Alan Turing: l'intelligenza come attività sociale - Teresa Numerico - Compatibility Mode
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04/03/20
Alan Turing: l’intelligenza
come attività sociale
Teresa Numerico teresa.numerico@uniroma3.it
20 febbraio 2020 – Università di Bologna
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Introduzione
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04/03/20
Alan Turing
} Nasce nel 1912 a Londra
} Nel 1936 ottiene il famoso risultato di
logica noto come tesi di Church-Turing
mentre si trova al King’s College di
Cambridge
} Nel biennio autunno 1936-autunno 1938
studia a Princeton in US con Alonzo Church.
Lì incontra tra gli altri von Neumann che si
interessa al suo lavoro e gli chiede di
restare in America come suo assistente, ma
Turing si rifiuta
} Durante gli anni della II Guerra Mondiale si
occupa della decodifica di Enigma, la
macchina elettromeccanica dei Tedeschi per
trasmettere messaggi in codice
} Dal 1945 lavora al NPL al progetto per
costruire un calcolatore a programma
memorizzato, l’ACE
} Tra il 1947 e il ’48 trascorre un anno
sabbatico a Cambridge
} Dal ’48 al ’54 si trasferisce a Manchester e
si occupa del Mark I un calcolatore
progettato da F.Williams
} Muore suicida nel 1954 a Manchester
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Perché la Macchina di Turing è
importante?
} Perché negli anni ’40 la macchina costituirà
un modello teorico per la costruzione dei
calcolatori di nuova generazione a programma
memorizzato e general-purpose
} Perché fornisce un modello generale e
intuitivo della nozione di calcolabilità, che
non è ancora stato confutato
} Perché manda definitivamente in crisi il
modello di conoscenza basato esclusivamente
sulla logica matematica, pur essendone la sua
espressione finale
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04/03/20
Una nozione di logica: la
decidibilità
} Un sistema formale è decidibile se
esiste un metodo che in un numero
finito di passi permette di
riconoscere, per ogni formula
espressa linguaggio nel sistema, se
appartiene all’insieme dei teoremi
del sistema o no.
Un metodo, quindi, che stabilisca in
linea di principio se esiste una
dimostrazione per quella formula o
no.
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Un nuovo modo di porre il
problema della decisione
} Dopo i risultati di Gödel, restava
da risolvere il problema della
decisione, che nella formulazione di
Turing era posto in questi termini:
} è possibile avere un metodo meccanico
che in un numero finito di passi
permetta di riconoscere se una formula
espressa nel linguaggio di un sistema
formale appartiene o non appartiene
all’insieme dei teoremi del sistema?
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04/03/20
MT universale
Turing (1939) definì così il risultato teorico:
“Si affermò che "una funzione è
effettivamente calcolabile se i suoi valori
possono essere trovati attraverso un
processo puramente meccanico". Possiamo
prendere alla lettera questa asserzione,
intendendo per processo puramente
meccanico, un processo che può essere
portato a termine da una macchina. E'
possibile dare una descrizione matematica
delle strutture di queste macchine.”
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Che vuol dire metodo meccanico?
} Secondo Turing un metodo meccanico è
una procedura eseguita da un
dispositivo meccanico, cioè da una
macchina
} Per dimostrare che questo metodo
meccanico non esisteva, Turing
doveva inventare la macchina più
generale possibile e mostrare che
nemmeno questa è adatta allo scopo
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04/03/20
Ma che cos’è una macchina?
} E’ difficile dare una definizione precisa
di macchina. Per Turing è:
} Lo strumento più generale che si può
usare per effettuare calcoli Ma
} I calcoli sono solo manipolazione di
simboli
Allora
} La macchina è lo strumento più generale
e più elementare in grado di manipolare
simboli
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A cosa serviva la macchina?
} La Macchina di Turing serviva a proporre
un modello formale dell’attività di un
essere umano che esegue un calcolo di
tipo algoritmico:
} un dispositivo astratto in grado di
emulare la funzione del calcolare, purché
essa sia definita attraverso una
successione di operazioni elementari.
} L’attività di calcolo è una generica
attività di manipolazione di simboli e
non semplicemente di effettuare
operazioni aritmetiche
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04/03/20
La Macchina di Turing
} Durante la primavera del 1936, Turing
inventò la macchina più generale mai
concepita, e probabilmente mai
concepibile.
