Turing’s imitation game and human thought

In 1950, the English mathematician Alan Mathison Turing proposed the basis of what some authors consider the test that a machine must pass to establish that it can think. This test is basically a game; nevertheless, it has had great infl uence in the development of the theories of the mind performance. The game specifications and some of its repercussions in the conception of thinking, the consciousness and the human will, will be ramifications of the path that will take us through the beginning of the artificial intelligence, passing along some of its singular manifestations, to culminate in the posing of certain restrictions of its fundaments.

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Resumen tomado de la publicación

Los programas While: bases para una teoría de la computabilidad

La Teoría de la Computabilidad estudia los límites teóricos de los sistemas computacionales. Uno de sus objetivos centrales consiste en clasificar los problemas en computables e incomputables, donde llamamos computable a un problema si admite solución informática. Para desarrollar estos resultados el modelo abstracto de computador más utilizado históricamente es la Máquina de Turing. Los estudiantes de Ingeniería Informática pueden percibir cierta lejanía entre el modelo teórico y los computadores reales por lo que es más adecuado utilizar un modelo más cercano a la programación como son los programas-while. Los Programas-while permiten resolver los mismos problemas que las máquinas de Turing, pero en cambio son mucho más sencillos de utilizar, sobre todo para personas que tienen una experiencia previa en la informática real, pues toman la forma de lenguaje imperativo clásico. Este texto además utiliza los Programas-while aprovechando sus ventajas y reformulándolos de manera que la computación quede definida en términos de manipulación de símbolos arbitrarios, algo que está mucho más en concordancia con la realidad informática. Además de explicar en detalle qué son los programas while y cómo se utilizan, se justifica por qué no es necesario incorporar otras instrucciones o tipos de datos.

While programak: konputagarritasun teoria oinarritzeko tresna

Konputagarritasun Teoriaren asmoa sistema konputazionalen muga teorikoak aztertzea da. Bere helburu nagusia problemak konputagarri eta konputaezinen artean bereiztea da, problema konputagarria ebazpide informatikoa onartzen duenari deitzen diogula kontuan hartuta. Emaitza horiek garatzeko konputagailu eredu abstraktu erabiliena, historikoki, Turing-en Makina izan da. Ingeniaritza Informatikoko ikasleek eredu abstraktuaren eta konputagailu errealen artean distantzia dagoela nabari dezakete, horregatik programaziotik hurbilago dagoen eredu bat erabiltzea egokiagoa da, while programak hain zuzen ere. While programekin Turingen makinekin ebazten diren problema berak ebazten dira. Aldiz, while programak erabiltzen askoz errazagoak dira, batez ere aurretik informatika errealean esperientzia duten pertsonentzat, lengoaia agintzaile klasikoen programen itxura hartzen baitute. Testu honek while programak erabiltzen ditu, behar denean hauek birformulatuz eta beraien abantailak aprobetxatuz, konputazioa sinbolo arbitrarioen manipulazioaren baitan definituta gera dadin. Horrela, errealitate informatikotik askoz hurbilagoa egongo da. While programak zer diren eta nola erabiltzen diren zehaztasunez azaltzen da, eta gainera, beste agindu edo datu-mota batzuk gehitzea zergatik ez den beharrezkoa justifikatzen da.

