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Alan Turing: l’intelligenza come attività sociale
Teresa Numerico [email protected]
20 febbraio 2020 – Università di Bologna 1
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Introduzione
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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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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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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.” 7
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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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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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
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Dispositivo di lettura/scrittura/cancellazione spostamento sul nastro secondo la tavola delle istruzioni
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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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Contro l’obiezione matematica
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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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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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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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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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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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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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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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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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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
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Cognitive vs data-driven machine learning
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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)
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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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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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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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Bibliographic sources/1
} Copeland J. (2004) (Ed.) The essential Turing, Clarendon Press, Oxford. } Copeland J. (2004a) (Ed.) "Proposed electronic calculator by Alan Turing" in Alan Turing's Automatic Computing Engine, Oxford University Press, Oxford; URL: http://www.alanturing.net/proposed_electronic_calculator/. } Cordeschi R. (2008) “Steps Toward the Synthetic Method: Symbolic Information Processing and Self- 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 } Davis M. (2000) The universal computer the road from Leibniz to Turing, W. W. Norton & Company, New York. } Godfrey M. D. (1993) "The First Draft Report on the EDVAC" by John von Neumann, IEEE Annals of the History of Computing, Vol. 15, No. 4, pp.27-75, URL: http://qss.stanford.edu/~godfrey/vonNeumann/vnedvac.pdf. } Greenberger M. (ed) Computers and the world of the future, Mit Press, Cambridge (Mass.), 1962. } Kline R. (2010) "Cybernetics, Automata Studies, and the Dartmouth Conference on Artificial Intelligence," IEEE Annals of the History of Computing, 26 May. 2010. IEEE computer Society Digital Library. IEEE Computer Society,
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Bibliographic sources/2
} Minsky M. (1961) “Steps toward artificial intelligence”, Proceedings of the Institute of the radio engineers, January, vol. 49, pp. 8-30, reprinted in Feigenbaum E.A., Feldman J. (Eds) Computers and thought, McGRaw-Hill Book, 1963, pp. 406-450.
} Newell A., Shaw J.C., Simon H. (1958) “Chess Playing programs and the problem of complexity”, IBM Journal of research and development, October 1958, 2, pp. 320-335, reprinted in Feigenbaum E.A., Feldman J. (Eds) Computers and thought, McGRaw-Hill Book, 1963, pp. 39-70. } Numerico T. (2005) Alan Turing e l’intelligenza meccanica, FrancoAngeli, Milano. } Numerico T. (2010) “The New Machine: from Logic to Organization. Turing, von Neumann and a Self-organized Device for Future Applications”, Special volume on the History of modern computing (eds. Jack Copeland, Carl Posy and Oron Shagrir), The Rutherford Journal: The New Zealand Journal for the History and Philosophy of Science and Technology, vol. 3. http://www.rutherfordjournal.org/article030102.html
} Pias C. (2003) (Ed.) Cybernetics. The Macy Conferences 1946-1953 - Transactions, Diaphanes, Zurich- Berlin. } Shannon C.E., McCarthy J. (1956) Automata Studies, Princeton University Press, Princeton (MASS.). } Turing A.M. (1947), "Lecture to the London Mathematical Society on 20 February 1947" reprinted in Collected Works of A. M. Turing: mechanical intelligence, D. C. Ince (Ed), North-Holland, Amsterdam 1992: 87-105, reprint in Copeland 2004: 378-394. } Turing A. M. (1948), “Intelligent Machinery” Report, National Physics Laboratory, in B. Meltzer D. Michie (Eds.), Machine intelligence, 5, Edinburgh Univ. Press, 1969: 3-23; reprint in Copeland 2004: 410-432. } Turing A.M. (1950), "Computing Machinery and Intelligence", MIND, 59: 433-460 reprinted in Collected Works of A. M. Turing: mechanical intelligence, D. C. Ince, (Ed.) North-Holland, Amsterdam 1992: 133-160 and in Copeland 2004: 441-464.
} Turing A.M. (1951) Intelligent Machinery, a heretical theory, in Copeland 2004, 472-475. } Turing A.M. et al. (1952) Can automatic calculating machines be said to think?, in Copeland 2004: 494-506.
} Von Neumann J. (1948/1961) “General and logical Theory of automata”, Hixon Symposium, reprinted in Taub A.H. (ed) Collected Works, Pergamon Press, Oxford 1963, Vol.V: 288-328. } Von Neumann J. (1958) The computer and the brain, Yale Univ. Press, New Haven.
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