} Il dispositivo era dotato solo di:
} un nastro bidimensionale diviso in quadrati
di lunghezza finita ma illimitata
} un dispositivo per la lettura, scrittura,
eliminazione di simboli e spostamento sul
nastro
} una tavola di istruzioni comprensibile alla
macchina che indicava tutte le attività da
svolgere senza ambiguità e tutti gli stati
in cui macchina poteva trovarsi
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Lo schema di una MT
| |
Dispositivo di
lettura/scrittura/cancellazione
spostamento sul nastro
secondo la tavola delle
istruzioni
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604/03/20
Perché T. ha bisogno della
macchina per dimostrare
l’indecidibilità?
1. Turing “dimostrò” che, se un compito
era eseguibile da una macchina, allora
era “simulabile” esisteva un
particolare tipo di Macchina di Turing,
che lo poteva simulare
2. Turing dimostrò che esistono calcoli
che non possono essere effettuati,
manipolazioni di simboli che non vanno
a buon fine, procedure che non hanno
mai termine anche per una MT
3. Il problema della decisione è uno dei
calcoli che non è possibile effettuare
con una MT
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Calcolabilità umana e
meccanica
} L’identificazione di computabilità
effettiva e T-calcolabilità è una tesi non
un teorema, e doveva essere argomentata
dal momento che non poteva essere
dimostrata
} I limiti ai quali la macchina era
sottoposta servivano per metterla in
condizione di emulare l’attività umana di
calcolo
} La macchina poteva così sostituire un
“calcolatore” umano in qualunque sua
operazione
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704/03/20
La MT universale come macchina
simulatrice
} La MT emula il comportamento delle
altre macchine attraverso una tavola
di istruzioni, inserita nella macchina
come se fossero i suoi dati
} La MT è una macchina general-purpose,
capace di svolgere qualsiasi compito
} La MT è perciò una macchina virtuale
} La MT è l’insieme di struttura e
tavola di istruzioni: Hardware +
Software
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La calcolabilità e l’agente
onnisciente isolato
} L’emulazione dell’attività di calcolo
umana realizzata attraverso una macchina
presuppone un modello, un certo approccio
alla conoscenza:
} Le operazioni della computazione si svolgono
senza bisogno dell’apporto dell’ambiente o di
altri soggetti esterni al calcolo
} Non ci sono sorprese nell’esecuzione delle
operazioni: data una tavola di istruzioni e
una serie di stati della macchina il risultato
è costante e immutabile
} Tutta la conoscenza necessaria al risultato è
presente nell’agente che esegue le operazioni
in modo non ambiguo ed è priva di incoerenze
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804/03/20
L’accelerazione della
II Guerra Mondiale
} La necessità di calcoli molto
complessi era particolarmente
sentita in vari campi:
} La ricerca atomica: calcoli per misurare
le caratteristiche esatte
dell’esplosione e della posizione del
materiale intorno alla fissione
} La ricerca balistica: equazioni
differenziali non lineari per la
misurazione delle tavole di lancio delle
armi a lunga gittata.
} La crittografia
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Von Neumann e l’influenza di
Turing
} Von Neumann aveva incontrato sicuramente
Turing a Princeton, restando colpito dal
suo valore
} Era al corrente del modello logico di
calcolo proposto con la macchina
universale
} Applica l’idea alla costruzione di un
calcolatore reale:
} Nella memoria (simile al nastro bidimensionale)
risiedevano dati e programmi
} C’era un unico controllo logico che, sulla base della
tavola di istruzioni (programma), gestiva in modo
centralizzato tutte le operazioni in successione
} Esistevano organi di input e di output (che nella MTU
erano porzioni del nastro)
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Sintesi
} L’intelligenza e l’importanza
dell’esternalizzazione della memoria
} La doppia natura del linguaggio nella
prima era dell’intelligenza artificiale
e il ruolo dell’errore
nell’apprendimento
} Il test di Turing o l’intelligenza come
fatto sociale
} Cognitive vs data-driven machine
learning (la modernità di Turing)
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Il ruolo della memoria
secondo Alan Turing
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1004/03/20
I calcolatori umani e la loro
controparte meccanica /macchina di
Turing/1
} The behaviour of the computer at any moment
is determined by the symbols which he is
observing, and his “state of mind” at that
moment. […]
} Let us imagine the operations performed by
the computer to be split up into “simple
operations” which are so elementary that it
is not easy to imagine them further divided.
