Turing machine

A myth has arisen concerning Turing's article of 1936, namely that Turing set forth a fundamental principle concerning the limits of what can be computed by machine—a myth that has passed into cognitive science and the philosophy of minds to wide and pernicious effect. This supposed principle, sometimes incorrectly termed the Church-Turing thesis, is the claim that the class of functions that can be computed by machines is identical to the class of functions that can be computed by Turing machines. In point of fact, Turing himself nowhere endorses or even states this claim (nor does Church). The author describes a number of notional machines, both analog and digital, that can compute more than a universal Turing machine. These machines are exemplars of the class of nonclassical computing machines. Nothing known at present rules out the possibility that machines in this class will one day be built or that the brain itself is such a machine. These theoretical considerations underc...

The study of simple stochastic games (SSGs) was initiated by Condon for analyzing the computational power of randomized space-bounded alternating Turing machines. The game is played by two players, MAX and MIN, on a directed multigraph, and when the play terminates at a sink vertex s, MAX wins from MIN a payoff p(s)∈[0,1]. Condon proved that the problem SSG-VALUE—given a

Church’s and Turing’s theses assert dogmatically that an informal notion of effective calculability is captured adequately by a particular mathematical concept of computabilty. I present analyses of calculability that are embedded in a rich historical and philosophical context, lead to precise concepts, and dispense with theses. To investigate effective calculability is to analyze processes that can in principle be carried out by calculators. This is a philosophical lesson we owe to Turing. Drawing on that lesson and recasting work of Gandy, I formulate boundedness and locality conditions for two types of calculators, namely, human computing agents and mechanical computing devices (or discrete machines). The distinctive feature of the latter is that they can carry out parallel computations. Representing human and machine computations by discrete dynamical systems, the boundedness and locality conditions can be captured through axioms for Turing computors and Gandy machines; models o...

Al igual que Wittgenstein hace en sus Observaciones de la Rama Dorada de Zattell yo observo la "Maquinaria computacional e Inteligencia De Alan Turing (1950)" y trabajo a partir de este la cuestión del pensar con respecto a las maquinas y la pregunta de Turing sobre si las maquinas piensan

An inner link has always connected the artistic avant-garde with acts of insurgency carried out by socially disenfranchised populations insofar as both embrace the possibility of an emancipated future that is radically at odds with the present (picture Gustave Courbet
helping to topple the Vendome Column in
1871), except something about such historical repetition and reenactment at this time  –a moment best described as an uncanny present: a present unfamiliar in its very presentness (Rebecca Bryant)– cries out for something like verification. The essay (published in ASAP Journal 3.2 2018) asks is such a thing as proof of authenticity even possible?

— In this paper, we describe how Turing machine(TM) with two head works. similarly, STM, two head model has a read-write head which is scanning a single cell on infinite one-dimension tape. In Two head model of machine, we changed the design with two head in left and right of tape and based on that we defined the new formal definition which finally decreases the complexity, reducing the use of states in each problem and it is much faster than standard ones.

Masterthesis. An universal Turing-Maschine has several interesting properties: It is (a) deterministic, (b) programmable, (c) self-changing, (d) very extensible and (e) it can be build as a mechanical aparatus. Is that enough to develop intelligent behavior? To properly understand this question, this masterthesis (1) reconstructs the developement of the concept of the Turing-Machine against the background of the history of mathematics and its philosophical implications and (2) follows Alan M. Turings thoughts about the de-limitation of  actual versions of Turing-Machines. It is explored which limits of his machines Turing did see and if any of these limits are supposed to be neccesary (in the sense of: not historically contingent).  As a result the starting question can be rephrased: "Is there something that we should attribute to a human beeing, but that we cannot attribute to a Turing-Machine?".
An introduction sums up the discourse about the relevance of the Turing-Test for the history of philosophy, especially in Germany. Chapter 5 collects some open questions about (a) the possible range of variation of embodiment of a Turing-Machine, (b) the relevance of Turings biography for Turings work and (c) the relevance of poetic narratives (like science fiction) for the developement of state-of-the-art technology.
In Chapters 6 an annotated history of Turing-Editions (and german translations) and scientific anthologies about the Turing-Test is given. Chaper 7 contains a useful bibliography.

