Alan Turing Enigma Chris Jager

Contents Introduction Introduction Childhood & Youth Childhood & Youth The Turing Machine The Turing Machine Second World War Second World War Turing Test Turing Test Turing’s Death Turing’s Death References References Questions Questions

Introduction Paper not finished (yet) Paper not finished (yet) A lot of information about the works of Turing A lot of information about the works of Turing Less information about the person itself Less information about the person itself

Childhood & Youth (1) Father, Julius Mathison Turing, Indian Civil Service Father, Julius Mathison Turing, Indian Civil Service Mother, Ethel Sarah Stoney, daughter of chief engineer of the Madras Railways Mother, Ethel Sarah Stoney, daughter of chief engineer of the Madras Railways Brother, John Turing, London solicitor Brother, John Turing, London solicitor Alan Turing, born at 23 rd of june, 1912 Alan Turing, born at 23 rd of june, 1912

Childhood & Youth (2) Father went to India Father went to India Grown up in different kind of families Grown up in different kind of families First Science book resulted in experiments First Science book resulted in experiments “If he is to be solely a Scientific Specialist, he is wasting his time at a Public School “ “If he is to be solely a Scientific Specialist, he is wasting his time at a Public School “

Turing Machine (1) Christopher Morcom’s death Christopher Morcom’s death 1931 King’s College 1931 King’s College “Could there exist, at least in principle, a definite method or process by which it could be decided whether any given mathematical assertion was provable” “Could there exist, at least in principle, a definite method or process by which it could be decided whether any given mathematical assertion was provable”

Turing Machine (2) Kurt Gödel : Kurt Gödel : “Any consistent system cannot be used to prove its own consistency““Any consistent system cannot be used to prove its own consistency“ “In any consistent formalization of mathematics that is sufficiently strong to define the concept of natural numbers, one can construct a statement that can be neither proved nor disproved within that system““In any consistent formalization of mathematics that is sufficiently strong to define the concept of natural numbers, one can construct a statement that can be neither proved nor disproved within that system“consistentnatural numbersconsistentnatural numbers

Turing Machine (3) 1: A tape which is divided into cells, one next to the other. 1: A tape which is divided into cells, one next to the other. 2: A head that can read and write symbols on the tape and move left and right. 2: A head that can read and write symbols on the tape and move left and right. 3: A state register that stores the state of the Turing machine 3: A state register that stores the state of the Turing machine 4: An action table (or transition function) 4: An action table (or transition function)

Turing Machine (4) Universal Turing Machine Universal Turing Machine Programs Programs Paper in 1936: no method could decide whether an assertion is provable, “On Computable Numbers, with an Application to the Entscheidungsproblem” at Princeton University Paper in 1936: no method could decide whether an assertion is provable, “On Computable Numbers, with an Application to the Entscheidungsproblem” at Princeton UniversityEntscheidungsproblem Lambda-calculus of Church Lambda-calculus of Church Church-Turing thesis: “ Church-Turing thesis: “

Turing Machine (5) Church-Turing thesis: “Any computer program in any of the conventional programming languages can be translated into a Turing machine, and any Turing machine can be translated into most programming languages, so the thesis is equivalent to saying that the conventional programming languages are sufficient to express any algorithm” Church-Turing thesis: “Any computer program in any of the conventional programming languages can be translated into a Turing machine, and any Turing machine can be translated into most programming languages, so the thesis is equivalent to saying that the conventional programming languages are sufficient to express any algorithm”

Turing Machine (6) Mechanical Turing Machine Mechanical Turing Machine

Second World War (1) 1918 Arthur Scherbius built the Enigma 1918 Arthur Scherbius built the Enigma Before that, all coding systems were lingual based Before that, all coding systems were lingual based Advantage Enigma: Enigma machine useless when stolen, cypher produced was very difficult Advantage Enigma: Enigma machine useless when stolen, cypher produced was very difficult Polish were good at cracking codes Polish were good at cracking codes