} Every such operation consists of some change
of the physical system consisting of the
computer and his tape. […]
} We may construct a machine to do the work of
this computer. To each “state of mind” of the
computer corresponds an “m-configuration” o
the machine
Turing 1936/2004, pp. 75-77
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I calcolatori umani e la loro
controparte meccanica /macchina
di Turing 2
} We avoid introducing the "state of mind" by considering
a more physical and definite counterpart of it.
} It is always possible for the computer to break off from
his work, to go away and forget all about it, and later
come back and go on with it.
} If he does this he must leave a note of instructions
(written in some standard form) explaining how the work
is to be continued. This note is the counterpart of the
"state of mind".
} We will suppose that the computer works in such a
desultory manner that he never does more than one step
at a sitting. The note of instructions must enable him
to carry out one step and write the next note.
} Thus the state of progress of the computation at any
stage is completely determined by the note of
instructions and the symbols on the tape.
Turing 1936/2004, 79
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1104/03/20
La teoria di Turing sulla
memoria per l’intelligenza
} The machine would incorporate a memory.
This does not need very much
explanation. It would simply be a list
of all the statements that had been
made to it or by it, and all the moves
it had made ant the cards it had played
in its games. This would be listed in
chronological order. Besides this
straightforward memory there would be a
number of “indexes of experiences”
Turing 1951/2004, p. 474
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Indici di esperienza
} It might be an alphabetical index of the
words that had been used giving the times
at which they had been used, so that they
could be looked up in the memory
} Another such index might contain patterns
of men or parts of a GO board that had
occurred
} At comparatively later stages of education
the memory might be extended to include
important parts of the configuration of
the machine at each moment […] it would
begin to remember what its thoughts had
been
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1204/03/20
Indici di esperienza/2
} This raises a number of problems. If
some of the indications are favourable
and some are unfavourable what is one
to do?
} The answer to this will probably differ
from machine to machine and will also
vary with its degree of education
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L’educazione come processo
comunicativo
Il ruolo del linguaggio
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1304/03/20
L’ambivalenza del concetto di
linguaggio nell’opera di Turing
} L’opera di Turing si trova su una faglia
che attraversa soprattutto la concezione
del linguaggio
} Essendo uno studioso di logica, riteneva
che il linguaggio fosse un sistema
simbolico governato da regole prestabilite
che consentisse di andare da un insieme di
assiomi alle loro conseguenze seguendo le
regole
} Nel progettare la macchina intelligente,
però, si imbatte nell’importanza del
linguaggio come complesso veicolo di
comunicazione, fondamentale per
l’educazione della macchina
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Il linguaggio come collegamento tra
corpo e intelligenza
} Among the fields in which the machine
will exercise its intelligence
opportunities there is also the
learning of languages
} Turing is rather ambivalent on this
field, declaring:
} Of the above possible fields the learning
of languages would be the most impressive,
since it is the most human of these
activities. The field seems however to
depend rather too much on sense organs and
locomotion to be feasible
} Turing 1948, in Copeland 2004, 421
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1404/03/20
Interferenza dall’esterno
} ‘Paper interference’ which consists in the
mere communication of information to the
machine, which alters its behaviour
} When it is possible to alter the behaviour of
the machine very radically we may speak of the
machine as being ‘modifiable’
} As a man is a machine he is one that is
subject to very much interference. In fact
interference is the rule rather than the
exception. He is in frequent communication
with other men, and is continually receiving
visual and other stimuli which themselves
constitute a form of interference
(Turing 1948 in Copeland 2004, 419-421)
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Education as communication
} Although Turing tries to avoid tasks
that involve too much interference, he
is aware that interference plays a
crucial role even in situations that
rely mainly on concentration
} If we want to produce an intelligent
machine, following the human model “by
applying appropriate interference,
mimicking education, we should hope to
modify the machine until it could be
relied on to produce definite reactions
to certain commands” (Turing 1948, 422)
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1504/03/20
Organization as a modification
through interference
} With B-type machines the possibility of
interference which could set in
appropriate initial conditions has not
arranged for. It is however not difficult
to think of appropriate methods by which
this could be done
} Organizing the machine is a form of
‘modification’ (Turing 1948, 422-423)
} I would like to investigate other types of
unorganised machine, and also to try out
organising methods that would be more
nearly analogous to our ‘methods of
education’ (Turing 1948: 428)
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34
Language as a critical tool for
intelligence
} The cortex as an unorganized machine
} But it is not enough to possess the cortex
if we don’t have the tools to organize it
} If the wolf by mutation acquired a human
cortex it would have no selective
advantage
} If the mutation occurred in a milieu where
speech had developed, and if the mutation
had permeated a small community, then some
selective advantage might be felt, because
it would be possible to pass information
from generation to generation
(Turing 1948, 424 passim)
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1604/03/20
Communication and language the
crucial element of education
} The example of miss Helen Keller shows
that education can take place provided
that communication in both direction
between teacher and pupil can take place
by some means or other.
