Computable Diagonalizations and Turing’s Cardinality Paradox

A. N. Turing’s 1936 concept of computability, computing machines, and computable binary digital sequences, is subject to Turing’s Cardinality Paradox. The paradox conjoins two opposed but comparably powerful lines of argument, supporting the propositions that the cardinality of dedicated Turing machines outputting all and only the computable binary digital sequences can only be denumerable, and yet must also be nondenumerable. Turing’s objections to a similar kind of diagonalization are answered, and the implications of the paradox for the concept of a Turing machine, computability, computable sequences, and Turing’s effort to prove the unsolvability of the Entscheidungsproblem, are explained in light of the paradox. A solution to Turing’s Cardinality Paradox is proposed, positing a higher geometrical dimensionality of machine symbol-editing information processing and storage media than is available to canonical Turing machine tapes. The suggestion is to add volume to Turing’s discrete two-dimensional machine tape squares, considering them instead as similarly ideally connected massive three-dimensional machine information cells. Three-dimensional computing machine symbol-editing information processing cells, as opposed to Turing’s two-dimensional machine tape squares, can take advantage of a denumerably infinite potential for parallel digital sequence computing, by which to accommodate denumerably infinitely many computable diagonalizations. A three-dimensional model of machine information storage and processing cells is recommended on independent grounds as better representing the biological realities of digital information processing isomorphisms in the three-dimensional neural networks of living computers.

Die Deutungen der hebräischen Buchstaben bei Ambrosius

von Dav. Heinr. Müller

Weiss auf Rot. Das Schweizer Kreuz zwischen nationaler Identität und Corporate Identity

Das Schweizer Kreuz hat als Zeichen ausserordentliche Qualitäten und ein enormes Potenzial. Seine Verwendung geht weit über den unmittelbaren Bereich von Staat und Nation hinaus. Die Publikation der Hochschule der Künste Bern HKB erschliesst dieses Phänomen mit illustrierten Beiträgen von Fachleuten aus verschiedenen wissenschaftlichen Fachrichtungen. Für Nation, Staat, Politik und im Sport steht es als Symbol, im Kontext Wirtschaft ist es Teil von Logos, im Zusammenhang von Lifestyle und Zeitgeist tritt es als modisches Ornament auf. Das Schweizer Kreuz macht TrägerInnen und AbsenderInnen identifizierbar: Abstimmungsunterlagen als staatliche Dokumente, die Sportlerin als Mitglied des Nationalteams, den Inhaber eines Pas-ses oder einer Identitätskarte als Schweizer Bürger; Post oder SBB als schweizerische Dienstleister; die Besitzerin einer Tasche als Vertreterin einer Lifestyle-Gruppe oder Nachzüglerin eines sinkenden Trends; das Mineralwasser als natürliches, gesundes Produkt; eine Alu-Trinkflasche als flottes Qualitätsprodukt. Interdisziplinärer Zugang «Weiss auf Rot. Das Schweizer Kreuz zwischen nationaler Identität und Corporate Identity» ist eine Textsammlung, die entsprechend der Vielfältigkeit des Themas auch eine Vielfalt von Annäherungen an den Gegenstand bietet. Die 13 wissenschaftlichen Texte werden ergänzt durch fünf Interviews mit VertreterInnen aus Politik, Wirtschaft, Sportwissenschaft und Gestaltung, die in ihrem berufli-chen Alltag einen praktischen Bezug zum Schweizer Kreuz haben.

Wie sich der heil. Johannes v. Nepomuk auf der Moldaubrücke mit dem Hintern gegen die Alt- und Neustadt umgekehrt hat, oder wunderbare und wahrhaftige Geschichte, welche sich am 2. Juli, im Jahre des Heils 1848 in Prag zugetragen hat: In der Nacht vom 1. auf den 2. Juli d. J., also vom Samstage auf den Sonntag dieser Woche ...

Welsch (Projektbearbeiter): Satire von pro-tschechischer Seite nach der Niederschlagung des Prager Pfingstaufstandes (17. Juni 1848). Der heilige Johannes von Nepomuk wurde als Symbol des habsburgischen Katholizismus sowie als Gegenbild zu Jan Hus von der nationaltschechischen Bewegung abgelehnt

Für Jedermann zu wissen nothwendig! Der Kampf um die schwarzgelben Bänder oder: Wer ist eigentlich ein Schwarzgelber? Ich glaube, man hätte viele Millionen Gulden, wenn man nur so viel Kreuzer bekäme, als das Wort - schwarzgelb - in Wien allein ausgesprochen worden ist ...

