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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.

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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

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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

VIDEOhttp://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

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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

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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

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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) 8

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

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Mathematical Logic (7)

• 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)

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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) 11

TURING’S PUBLICATIONS

Pure Mathematics (8) • 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.

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TURING’S PUBLICATIONS

Morphogenesis (1)

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

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TURING’S PUBLICATIONS

http://www.wired.com/wiredscience/2011/02/turing-patterns/?pid=971

Alan Turing’s Patterns in Nature, and Beyond

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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?

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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

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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 AND COMPUTABILITY

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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

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DEEP BLUE WINNING OVER CHESS MASTER CASPAROV

WATSON WINNING JEOPARDY

But: as soon as it works it is no more considered to be intelligence!

SUCCESSES OF INTELLIGENT MACHINERY, WITHIN TURING MACHINE PARADIGM

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/>.

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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

BIOLOGICALLY INSPIRED ”UNORGANIZED MACHINES”

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

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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

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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/

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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?

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2012 TURING CELEBRATION

“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 25

CONCLUSION

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“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

CONCLUSION