ALAN TURING AND HIS LEGACY IDT Open Seminar ALAN TURING AND HIS LEGACY 100 Years Turing celebration Gordana Dodig Crnkovic, Computer Science and Network Department Mälardalen University March 8th 2012 http://www.mrtc.mdh.se/~gdc/work/TuringCentenary.pdf http://www.mrtc.mdh.se/~gdc/work/TuringMachine.pdf

2012 ALAN TURING YEAR 2012 has been officially declared Alan Turing Year to celebrate the centenary of his birth. http://www.youtube.com/watch?v=3BEAxoknHgo (2 min) Alan Turing Documentary http://www.youtube.com/watch?v=iKk8qYIf4oI (4.27 min) Remembering Alan Turing

TURING RESOURCES Alan Turing as a founder of computability theory, mathematician, philosopher, codebreaker, natural philosopher, visionary man before his time: http://www.cs.usfca.edu/www.AlanTuring.net/turing_archive/index.html Jack Copeland and Diane Proudfoot http://www.turing.org.uk/turing The Alan Turing Home Page, Andrew Hodges

VIDEO http://www.youtube.com/watch?v=3BEAxoknHgo (2 min) Alan Turing Documentary Teaser http://www.youtube.com/watch?v=iKk8qYIf4oI (4.27 min) Remembering Alan Turing http://www.youtube.com/watch?v=61s2_UEhJg8&feature=related (6 min) The Dream Machine - BBC - Giant Brains 4 http://www.youtube.com/watch?v=S23yie-779k&feature=youtube_gdata_player (90 min) Turing Biography http://www.youtube.com/watch?v=jhhXy8TITqM&feature=related (44 min) Dangerous Knowledge (part 2) http://www.youtube.com/watch?v=WMhfuQ16SS0&feature=related (44 min) Dangerous Knowledge (part 1) http://www.youtube.com/watch?NR=1&v=i-1LxIEMC58&feature=endscreen (0.26 min) LEGO Turing machine http://www.youtube.com/watch?v=983lhh20rGY&feature=related (3 min) DNA Transcription and Protein Assembly http://www.youtube.com/watch?v=uya91t4rAlE&feature=related (3.17 min) (in Spanish, beautiful documentary material) http://www.youtube.com/watch?v=gZUxJ6rCx4A&feature=related (part 1) (5.53 min) (Italian, very good documentary material) http://www.youtube.com/watch?v=T8mxeIDw-0s&feature=related (part 2) (7.29 min) (Italian, rich documentary material) http://www.youtube.com/watch?v=AgW6HplOZV0&feature=youtubegdata_player (7.27 min) Alan Turing, Enigma http://www.youtube.com/watch?v=g7_WzNzHwJY (9.58 min) The Death of Alan Turing

TIMELINE OF ALAN TURING’S LIFE 1912 (23 June): Birth, London 1926-31: Sherborne School 1930: Death of friend Christopher Morcom 1931-34: Undergraduate at King's College, Cambridge University 1932-35: Quantum mechanics, probability, logic 1935: Elected fellow of King's College, Cambridge 1936: The Turing machine, computability, universal machine 1936-38: Princeton University. Ph.D. Logic, algebra, number theory 1938-39: Return to Cambridge. Introduced to German Enigma cipher machine 1939-40: The Bombe, machine for Enigma decryption 1939-42: Breaking of U-boat Enigma, saving battle of the Atlantic

TIMELINE OF ALAN TURING’S LIFE 1943-45: Chief Anglo-American crypto consultant. Electronic work. 1945: National Physical Laboratory, London 1946: Computer and software design, world leading. 1947-48: Programming, neural nets, and artificial intelligence 1948: Manchester University 1949: First serious mathematical use of a computer 1950: The Turing Test for machine intelligence 1951: Elected FRS. Non-linear theory of biological growth 1952: Arrested as a homosexual, loss of security clearance 1953-54: Unfinished work in biology and physics 1954 (7/6, 42 years old): Death (suicide) by cyanide poisoning