Welsch (Projektbearbeiter): Aufruf gegen die Unsitte der Schikanierung von Bürgern, die schwarzgelbe Bänder tragen. Das schwarzgelbe Band ist nicht der Ausdruck einer reaktionären Gesinnung, sondern vielmehr das Symbol des geborenen Österreichers und treuen Kaiseranhängers: " ... ich behaupte, daß der, welcher ein [schwarzgelbes Band] trägt, doch dabei der freisinnigste Mann und dessenungeachtet für den Anschluß an Deutschland sein kann."

Götter, Bilder und Symbole nach den Traktaten über fremden Dienst (Aboda zara) in Mischna, Tosefta, Jerusalemer und babylonischem Talmud

von Hans Blaufuss

A focused ethnographic study of women in recovery from alcohol abuse

Alcohol abuse and its related problems are among the most pervasive health and social concerns in the United States (U.S.) today. Women are especially vulnerable to the physical and social devastation of alcohol abuse. Yet, although there is extensive research about alcohol drinking patterns, treatment strategies, and early recovery, there is little information about the factors that facilitate successfully sustained abstinence in women. The purpose of this study was to examine and describe the common factors to successful recovery from alcohol abuse among women and to place these factors within both the context of their social networks and the larger social environment. This study draws from the population of New Mexico, where alcohol-related deaths are the highest of any state in the U.S. and the leading cause of death for individuals under the age of 65 years. The study was a focused ethnography of women who had successfully maintained long-term recovery from alcohol abuse. As an ethnographic study, data collection included participant observation, in-depth interviews with 21 women, and the collection of historical and current culturally relevant data. A purposive sampling plan was used to maximize the selection of participants who had used traditional and non-traditional approaches to recovery. As such, the analysis of the success narratives revealed two distinct findings: the first that women used several different trajectories to achieve long-term recovery. Three trajectory typologies were identified from the success narratives and labeled, A.A. as ceremony, A.A. as grounding, and Recovery as self-management. ^ However, within each of these trajectories, variations in successful recovery were seen. The second major finding was that all women articulated an overarching theme of connections as an indispensable aspect of sustained recovery. The success narratives demonstrated the powerful role that connections played in their long-term recovery and the analysis distinguished two unifying concepts of connections—those that focused beyond self (spirituality, social support, and pets) and those that focused toward self (self-nurturance, agency, and identity). This discussion will focus on the implications for clinical practice related to both women who are still actively abusing alcohol and for those who are successfully maintaining long-term recovery. ^

Facies analysis on sediment core CRP-3 from the Ross Sea, Antarctica

Cape Roberts Project drill core 3 (CRP-3) was obtained from Roberts ridge, a sea-floor high located at 77°S, 12 km offshore from Cape Roberts in western McMurdo Sound, Antarctica. The recovered core is about 939 m long and comprises strata dated as being early Oligocene (possibly latest Eocene) in age, resting unconformably on ~116 m of basement rocks consisting of Palaeozoic Beacon Supergroup sediments. The core includes ten facies commonly occurring in five major associations that are repeated in particular sequences throughout the core and which are interpreted as representing different depositional environments through time. Depositional systems inferred to be represented in the succession include: outer shelf, inner shelf, nearshore to shoreface each under iceberg influence, deltaic and/or grounding-line fan, and ice proximal-ice marginal-subglacial (mass flow/rainout diamictite/subglacial till) singly or in combination. The record is taken to represent the initial talus/alluvial fan setting of a glaciated rift margin adjacent to the block-uplifted Transantarctic Mountains. Development of a deltaic succession upcore was probably associated with the formation of palaeo-Mackay valley with temperate glaciers in its headwaters. At that stage glaciation was intense enough to support glaciers ending in the sea elsewhere along the coast, but a local glacier was fluctuating down to the sea by the time the youngest part of CRP-3 was being deposited. Changes in palaeoenvironmental interpretations in this youngest part of the core are used to estimate relative glacial proximity to the drillsite through time. These inferred glacial fluctuations are compared with the global d180 and Mg/Ca curves to evaluate the potential of glacial fluctuations on Antarctica for influencing these records of global change. Although the comparisons are tentative at present, the records do have similarities, but there are also some differences that require further evaluation.