Algunas demostraciones de incomputabilidad usando la técnica de diagonalización

Los supuestos fundamentales de la Teoría de la Computabilidad se establecieron antes de la aparición de los primeros ordenadores (a finales de los años 40), supuestos que muchos años de vertiginoso cambio no han conseguido alterar. Alan Mathison Turing demostró ya entonces que ningún ordenador, por muy potente que lo imaginemos, podría resolver algunas cuestiones. Estos problemas para los que no existe ningún algoritmo posible, los incomputables, no son excepcionales y hay un gran número de ellos entre los problemas que se plantean en torno al comportamiento de los programas. El problema de parada, es sin duda el miembro más conocido de esta familia: no existe un algoritmo para decidir con carácter general si un programa ciclará o no al recibir unos datos de entrada concretos. Para demostrar la incomputabilidad de un problema necesitamos un argumento lógico que certifique la inexistencia de algoritmo, o lo que es lo mismo, que pruebe que ninguno de los algoritmos existentes es capaz de resolver dicho problema. Tal argumento de carácter universal no suele ser sencillo de establecer, y normalmente suele estar relacionado con una demostración por reducción al absurdo. Existen distintas técnicas para lograr este objetivo. La técnica de diagonalización es la más básica de ellas, y resulta bastante conocida al no tratarse de una herramienta específica de la Informática Teórica. En este documento no se trata de explicar la técnica en sí, que se supone conocida, sino de ilustrarla con una colección de ejemplos de diferente grado de dificultad.

Konputaezintasun frogapen batzuk diagonalizazio teknika erabiliz

Konputagarritasunaren Teoriaren oinarriak lehenengo ordenadoreak azaldu aurretik (40. hamarkadaren bukaera aldera) ezarri ziren, eta ziztu biziko eta etenik gabeko eraldaketek aldatzea lortu ez duten oinarriak dira. Alan Mathison Turing-ek jadanik garai hartan frogatu zuen, ahalik eta potentzia handienekoa imajinatuta ere, inolako ordenadorek ebatzi ezingo zituen zenbait gai edo arazo bazeudela. Balizko algoritmorik ez duten problema horiek, konputaezinak deitzen ditugunak, ez dira salbuespenak eta adibide ugari aurki dezakegu. Programen portaeraren inguruan planteatzen diren problemen artean, asko konputaezinak dira. Familia horretako kide ezagunena, zalantzarik gabe, geratze problema da: sarrerako datu zehatz batzuk hartzerakoan, programa bat begizta infinituan geratuko ote den era orokorrean erabakitzeko algoritmorik ez dago. Problema baten konputaezintasuna frogatzeko, hau ebatziko duen algoritmo zehatz bat existitzen ez dela ziurtatuko duen argumentu logikoa behar dugu, edo beste era batera esanda, existitzen diren algoritmoak problema hori ebazteko gai izango ez direla egiaztatuko duen argumentua. Izaera unibertsaleko argumentu hori ezartzea ez da batere erraza izaten, eta normalean, absurduraino eramandako frogapen batekin erlazionatuta egon ohi da. Helburu hori lortzeko zenbait teknika daude. Diagonalizazioaren teknika horien artean oinarrizkoena da, eta nahiko ezaguna, ez baita Informatika Teorikoaren tresna espezifikoa. Dokumentu honen helburua ez da teknika bera azaldu edo deskribatzea, ezaguntzat hartzen baita, zailtasun maila desberdineko hainbat adibideren bitartez argitzea baizik.

Técnicas básicas de computabilidad

La Teoría de la Computabilidad es una disciplina encuadrada en la Informática Teórica que tiene como objetivo establecer los límites lógicos que presentan los sistemas informáticos a la hora de resolver problemas mediante el diseño de algoritmos. Frente a las disciplinas y técnicas que día a día amplían el campo de aplicabilidad práctica de los computadores, esta teoría establece una serie de barreras insalvables por ninguna tecnología digital de procesamiento de la información. Los métodos propios de la Teoría de la Computabilidad pueden ser extraordinariamente complejos, sin embargo, existe un núcleo de resultados fundamentales que son abordables mediante técnicas más asequibles, y que tienen la virtud de reflejar razonablemente el concepto central de indecidibilidad computacional. Este informe incluye una descripción de los conceptos y técnicas que configuran ese núcleo básico de la Teoría. Su propósito es dar cuenta de la primera batería de resultados relacionados con la incomputabilidad de algunos problemas conocidos y relevantes en Informática. Los resultados se presentan utilizando como estándar de programación los programas-while, incluyéndose una explicación detallada y sistemática de la técnica de Diagonalización, además de resultados tan importantes como la tesis de Church-Turing, la función universal o el problema de parada.

ken

From the beginning, the world of game-playing by machine has been fortunate in attracting contributions from the leading names of computer science. Charles Babbage, Konrad Zuse, Claude Shannon, Alan Turing, John von Neumann, John McCarthy, Alan Newell, Herb Simon and Ken Thompson all come to mind, and each reader will wish to add to this list. Recently, the Journal has saluted both Claude Shannon and Herb Simon. Ken’s retirement from Lucent Technologies’ Bell Labs to the start-up Entrisphere is also a good moment for reflection.