} It is necessary therefore to have some
other [than punishments and rewards]
‘unemotional’ channels of communication.
} If these are available it is possible to
teach a machine by punishments and rewards
to obey orders given in some language […]
the use of this language will diminish
greatly the number of punishments and
rewards required
Turing 1950, in Copeland 2004,p. 461
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36
Education cannot be put in
mathematical terms
} In order for the machine to be interesting as
an intelligent subject it is necessary to
allow it to make mistakes as the human being
(even if he/she is a mathematician) does
} If the machine could ‘learn by experience’ it
would be much more impressive
} Turing imagines to take a simple machine and
“by subjecting it to a suitable range of
‘experience’ transform it into one which was
more elaborate, and was to deal with a far
greater range of contingencies […]
} The criterion as to what would be considered
reasonable in the way of ‘education’ cannot be
put into mathematical terms”
Turing 1951, in Copeland 2004, 473
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1704/03/20
Disciplina e initiativa
So far we have been considering only
discipline. To convert a brain or machine into
a universal machine is the extremest form of
discipline. Without something of this kind one
cannot set up proper communication. But
discipline is certainly not enough in itself to
produce intelligence. That which is required in
addition we call initiative. […] Our task is to
discover the nature of this residue as it
occurs in man, and to try and copy it in
machines.
Turing 1948 in Copeland 2004,429
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Cos’è un’attività intelligente
} Well, yes, I see that a machine could do
all that, but I wouldn’t call it
thinking.’ As soon as one can see the
cause and eVect working themselves out in
the brain, one regards it as not being
thinking, but a sort of unimaginative
donkey-work. From this point of view one
might be tempted to define thinking as
consisting of ‘those mental processes that
we don’t understand’. If this is right
then to make a thinking machine is to make
one which does interesting things without
our really understanding quite how it is
done.
Turing et al. (1952, p.500)
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1804/03/20
Per essere intelligente la
macchina deve poter sbagliare
} Computing machines aren’t really infallible at
all. Making up checks on their accuracy is
quite an important part of the art of using
them. (turing et al. 1952, 502)
} My contention is that machines can be
constructed which will simulate the behaviour
of the human mind very closely. They will make
mistakes at times, and at times they may make
new and very interesting statements, and on
the whole the output of them will be worth
attention to the same sort of extent as the
output of a human mind. (Turing 1951, p. 472)
} Processes that are learnt do not produce a
hundred per cent. certainty of result; if they
did they could not be unlearnt. (Turing 1950,
p. 463)
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40
Turing’s vision of ‘machine
intelligence’
} He was open to both approaches that were
developing at the time
} He was interested in creating a language
capable of maintaining some of the
characteristics of mathematics, but also
versatile so that it could allow
communication, education and organization (3
terms almost synonymous with respect to
machine intelligence)
} He was instead misinterpreted and connected to
his previous notable achievements (the Turing
Machine)
} Turing’s imitation game was conceived as a
tool that allows the perception of the
epistemological subjectivity of intelligence
definition among people
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1904/03/20
Contro l’obiezione
matematica
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49
Gödel critical positioning on
Turing’s machines
} Turing gives an argument which is
supposed to show that mental procedures
cannot go beyond mechanical procedures
} What Turing disregards completely is the
fact that the mind in its use is not
static, but constantly developing, i.e.
that we understand abstract terms more
and more precisely as we go on using
them, and that more and more abstract
terms enter the sphere of our
understanding
Gödel 1972a/1990: 306
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2004/03/20
Various Machines
If you think of various machines, I
don’t see your difficulty. One imagines
different machines allowing different
sets of proofs, and by choosing a
suitable machine one can approximate
‘truth’ by ‘provability’ better than
with a less suitable machine, and can in
a sense approximate it as well as you
please. The choice of a proof checking
involves intuition, […]
Turing’s letter to M. H. A. Newman undated, but probably written
in 1940 : KCCMA Turing’s Papers: D2, Copeland 2004: 215
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51
Confutation of the mathematical
argument
} There would be no question of
triumphing simultaneously over all
machines. In short, then there might be
men cleverer than any given machine,
but then again there might be other
machines cleverer again and so on.