Second World War (2)

Second World War (3) Polish enable to crack the code Polish enable to crack the code Bought a commercial Enigma Bought a commercial Enigma Called for help: mathematicians Called for help: mathematicians The French bought keys, couldn’t do anything with it The French bought keys, couldn’t do anything with it Poland foresaw its invasion by Germany: gave all knowledge to England and France, destroyed it afterwards (1939) Poland foresaw its invasion by Germany: gave all knowledge to England and France, destroyed it afterwards (1939)

Second World War (4) Enigma machine exists out of: Enigma machine exists out of: PlugboardPlugboard 3/ 4/ 5 rotors3/ 4/ 5 rotors “mirror” rotor“mirror” rotor

Second World War (5) 1939 Turing was asked to help to crack the Enigma 1939 Turing was asked to help to crack the Enigma Built with a team the Colussus, the first programmable computer Built with a team the Colussus, the first programmable computer Based on: Based on: his own 1936 concept of the universal machinehis own 1936 concept of the universal machine the potential speed and reliability of electronic technologythe potential speed and reliability of electronic technology the inefficiency in designing different machines for different logical processesthe inefficiency in designing different machines for different logical processes Cyphercode could be decrypted from 1943 Cyphercode could be decrypted from 1943 All computers were destroyed, ordered by Churchill All computers were destroyed, ordered by Churchill

Second World War (6)

Second World War (7)

Second World War (8)

Turing Test (1) Because of the construction of the Colussus Turing thought it could be possible to construct a computer with the mind of a human being Because of the construction of the Colussus Turing thought it could be possible to construct a computer with the mind of a human being Wasn’t focused anymore on what a TM could NOT do, but could do Wasn’t focused anymore on what a TM could NOT do, but could do “Turing was convinced that if a computer could do all mathematical operations, it could also do anything a person can do, a still highly controversial opinion“ “Turing was convinced that if a computer could do all mathematical operations, it could also do anything a person can do, a still highly controversial opinion“

Turing Test (2) Manchester University Manchester University Neurology & physiology Neurology & physiology Neville Johnson Neville Johnson Turing liked running very much: he even ran the Marathon Turing liked running very much: he even ran the Marathon andrews.ac.uk/history/Miscellaneous /Turing/Running.html andrews.ac.uk/history/Miscellaneous /Turing/Running.htmlhttp://www-history.mcs.st- andrews.ac.uk/history/Miscellaneous /Turing/Running.htmlhttp://www-history.mcs.st- andrews.ac.uk/history/Miscellaneous /Turing/Running.html

Turing Test (3) 1950 “Computing Machinery and Intelligence” 1950 “Computing Machinery and Intelligence” Turing Test Turing Test 2000 a computer could pass 2000 a computer could pass Round 1990 no computer came near breaking through the test, and still there isn’t any computer who can Round 1990 no computer came near breaking through the test, and still there isn’t any computer who can

Turing Test (4) Focused more on biology Focused more on biology Used computers for his equations Used computers for his equations First one who used computers for that purpose First one who used computers for that purpose

Turing’s Death Arrested for being homosexual Arrested for being homosexual Accepted a year being treated with oestrogen Accepted a year being treated with oestrogen Because of Cold War he was excluded from main projects Because of Cold War he was excluded from main projects He wasn’t accepted anymore He wasn’t accepted anymore Committed suicide by eating a cyanide poisoned apple, 8th of June 1954 Committed suicide by eating a cyanide poisoned apple, 8th of June 1954

References Turing/ Turing/ Turing/ Turing/ tml tml tml tml andrews.ac.uk/history/Miscellaneous /Turing/Running.html andrews.ac.uk/history/Miscellaneous /Turing/Running.html andrews.ac.uk/history/Miscellaneous /Turing/Running.html andrews.ac.uk/history/Miscellaneous /Turing/Running.html

Questions?