2009: APOLOGY In August 2009, petition started urging the British Government to posthumously apologize to Alan Turing for prosecuting him as a homosexual. The petition received thousands of signatures. Prime Minister Gordon Brown acknowledged the petition, releasing a statement on 10 September 2009 apologizing and describing Turing's treatment as "appalling":[ “Thousands of people have come together to demand justice for Alan Turing and recognition of the appalling* way he was treated. While Turing was dealt with under the law of the time and we can't put the clock back, his treatment was of course utterly unfair and I am pleased to have the chance to say how deeply sorry I and we all are for what happened to him ... So on behalf of the British government, and all those who live freely thanks to Alan's work I am very proud to say: we're sorry, you deserved so much better.” * = inexcusable

TURING’S GROUNDBREAKING CONTRIBUTIONS Logic (Computability) Computing (Universal Machine, Stored program, algorithm) Artificial intelligence (Turing Test, ”Unorganized machines”) Biology (Morphogenesis) Codebreaking during the WWII (Enigma machine)

TURING’S PUBLICATIONS Even though Turing made truly profound impact on all of the fields he was active in, his production of published articles was modest – less than 30 in total from 1937 to 1954.* *17 years, less than 2 papers published per year

Mathematical Logic (7) TURING’S PUBLICATIONS On Computable Numbers, with an application to the Entscheidungsproblem, Proc. Lond. Math. Soc. (2) 42 pp 230-265 (1936); correction ibid. 43, pp 544-546 (1937). Computability and λ-definability, J. Symbolic Logic 2 pp 153-163 (1937) The p-function in λ-K conversion, J. Symbolic Logic 2 p 164 (1937) Systems of logic based on ordinals, Proc. Lond. Math. Soc (2) 45 pp 161-228 (1939) This was also Turing's Princeton Ph.D. thesis (1938) (with M. H. A. Newman) A formal theorem in Church's theory of types, J. Symbolic Logic 7 pp 28-33 (1942) The use of dots as brackets in Church's system, J. Symbolic Logic 7, pp 146-156 (1942) Practical forms of type-theory, J. Symbolic Logic 13, pp 80-94 (1948)

Mechanical Intelligence (11) TURING’S PUBLICATIONS Mechanical Intelligence (11) Proposed Electronic Calculator, Turing's ACE computer plan, was produced as a typescript in early 1946, an internal National Physical Laboratory document. The original copy is in the (British) National Archives, in the file DSIR 10/385. The report was first published as the NPL report, Com. Sci. 57 (1972), with a foreword by Donald W. Davies. Lecture to the London Mathematical Society, February 1947. Published in 1986 as a companion to the 1946 report in the same MIT Press volume. Intelligent Machinery, report written by Turing for the National Physical Laboratory, 1948. The paper was first published in 1968, within the book Cybernetics: Key Papers, eds. C. R. Evans and A. D. J. Robertson, University Park Press, Baltimore Md.and Manchester (1968). Programmers' Handbook for the Manchester electronic computer, Manchester University Computing Laboratory (1950) Local Programming Methods and Conventions, in the Manchester University Computer Inaugural Conference, July 1951. Computing Machinery and Intelligence, Mind 49, pp 433-460 (1950) Chess, a subsection of chapter 25, Digital Computers Applied to Games, of Faster than Thought, ed. B. V. Bowden, Pitman, London (1953) Intelligent Machinery: A heretical theory, a talk given by Turing at Manchester, typescript in the Turing Archive, included in Sara Turing's memoir (see below). Not included in the Collected Works, but included (ed. B. J. Copeland) in K. Furukawa, D. Michie, S. Muggleton (eds.), Machine Intelligence 15, Oxford University Press (1999) and also in The Essential Turing. Can digital computers think?, Radio broadcast, 1951 not included in the Collected Works, but included (ed. B. J. Copeland) in K. Furukawa, D. Michie, S. Muggleton (eds.), Machine Intelligence 15, Oxford University Press (1999), and in The Essential Turing. Can automatic calculating machines be said to think? Radio broadcast, 1952: discussion with M. H. A. Newman, G. Jefferson, R. B. Braithwaite, not included in the Collected Works, but included (ed. B. J. Copeland) in K. Furukawa, D. Michie, S. Muggleton (eds.), Machine Intelligence 15, Oxford University Press (1999), and in The Essential Turing. Solvable and Unsolvable Problems, Science News 31, pp 7-23 (1954)