Truth in complex adaptive systems models should be based on truth by constructive verification

It is argued that the truth status of emergent properties of complex adaptive systems models should be based on an epistemology of proof by constructive verification and therefore on the ontological axioms of a non-realist logical system such as constructivism or intuitionism. ‘Emergent’ properties of complex adaptive systems (CAS) models create particular epistemological and ontological challenges. These challenges bear directly on current debates in the philosophy of mathematics and in theoretical computer science. CAS research, with its emphasis on computer simulation, is heavily reliant on models which explore the entailments of Formal Axiomatic Systems (FAS). The incompleteness results of Gödel, the incomputability results of Turing, and the Algorithmic Information Theory results of Chaitin, undermine a realist (platonic) truth model of emergent properties. These same findings support the hegemony of epistemology over ontology and point to alternative truth models such as intuitionism, constructivism and quasi-empiricism.

Perspex machine VII: The universal perspex machine

The perspex machine arose from the unification of projective geometry with the Turing machine. It uses a total arithmetic, called transreal arithmetic, that contains real arithmetic and allows division by zero. Transreal arithmetic is redefined here. The new arithmetic has both a positive and a negative infinity which lie at the extremes of the number line, and a number nullity that lies off the number line. We prove that nullity, 0/0, is a number. Hence a number may have one of four signs: negative, zero, positive, or nullity. It is, therefore, impossible to encode the sign of a number in one bit, as floating-, point arithmetic attempts to do, resulting in the difficulty of having both positive and negative zeros and NaNs. Transrational arithmetic is consistent with Cantor arithmetic. In an extension to real arithmetic, the product of zero, an infinity, or nullity with its reciprocal is nullity, not unity. This avoids the usual contradictions that follow from allowing division by zero. Transreal arithmetic has a fixed algebraic structure and does not admit options as IEEE, floating-point arithmetic does. Most significantly, nullity has a simple semantics that is related to zero. Zero means "no value" and nullity means "no information." We argue that nullity is as useful to a manufactured computer as zero is to a human computer. The perspex machine is intended to offer one solution to the mind-body problem by showing how the computable aspects of mind and. perhaps, the whole of mind relates to the geometrical aspects of body and, perhaps, the whole of body. We review some of Turing's writings and show that he held the view that his machine has spatial properties. In particular, that it has the property of being a 7D lattice of compact spaces. Thus, we read Turing as believing that his machine relates computation to geometrical bodies. We simplify the perspex machine by substituting an augmented Euclidean geometry for projective geometry. This leads to a general-linear perspex-machine which is very much easier to pro-ram than the original perspex-machine. We then show how to map the whole of perspex space into a unit cube. This allows us to construct a fractal of perspex machines with the cardinality of a real-numbered line or space. This fractal is the universal perspex machine. It can solve, in unit time, the halting problem for itself and for all perspex machines instantiated in real-numbered space, including all Turing machines. We cite an experiment that has been proposed to test the physical reality of the perspex machine's model of time, but we make no claim that the physical universe works this way or that it has the cardinality of the perspex machine. We leave it that the perspex machine provides an upper bound on the computational properties of physical things, including manufactured computers and biological organisms, that have a cardinality no greater than the real-number line.

