpose
computer.
![Page 43: A Brief, Incomplete, and Mostly Wrong Introduction to Alan Turing's Work](https://reader033.fdocuments.in/reader033/viewer/2022052823/5556836fd8b42a182f8b48d2/html5/thumbnails/43.jpg)
Howard H. Aiken
![Page 44: A Brief, Incomplete, and Mostly Wrong Introduction to Alan Turing's Work](https://reader033.fdocuments.in/reader033/viewer/2022052823/5556836fd8b42a182f8b48d2/html5/thumbnails/44.jpg)
“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.”
![Page 45: A Brief, Incomplete, and Mostly Wrong Introduction to Alan Turing's Work](https://reader033.fdocuments.in/reader033/viewer/2022052823/5556836fd8b42a182f8b48d2/html5/thumbnails/45.jpg)
![Page 46: A Brief, Incomplete, and Mostly Wrong Introduction to Alan Turing's Work](https://reader033.fdocuments.in/reader033/viewer/2022052823/5556836fd8b42a182f8b48d2/html5/thumbnails/46.jpg)
![Page 47: A Brief, Incomplete, and Mostly Wrong Introduction to Alan Turing's Work](https://reader033.fdocuments.in/reader033/viewer/2022052823/5556836fd8b42a182f8b48d2/html5/thumbnails/47.jpg)
![Page 49: A Brief, Incomplete, and Mostly Wrong Introduction to Alan Turing's Work](https://reader033.fdocuments.in/reader033/viewer/2022052823/5556836fd8b42a182f8b48d2/html5/thumbnails/49.jpg)
http://amzn.to/sLiy1Y
![Page 50: A Brief, Incomplete, and Mostly Wrong Introduction to Alan Turing's Work](https://reader033.fdocuments.in/reader033/viewer/2022052823/5556836fd8b42a182f8b48d2/html5/thumbnails/50.jpg)
http://amzn.to/rFpXVk
![Page 51: A Brief, Incomplete, and Mostly Wrong Introduction to Alan Turing's Work](https://reader033.fdocuments.in/reader033/viewer/2022052823/5556836fd8b42a182f8b48d2/html5/thumbnails/51.jpg)
http://bit.ly/s643dS