Pure Mathematics (8) TURING’S PUBLICATIONS Equivalence of Left and Right Almost Periodicity, J. London Math. Soc. 10, pp 284-285 (1935) Finite Approximations to Lie Groups, Ann. of Math. 39 (1), pp 105-111 (1938) The Extensions of a Group, Compositio Math. 5, pp 357-367 (1938) A Method for the Calculation of the Zeta-Function, Proc. London Math. Soc. (2) pp 180-197 (1943, submitted 1939) Rounding-off Errors in Matrix Processes, Quart. J. Mech. Appl. Math. 1, pp 287-308 (1948) The Word problem in Semi-Groups with Cancellation, Ann. of Math. 52 (2), pp 491-505 (1950) Some Calculations of the Riemann Zeta-function, Proc. London Math. Soc. (3) pp 99-117 (1953) Solvable and Unsolvable Problems, Science News 31, pp 7-23 (1954) is included in this volume of the Collected Works as well as in the Mechanical Intelligence volume.

Morphogenesis (1) TURING’S PUBLICATIONS The Chemical Basis of Morphogenesis, Phil. Trans. R. Soc. London B 237 pp 37-72 (1952). http://www.springerlink.com/content/n5702206663870g9/fulltext.pdf On Turing’s morphogenesis: http://www.wired.com/wiredscience/2011/02/turing-patterns/?pid=978&viewall=true http://www.wired.com/wiredscience/2011/02/turing-patterns/?pid=971 Alan Turing’s Patterns in Nature, and Beyond

AXIOMATIZATION/ AUTOMATIZATION OF MATHEMATICS HILBERT’S PROGRAM, 1900 Hilbert’s hope was that mathematics would be reducible to finding proofs (manipulating the strings of symbols) from a fixed system of axioms, axioms that everyone could agree were true. Can all of mathematics be made algorithmic?

TURING MACHINES AND COMPUTABILITY Turing made the idea of algorithm precise, relating algorithm to the property of computability. Turing wrote: “The "computable" numbers may be described briefly as the real numbers whose expressions as a decimal are calculable by finite means... a number is computable if its decimal can be written down by a machine. “ http://www.turing.org.uk/turing/scrapbook/machine.html

TURING MACHINES AND COMPUTABILITY The Turing machine (LCM, Logical Computing Machine) concept involves specifying a very simple set of logical operations, but Turing showed how other more complex mathematical procedures could be built out of these atomic components. Turing argued that his formalism was sufficiently general to encompass anything that a human being could do when carrying out a definite (mechanical, effective) method.

TURING MACHINES USED IN A MODELLING OF MORE COMPLEX SYSTEMS Simplified, one can say: anything can be used to model anything else – in some way. The question is how meaningful (or applicable or adequate) the model is. http://www.mrtc.mdh.se/~gdc/work/TuringMachine.pdf More about Turing Machine

SUCCESSES OF INTELLIGENT MACHINERY, WITHIN TURING MACHINE PARADIGM DEEP BLUE WINNING OVER CHESS MASTER CASPAROV WATSON WINNING JEOPARDY But: as soon as it works it is no more considered to be intelligence!