Grain size analysis on CRP sediment cores from the Ross Sea, Antarctica

The upper 1200 m of pre-Pliocene sediment recovered by Cape Roberts Project (CRP) drilling off the Victoria Land coast of Antarctica between 1997-1999 has been subdivided into 54 unconformity-bound stratigraphic sequences, spanning the period c. 32 to 17 Ma. The sequences are recognised on the basis of the cyclical vertical stacking of their constituent lithofacies, which are enclosed by erosion surfaces produced during the grounding of the advancing ice margin onto the sea floor. Each sequence represents deposition in a range of offshore shelf to coastal glacimarine sedimentary environments during oscillations in the ice margin across the Western Ross Sea shelf, and coeval fluctuations in water depth. This paper applies spectral analysis techniques to depth- and time-series of sediment grain size (500 samples) for intervals of the core with adequate chronological data. Time series analysis of 0.5-l.0m-spaced grainsize data spanning sequences 9-11 (CRP-2/2A) and sequences 1-7 (CRP-3) suggests that the length of individual sequences correspond to Milankovitch frequencies, probably 41 k.y., but possibly as low as 100 k.y. Higher frequency periodic components at 23 k.y. (orbital precession) and 15-10 k.y. (sub-orbital) are recognised at the intrasequence-scale, and may represent climatic cycles akin to the ice rafting episodes described in the North Atlantic Ocean during the Quaternary. The cyclicity recorded by glacimarine sequences in CRP core provides direct evidence from the periphery of Antarctica for orbital oscillations in the size of the Oligocene-Early Miocene East Antarctic Ice Sheet.

La seducción del continente americano. Simbolismo e ideología en La piedra que crece, de Albert Camus

En el cuento "La piedra que crece" Albert Camus textualiza de manera sugerente, la seducción que el continente americano, en su porción más agreste y natural, adquiere para este pensador de mediados del siglo pasado. Continente y cultura que parecen ofrecer al escritor francés una posible salida a ese universo cerrado, sin horizontes, que postula el Existencialismo. Este cuento se erige como símbolo contenedor de ideas tangenciales a las manifestadas por Camus en el resto de sus escritos. Aquí se advierte una mirada esperanzada acerca del porvenir de la cultura y, en definitiva, de la humanidad que le da sentido, que se contrapone diametralmente con la postura existencialista. Por ello en este trabajo me propongo, por una parte transmitir una impresión de lectura, y por otra, demostrar de qué manera la captación de un espacio-otro, adquiere una dimensión simbólica e ideológica que socava los postulados existenciales en sus raíces más profundas

Rodó y su Ariel. El Ariel de Rodó

El artículo presenta al autor de Ariel, Rodó, como integrante de la promoción literaria uruguaya, como uno de los exponentes del modernismo y como pensador que pertenece a la generación de los Fundadores. Parte de la problemática Ariel- Calibán como símbolo latinoamericano y de la postulación de Ariel como discurso antiimperialista para situar la pregunta respecto de la función de la educación en la constitución del joven latinoamericano como sujeto social portador de sentido del proyecto nacional. Se tratan luego las figuras que se desprenden de los Prósperos, los Calibanes y los Arieles concebidos como la pluralidad de perspectivas desde las que transcurren las vidas de los sujetos y de los espacios desde los cuales las naciones se paran para mirarse unas a otras.

El símbolo cristiano del pez : origen y proyecciones

Desde hace tiempo se sabía que el nombre griego ij÷qýò (pez) encerraba como acróstico una frase cuyo contenido es una antigua fórmula cristológica: Jesús-Cristo-Hijo de Dios-Salvador que se conservaba en diversos medios poéticos del siglo II. Pero últimamente se ha comprobado la función que el símbolo del pez y la palabra como criptograma desempeñaba en algunos textos de la biblioteca de Nag Hammadi y se ha descubierto su presencia en una versión diferente de la parábola de la red y el pescador, el panorama se amplía notablemente. Porque con estos elementos a disposición es posible comparar estructuras narrativas paralelas y contenidos significativos divergentes que permiten ampliar el horizonte de la investigación de los primeros tiempos cristianos y deducir las diferencias en la interpretación de los mismos motivos religiosos de algunos textos cristianos primitivos.