alanturing: acenturyofcomputingusers.metu.edu.tr/bozsahin/turing-metu-econ.pdf · alanturing:...

Alan Turing:A Century of Computing

Cem Bozşahin

Cognitive Science Department, The Informatics Institute, METU

www.ii.metu.edu.tr

Department of Economics Seminars, METU

28.5.2012

Bozşahin Alan Turing Centenary

Alan Mathison Turing: 1912–1954

Bozşahin Alan Turing Centenary 2/23

What was Turing up to?

He tried just about everything

ChemistryCryptology (Enigma)Bio-genetics (morphogenesis)Abstract computing (algorithms)Applied computing (programming)Mind-body problem (round-the-house chess)Turing testArtificial lifeFoundations of mathematicsArtificial IntelligenceMarathon


AMT the athlete


Perhaps the right question is:

How was Turing trying to do everything he did?


Mark I, 1948. Manchester’s Ferranti Bros.


Mark I, 2011


Turing Machine

. . . b b a a a a . . . Input/Output Tape

q0q1

q2

q3 . . .

qn

Finite Control

q1

Reading and Writing Head(moves in both directions)


A TM

aL L LI

#

#L #

aR # L

#R

#

R

a

I#Ra

#I

IR L#

a

#

a

a

a

#

# aaR #CaL #

not I

‘#’

x

L

R

L

R

find first x on left

x

x

find first x on right

move right

move left

write x

blank

#

A Turing machine to compute f(n,m)=n x m

It copies the second string a number of times given by the first string.

From Lewis and Papadimitriou (1981).

Representation: maps #I #I #m n

to aI aI m n

first__ __


k-tape TM

1

2

k

FSM


Putnam-Gold TM

1

2

3

FSM

TM

deneme

E E H


Non-Turing extensions to Computing

Analog devices (where everything represents itself)Quantum computing

Bankers bewareNew measures of complexity


What is essential to Turing?

P-G machine is a TMThe nature of relation between representation and computing.Complexity is defined over representation rather than physicaltime and space.One more move of a TM makes the solution one step moreinvolved.


TM

. . . b b a a a a . . . Input/Output Tape

q0q1

q2

q3 . . .

qn

Finite Control

q1

Reading and Writing Head(moves in both directions)


k-TTM

1

2

k

FSM


Problems

Formulable but unsolvable problems

diagonal(X):a: if halt(X,X) goto a otherwise halt.

diagonal(diagonal) ?

Expressible but unformulable problems

What is the next number after π?

The difference is TM representability.


Foundations of Math and AMT

Turing’s universal combinatorUfg = g(ffg)

U = (λxλy .y(xxy))(λxλy .y(xxy))

Uf = [ (λxλy .y(xxy))(λxλy .y(xxy)) ] f[λy .y([ λx1λy1.y1(x1x1y1) ] [ λx2λy2.y2(x2x2y2) ] y) ] ff ([ λx1λy1.y1(x1x1y1) ] [ λx2λy2.y2(x2x2y2) ] f )f (Uf )

Uf = f (Uf )

Recursion without names, programs without variables!


Turing Test

(Ann Witbrock; Copeland, B.J., Artificial Intelligence BlackwellPublishers, Oxford, 1993.)


Searle and Turing


Programming and Searle

ConceptualIntentional System

ArticulatoryPerceptual System

Person

Performance System

PhonologicalForm

LogicalForm

Grammar

Lexicon(meaning bearing items)

(meaning bearing phrases)

Virtual Machine

Interpretive systemTransductive system

Computer

I/O CPU

Alphabet (finite vocabulary)

Well−formed

programs

(source code)

meaningful

computation

(interp. code)

Grammar

Lexicon(finitely characterizable tokens)

(finitely characterizable sentences)


does it look like a TM?AMT: intelligent behavior can arise from manipulation ofrepresentation.With representations, we can build models. Without them wetalk about them.Turing representability is the key to Turing’s computing.


AMT @ 13

“I always seem to want to make things from the thing that iscommonest in nature.”


AMT @ 9


alanturing: acenturyofcomputingusers.metu.edu.tr/bozsahin/turing-metu-econ.pdf · alanturing:...

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