Artykuł opublikowany w 13 numerze czasopisma "Problemy Studiów Nauczycielskich" przedstawia podręcznik dla studentów kształcących się w kierunku nauczania informatyki, wydany nakładem Wyższej Szkoły Pedagogicznej w Krakowie. W artykule uzasadniona jest celowość uwzględnienia teoretycznych podstaw informatyki w profilu wykształcenia przyszłych nauczycieli informatyki, a także przedstawiona jest zawartość (spis treści) wydanego podręcznika.

Negli anni sessanta Gilbert Simondon notò come le macchine industriali fossero già relais informazionali, in quanto introducevano per la prima volta una biforcazione tra la sorgente di lavoro meccanico (l’energia naturale) e la sorgente di informazione (il lavoratore). Nel 1963, descrivendo le nuove condizioni di lavoro alla fabbrica Olivetti di Ivrea, Romano Alquati coniò la nozione di informazione valorizzante come ponte concettuale tra il valore marxiano e la definizione cibernetica di informazione. Nel 1972, Gilles Deleuze e Felix Guattari inaugurarono la loro ontologia macchinica, cogliendo il momento in cui la cibernetica abbandonava la fabbrica per innervare l’intera società.
Attraverso questi attrezzi concettuali (sviluppati quasi mezzo secolo fa) si introduce la macchina di Turing come il modello più empirico tra quelli disponibili per studiare gli intestini del capitalismo cognitivo contemporaneo. In accordo con la definizione marxiana di macchina come mezzo per l’amplificazione di plusvalore, l’algoritmo della macchina di Turing è proposto come motore delle nuove forme di valorizzazione, misura del plusvalore di rete e ‘cristallo’ del conflitto sociale. La macchina informatica non è semplicemente una ‘macchina linguistica’ ma invero un nuovo relais tra informazione e metadati. Questa ulteriore biforcazione tecnologica apre in particolare a nuove forme di controllo biopolitico: una società dei metadati viene delineata come evoluzione di quella ‘società del controllo’ già descritta da Deleuze nel 1990 in relazione al ‘potere’ esercitato attraverso le banche dati.

Análisis y comentarios de la película EX MACHINA: el curioso límite entre los seres humanos y las creaciones humanas, entre la inteligencia y la conciencia de unos y de otros. Y la posibilidad de encontrar un nuevo paraíso terrenal en el que jueguen DIOSES, HOMBRES Y ANDROIDES.

Nos anos sessenta Gilbert Simondon observou que as máquinas industriais já eram relés informacionais [it. relais informazionali; fr. régimes d’information à relais], que pela primeira vez fazem bifurcar a fonte do trabalho mecânico (a energia natural) e a fonte da informação (o operário). Em 1963, para descrever a nova condição do trabalho industrial na fábrica Olivetti, Romano Alquati cunhou a noção de informação valorizante [informazione valorizzante] como ponte conceitual entre o valor marxiano e a definição cibernética de informação. Em 1972, Deleuze e Guattari iniciaram sua ontologia maquínica, colhendo o momento em que a cibernética abandonava a fábrica para enervar toda a sociedade. Com a ajuda dessa caixa de ferramentas conceituais (desenvolvidas há quase meio século), apresento nesse ensaio a máquina de Turing como o modelo mais empírico disponível para estudar as entranhas do capitalismo cognitivo.

Here, we introduce a new class of computer which does not use any circuit or logic gate. In fact, no program needs to be written: it learns by itself and writes its own program to solve a problem. Godels incompleteness argument is explored here to devise an engine where an astronomically large number of IfThen arguments are allowed to grow by self assembly, based on the basic set of arguments written in the system, thus, we explore the beyond Turing path of computing but following a fundamentally different route adopted in the last half a century old non Turing adventures. Our hardware is a multilayered seed structure. If we open the largest seed, which is the final hardware, we find several computing seed structures inside, if we take any of them and open, there are several computing seeds inside. We design and synthesize the smallest seed, the entire multilayered architecture grows by itself. The electromagnetic resonance band of each seed looks similar, but the seeds of any layer...