} The imitation game can be a basis for
discussion of this objection
Turing 1950, in copeland 2004, p.451
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2104/03/20
Mathematical objection and
education: interaction as a way out
} As suggested by Copeland in the intro
to Intelligent Machinery, a heretical
theory it is possible that Turing
envisaged the idea of education as an
overcoming of the mathematical
objection. But why?
} In the actual confutation of the
objection that was definitively
considered by Turing the hardest, he
suggested that, although each machine
could be beaten by a particular man,
this is not the case with every machine
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53
Education as interaction between
machines and masters
} A possible association of education
with the overcoming of the mathematical
objection can be the following
argument:
} if the machine learn by experience, learn
how to communicate with a language, make
mistakes, adopt random choices, etc. and
if it is difficult to foresee machine’s
behavior even obeying orders,
} then the machine becomes a sort of hybrid
i.e. the interference between master and
machine causes a transformation of both
actors of the educative dialogue
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2204/03/20
Machine intelligence and human-
machine interaction
} Turing’s idea can be described as an
embryonic project of creating an
interaction between machines and human
educators
} Educators should be of a certain type: not
expert of the mechanism of the device
} ‘Fair play’ with machine means accepting
that they share the same educational
process before evaluating its performances
} Also the idea of different machines and of
programming the universal machine seems to
imply the idea of communication with the
machine
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Intelligenza come attività
sociale
Una rivisitazione del gioco dell’imitazione
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2304/03/20
The first description of the
imitation game
} Intelligence must be regarded as a
subjective concept
} What are we prepared to consider
intelligence is related to “our own
state of mind and training as by the
properties of the object under
consideration” (Turing 1948, 431)
} “With the same object therefore it is
possible that one man would consider it
as intelligent and another would not;
the second man would have found out the
rules of its behaviour” (Turing 1948, 431)
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57
La riformulazione del gioco
dell’imitazione(1952)
} The idea of the test is that the machine
has to try and pretend to be a man, by
answering questions put to it, and it will
only pass it if the pretence is reasonably
convincing. A considerable proportion of a
jury, who should not be expert about
machines, must be taken in by the
pretence. Turing 1952, p. 495
} This means that if the machine was being
put through one of my imitation tests, it
would have to do quite a bit of acting,
but if one was comparing it with a man in
a less strict sort of way [for ex. in
education] the resemblance might be quite
impressive
Turing 1952, p. 503
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2404/03/20
The imitation game: interacting
with the machine
} There were plenty of interpretations of
the Turing test. I agree with that offered
in Copeland 2000 that the game is not an
operational definition of intelligence
} But what if we stick to the letter of
Turing’s proposal? It is related to the
creation of a setting of possible
questions and answers between the user
(not particularly expert) and the machine,
in which the machine is supposed to use
language to interact with the user,
considering that “the best strategy is to
try to provide answers that would
naturally be given by a man”
Turing 1950, Copeland 2004, 443
59
Cognitive vs data-driven machine
learning
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2504/03/20
L’interpretazione del gioco
dell’imitazione
} McCarthy and Shannon discussed the question in the
introduction of the seminal book (1956)on Automata
Studies
} As underlined by Copeland 2000, p.532 this is the first
formulation of block objection and it is based on the
vision of the test as an operative definition of
intelligence
} They described it as a “definition of the concept of
thinking”
} They suggested that it has the disadvantage of a
possible design with a complete set of arbitrarily
chosen responses to all possible input stimuli. The
machine merely looks up in the dictionary the
appropriate response
} With a suitable dictionary it satisfies Turing’s
definition, but does not reflect our usual intuitive
concept of thinking
} A more fundamental definition must involve something
relating to the manner in which the machine arrives at
its responses (Shannon, McCarthy 1956, v-vi)
61
Il principale risultato di
Turing secondo von Neumann
} A general definition of a general
automaton, which is at least as
effective as any conceivable automaton
} An automaton that “when fed the
functions that […] define a specific
automaton, will thereupon function like
the object described. The ability to do
this is no more mysterious than the
ability to read a dictionary and a
grammar and to follow their
instructions about the principles of
combination of words” von Neumann 1948, 27
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2604/03/20
L’associazione tra Tesi di Turing e
approccio all’intelligenza meccanica
} La tesi è perfettamente esemplificata
da S.Shanker 1998 p. 59:
} Turing could then assume that the
machine’s ‘behaviour’ only satisfies our
criteria for saying that it is calculating
because its internal operations are
isomorphic with those guiding the human
computer when he passes the Turing Test
[…]
} It follows that the Mechanistic Thesis and
Turing’s psychological thesis are
internally related: that machines can be
said to think precisely because thinkers
compute
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Secondo Turing le macchine
possono pensare?