BEYOND THE TM MODEL Turing did not show that his machines can solve any problem that can be solved "by instructions, explicitly stated rules, or procedures", nor did he prove that the universal Turing machine "can compute any function that any computer, with any architecture, can compute". He proved that his universal machine can compute any function that any Turing machine can compute. But a thesis concerning the extent of procedures of a certain sort that a human being unaided by machinery is capable of carrying out -- carries no implication concerning the extent of the procedures that machines are capable of carrying out, even machines acting in accordance with ‘explicitly stated rules’. For among a machine's repertoire of atomic operations there may be those that no human being unaided by machinery can perform. Copeland, B. Jack, "The Church-Turing Thesis", The Stanford Encyclopedia of Philosophy (Fall 2008 Edition), Edward N. Zalta (ed.), URL = <http://plato.stanford.edu/archives/fall2008/entries/church-turing/>.

BIOLOGICALLY INSPIRED ”UNORGANIZED MACHINES” In a far-sighted 1948 report Alan Turing suggested that the infant human cortex was an "unorganized machine". Turing defined the class of unorganized machines as largely random in their initial construction, but capable of being trained to perform particular tasks. Turing's unorganized machines were in fact very early examples of randomly-connected, binary neural networks, and he claimed that these were the simplest possible model of the nervous system. Wikipedia

TM AND PHYSICAL (NATURAL) COMPUTING http://www.youtube.com/watch?NR=1&v=i- 1LxIEMC58&feature=endscreen (0.26 min) LEGO Turing machine http://www.youtube.com/watch?v=983lhh20rGY&feature=related (3 min) DNA Transcription and Protein Assembly

2012 TURING CELEBRATION http://www.mathcomp.leeds.ac.uk/turing2012/ http://www.mathcomp.leeds.ac.uk/turing2012/give-page.php?408 2012 The Alan Turing World http://www.mathcomp.leeds.ac.uk/turing2012/WScie12/ CiE 2012 - How the World Computes University of Cambridge18 June - 23 June, 2012: http://www.cie2012.eu

AIBS/IACAP WORLD CONGRESS 2-6 June 2012 in Birmingham there will be a World congress celebrating Turing centenary I am, together with Raffaela Giovagnoli organizing a symposium on Natural computing: https://sites.google.com/site/naturalcomputingaisbiacap2012/ and together with Judith Simon and a group of AI researchers a symposium on: Social Computing - Social Cognition - Social Networks and Multiagent Systems https://sites.google.com/site/socialturnsnamasaisbiacap2012/

2012 TURING CELEBRATION Mathematician Barry Cooper is one of the world-leading figures in the computability theory and President of Computability in Europe, also Turing Centenary Advisory Committee president. He has written on the occasion of Turing centenary in both Nature and Communications of ACM: http://www.nature.com/nature/journal/v482/n7386/full/482465a.html The incomputable reality http://cacm.acm.org/magazines/2012/3/146259-turings-titanic- machine/fulltext Turing's Titanic Machine?

CONCLUSION “So Turing's approach is seminal, illuminating the connection between in-computability, mathematics, and natural phenomena. It has been carried forward by James D. Murray and others, and though things get a lot more complex than the examples tackled by Turing, it is enough to make something more coherent from the confusion of impressions and models. All that the hypercomputability theorists are getting excited about is embodiment and reframing of the standard model, with or without oracles. But the embodiment does extend to the emergent halting set and possibly hierarchically beyond, taking us into a world beyond basic algorithms (see Chaitin's recent take on creativity and biology.) There is some elementary but not widely understood theory that glues the whole thing together. As more and more people are coming to see, going back to Turing with the eyes of a Turing will do wonders.” Barry Cooper: Turing's Titanic Machine? http://cacm.acm.org/magazines/2012/3/146259-turings-titanic-machine/fulltext

CONCLUSION “We can only see a short distance ahead, but we can see plenty there that needs to be done.” Turing , A.M. (1950) Computing machinery and intelligence, Mind LIX, 433-60. http://cogprints.org/499/0/turing.html