The creation of a process ontology for biology is one of the most ambitious and important projects of current philosophy of biology. Process ontology is usually seen as opposing mechanistic ontology which currently dominates biology. However, the terms 'process' and 'mechanistic' are not always clearly defined in current debates. In this paper I provide a new definition of 'mechanism' and 'mechanistic ontology' based on the most abstract definition of 'machine'—von Foerster's 'non-trivial machine' that is related to Turing machine. I argue that the main methods of modeling used in systems biology rest upon the implicit assumption that organisms abide by the non-trivial or Turing machine logic. By showing that organisms and machines obey two incompatible logics of causality I demonstrate the limits of this assumption. The paper concludes by introducing an organism centered concept of process and arguing that Whitehead's process metaphysics offers a way of understanding organisms as exemplifications of a specific category of process.

This paper explores if humanoid robots can be thought of as conscious, deserving of person rights, and even divine in a Buddhist context. What are the practical and ethical implications of the possible Buddhist claim "all humanoids have Buddha-nature"?

The political economy of the information machine is discussed within the Marxist tradition of Italian operaismo by posing the hypothesis of an informational turn already at work in the age of the industrial revolution. The idea of valorizing information introduced by Alquati (1963) in a pioneering Marxist approach to cybernetics is used to examine the paradigms of mass intellectuality, immaterial labour and cognitive capitalism developed by Lazzarato, Marazzi, Negri, Vercellone and Virno since the 1990s. The concept of machinic by Deleuze and Guattari (1972, 1980) is then adopted to extend Marx’s analysis of the industrial machine to the algorithms of digital machines. If the industrial machine can be described as a bifurcation of the domains of energy and information, this essay proposes to conceive the information machine itself as a further bifurcation between information and metadata. In conclusion, the hypothesis of the society of metadata is outlined as the current evolution of that society of control pictured by Deleuze (1990) in relation to the power embodied in databases.

In many philosophical discussions, it is assumed that the computational explanation of the mind implies that it is being explained as a Universal Turing Machine (UTM). The reason why it is being proposed as a model of the mind is that it is the standard model of computation, and that is a universal machine – i.e., any other digital computer might be simulated by the UTM. So if the mind is a computer that is not able to compute everything that the UTM can, the UTM might still simulate it.�In recent years, several criticisms to such a proposal have been raised. First, it was argued that the UTM requires an infinite tape, which is something that is impossible physically (or impossible as a physical part of the brain). Second, it was argued that the UTM is not a good candidate for explaining the intricacies of the human mind as it has a completely different architecture: so, while the set of functions computed by the machine could be the same as the one computed by the mind, it would differ dramatically in terms of speed and space requirements. Third, some have claimed that there are physical systems capable of hyper-Turing computation, so the UTM might not be the strongest model of computation available. I focus on the epistemic question: how could one tell that a physical system is a UTM? I will distinguish two senses in which one could say that a physical system “is” a UTM: (1) when a physical system has a function that could be simulated with a UTM (functional sense); (2) when a physical system is a mechanism best described as a UTM (mechanistic sense). I will enumerate conditions that must be fulfilled to qualify a physical system to be a UTM in both senses and show differences between the two. It will turn out that in the functional sense, many physical systems might be UTMs, whereas in the mechanistic sense, the set will be much restricted. I will also discuss the problem of finiteness: it seems that for many algorithms, the tape length is restricted anyway (especially if the restriction of the input value range is the part of the algorithm), so the finiteness might not be the biggest problem. Moreover, in the mechanistic sense, one does not select the model of computation simply by picking the strongest model possible, so the hyper-Turing models must also match the mental mechanisms as strictly as any other descriptions of mechanisms that we posit in science.�The mind does not seem to be a UTM in the mechanistic sense at all because of its architecture; and proper computational explanations in cognitive science require that the architecture is matched strictly. I will discuss the problem of the required level of detail in mechanistic computational explanations: it transpires that the philosophically popular UTM is not a good candidate for a scientific model of the mind, even if we accept the standard computational theory of mind.