} A question too meaningless to deserve discussion
} Turing’s idea was that interacting with the machine
in order to pursue an education program would end
up in a machine capable of simulating intelligence,
while playing the imitation game
} By the end of the century the use of words and
general educated opinion will have altered so much
that one will be able to speak of machines thinking
without expecting to be contradicted
} The popular view that scientists proceed inexorably
from well-established fact to well-established
fact, never being influenced by any unproven
conjecture, is quite mistaken (Turing 1950, 449)
} I can also suggest that Turing was influenced by
the discussion of language as a role playing game,
introduced by Wittgenstein
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2704/03/20
La visione di Turing
} He was interested in creating a language capable of
maintaining some of the characteristics of
mathematics, but also versatile so that it could
allow communication, education and organization
} He wanted to substitute the embodiment
characteristics with a suitable language that could
at least allow the interference necessary in all
education processes
} From the beginning of the ‘40s he imagined that the
machine could not be considered in isolation. There
was a continuous dialectic between truth and
provability, via the choice of suitable
assumptions, and of the corresponding adequate
language
} Turing’s imitation game was conceived as a tool to
evaluate the average epistemological perception of
intelligence by common(inexpert) people
} The perception of intelligence is considered a
social activity both for human and mechanical
subjects. It is determined as well as attributed
inside the social environment
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Intelligenza meccanica
attribuita per ignoranza
} One might be tempted to define thinking as consisting
of ‘those mental processes that we don’t understand’
If this is right then to make a thinking machine is to
make one which does interesting things without our
really understanding quite how it is done
Turing 1952, 500
} Il test di Turing come indicatore
dell’attribuzione sociale di intelligenza a
dispositivi software è già stato superato da
molti sistemi:
} Eliza e gli altri virtual personal assistant
(Cortana, Siri, Alexa, Google assistant)
} Search engines technology (see for ex. Google
algoritmi di raccomandazione)
} Text and Data mining usati dai networks per
comprendere le nostre preferenze e fare
previsioni sui nostril comoportamenti
} Algoritmi di raccomandazione per l’acquisto di
merci e la visione di film e serie sulle
streaming tv 66
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Organizing Systems in Early Artificial Intelligence Modeling” in Husband P., Holland O., Wheeler M.
The Mechanical Mind in History, MIT Press, Cambridge (Mass.) pp.219-248
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York.
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History of Computing, Vol. 15, No. 4, pp.27-75, URL:
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} Greenberger M. (ed) Computers and the world of the future, Mit Press, Cambridge (Mass.), 1962.
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Intelligence," IEEE Annals of the History of Computing, 26 May. 2010. IEEE computer Society Digital
Library. IEEE Computer Society, .
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40 Iss: 1/2, pp.110 - 123.
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O., Wheeler M. The Mechanical Mind in History, MIT Press, Cambridge (Mass.) pp.91-148.
} McCarthy J. et al. (1955) A proposal for the Dartmouth summer research project on Artificial
intelligence, URL: http://www-formal.stanford.edu/jmc/history/dartmouth.pdf
} McCarthy J. (1959) Programs with common sense, in Mechanization of thought processes: proceedings of a
symposium held at the National Physical Laboratory on 24th, 25th, 26th and 27th November 1958, Her
Majesty's Stationary Office, London, URL: http://www-formal.stanford.edu/jmc/mcc59.pdf
} McCarthy J. (1971-1987) “Generality in artificial intelligence”,Communication of the ACM, Vol. 30, pp.
1030—1035. URL: http://www-formal.stanford.edu/jmc/generality.pdf
} McCulloch W. (1948) “Why the mind is in the head”, in Cerebral mechanisms in behavior, the Hixon
Symposium, John Wiley and Son, New York, 1951, pp. 42-57.
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Book, 1963, pp. 406-450.
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} Shannon C.E., McCarthy J. (1956) Automata Studies, Princeton University Press, Princeton (MASS.).
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