Perspex machine IX: transreal analysis

We introduce transreal analysis as a generalisation of real analysis. We find that the generalisation of the real exponential and logarithmic functions is well defined for all transreal numbers. Hence, we derive well defined values of all transreal powers of all non-negative transreal numbers. In particular, we find a well defined value for zero to the power of zero. We also note that the computation of products via the transreal logarithm is identical to the transreal product, as expected. We then generalise all of the common, real, trigonometric functions to transreal functions and show that transreal (sin x)/x is well defined everywhere. This raises the possibility that transreal analysis is total, in other words, that every function and every limit is everywhere well defined. If so, transreal analysis should be an adequate mathematical basis for analysing the perspex machine - a theoretical, super-Turing machine that operates on a total geometry. We go on to dispel all of the standard counter "proofs" that purport to show that division by zero is impossible. This is done simply by carrying the proof through in transreal arithmetic or transreal analysis. We find that either the supposed counter proof has no content or else that it supports the contention that division by zero is possible. The supposed counter proofs rely on extending the standard systems in arbitrary and inconsistent ways and then showing, tautologously, that the chosen extensions are not consistent. This shows only that the chosen extensions are inconsistent and does not bear on the question of whether division by zero is logically possible. By contrast, transreal arithmetic is total and consistent so it defeats any possible "straw man" argument. Finally, we show how to arrange that a function has finite or else unmeasurable (nullity) values, but no infinite values. This arithmetical arrangement might prove useful in mathematical physics because it outlaws naked singularities in all equations.

Perspex machine VIII: axioms of transreal arithmetic

Transreal arithmetic is a total arithmetic that contains real arithmetic, but which has no arithmetical exceptions. It allows the specification of the Universal Perspex Machine which unifies geometry with the Turing Machine. Here we axiomatise the algebraic structure of transreal arithmetic so that it provides a total arithmetic on any appropriate set of numbers. This opens up the possibility of specifying a version of floating-point arithmetic that does not have any arithmetical exceptions and in which every number is a first-class citizen. We find that literal numbers in the axioms are distinct. In other words, the axiomatisation does not require special axioms to force non-triviality. It follows that transreal arithmetic must be defined on a set of numbers that contains{-8,-1,0,1,8,&pphi;} as a proper subset. We note that the axioms have been shown to be consistent by machine proof.

Chatterbox challenge as a test-bed for synthetic emotions

Chatterbox Challenge is an annual web-based contest for artificial conversational systems, ACE. The 2010 instantiation was the tenth consecutive contest held between March and June in the 60th year following the publication of Alan Turing’s influential disquisition ‘computing machinery and intelligence’. Loosely based on Turing’s viva voca interrogator-hidden witness imitation game, a thought experiment to ascertain a machine’s capacity to respond satisfactorily to unrestricted questions, the contest provides a platform for technology comparison and evaluation. This paper provides an insight into emotion content in the entries since the 2005 Chatterbox Challenge. The authors find that synthetic textual systems, none of which are backed by academic or industry funding, are, on the whole and more than half a century since Weizenbaum’s natural language understanding experiment, little further than Eliza in terms of expressing emotion in dialogue. This may be a failure on the part of the academic AI community for ignoring the Turing test as an engineering challenge.

From the buzzing in Turing’s head to machine intelligence contests

This paper presents an analysis of three major contests for machine intelligence. We conclude that a new era for Turing’s test requires a fillip in the guise of a committed sponsor, not unlike DARPA, funders of the successful 2007 Urban Challenge.

Perspex machine

We introduce the perspex machine which unifies projective geometry and the Turing machine, resulting in a supra-Turing machine. Specifically, we show that a Universal Register Machine (URM) can be implemented as a conditional series of whole numbered projective transformations. This leads naturally to a suggestion that it might be possible to construct a perspex machine as a series of pin-holes and stops. A rough calculation shows that an ultraviolet perspex machine might operate up to the petahertz range of operations per second. Surprisingly, we find that perspex space is irreversible in time, which might make it a candidate for an anisotropic spacetime geometry in physical theories. We make a bold hypothesis that the apparent irreversibility of physical time is due to the random nature of quantum events, but suggest that a sum over histories might be achieved by sampling fluctuations in the direction of time flow. We propose an experiment, based on the Casimir apparatus, that should measure fluctuations of time flow with respect to time duration- if such fluctuations exist.