In light of the pervasive developments of new technologies, such as NBIC (Nanotechnology, biotechnology, information technology, and cognitive science), it is imperative to produce a coherent and deep reflexion on the human nature, on human intelligence and on the limit of both of them, in order to successfully respond to some technical argumentations that strive to depict humanity as a purely mechanical system. For this purpose, it is interesting to refer to the epistemology and metaphysics of Thomas Aquinas as a stable philosophical reference on Human Nature. Indeed, we find in the works of Aquinas some of the most productive elements that could form a base to our deeper understanding of, and possibly even solutions to some of the most perplexing questions raised in our times by the existence of AI.

Gli algoritmi sono metodi per la soluzione di problemi. Possiamo caratterizzare un problema mediante i dati di cui si dispone all'inizio e dei risultati che si vogliono ottenere: risolvere un problema significa ottenere in uscita i risultati desiderati a partire da un certo insieme di dati presi in ingresso. I dati in ingresso vengono anche detti (valori in) input ei risultati in uscita (valori in) output. Possiamo assumere che ciascun problema consista di un insieme di casi particolari, o istanze.

We note that contrary to a common impression Socrates not only did not endorse knowledge as justified belief he explicitly denied it.  We look at Socrates' reason for rejecting the equation knowledge = JTB and consider a similar recognition problem faced by Turing when defining Turing machines. 

There is also some material on Indian Epistemology which is relevant and which is available as another short note to download.

What is business getting itself into in its embrace of so-called artificial intelligence? What is it getting the world into?

In approaching these questions, it may be useful to set aside the term "artificial intelligence" in favour of "interpretation machines."

To do so is to point to ecological and political continuities between 19th-century and 21st-century automation -- continuities that may help clarify strategies for popular struggle.

I shall argue that a resolution of the PvNP problem requires building an iff bridge between the domain of provability and that of computability. The former concerns how a human intelligence decides the truth of number-theoretic relations, and is formalised by the first-order Peano Arithmetic PA following Dededekind's axiomatisation of Peano's Postulates. The latter concerns how a human intelligence computes the values of number-theoretic functions, and is formalised by the operations of a Turing Machine following Turing's analysis of computable functions. I shall show that such a bridge requires objective definitions of both an `algorithmic' interpretation of PA, and an `instantiational' interpretation of PA. I shall show that both interpretations are implicit in the definition of the subjectively defined `standard' interpretation of PA. However the existence of, and distinction between, the two objectively definable interpretations---and the fact that the former is sound whilst the latter is not---is obscured by the extraneous presumption under the `standard' interpretation of PA that Aristotle's particularisation must hold over the structure N of the natural numbers. I shall argue that recognising the falseness of this belief awaits a paradigm shift in our perception of the application of Tarski's analysis (of the concept of truth in the languages of the deductive sciences) to the `standard' interpretation of PA. I shall then show that an arithmetical formula [F] is PA-provable if, and only if, [F] interprets as true under an algorithmic interpretation of PA. I shall finally show how it then follows from Goedel's construction of a formally `undecidable' arithmetical proposition that there is a Halting-type PA formula which---by Tarski's definitions---is algorithmically verifiable as true, but not algorithmically computable as true, under a sound interpretation of PA.

In a recent historical overview, Cristian S. Calude, Elena Calude, and Solomon Marcus identify eight stages in the development of the concept of a mathematical proof in support of an ambitious conjecture: we can express classical mathematical concepts adequately only in a mathematical language in which both truth and provability are essentially unverifiable. In this paper we show, firstly, that

This paper concentrates on Emil Post's critical analysis of Turing machines and on the alternative models of the mind that he attempts to define. Without going into Post's technical results, I rely on the logician's unpublished notebooks to show that, though he may have anticipated Turing's thesis, Post criticizes, after 1938, Turing machines on the ground that the mind as  represented in Turing's analysis is essentially linear. States of mind succeed on another. They come one after the other. On the other hand, Post aims at describing the mind as essentially plural, with different lines of thoughts developing in parallel or different “workers”, various homonculi so to speak, acting together. I discuss two unformal models, which may be found in Post's notebooks, for this plurality of the mind.