Origin of Geometry and Origin of the Work of Art: Reduction, Truth, and History in Husserl and Heidegger Husserl’s The Origin of Geometry and Heidegger’s The Origin of the Work of Art were surprisingly developed in parallel and deal with the same subject, the question of the origin: of a science, in one case, and of the artwork, in the other. From their comparison, the different conception that Husserl and Heidegger have of origin and truth clearly emerge. It concerns what (...) Heidegger identified as the real point of his divergence from Husserl, when they tried to write the entry “Phenomenology” for the Encyclopaedia Britannica, namely the method of reduction. For Husserl, the reduction opens up a material content, an essence, which ensures the persistence of truth in historical transmission, beyond linguistic variability, as happens in geometry; for Heidegger, reduction brings to light the ontological and, we might say, grammatical condition of truth, that is, its being an event and giving rise to an original syntax, to a world. This is the function of the work of art, whose essence consists in its mere being-made, in its being, that is, a work: the actualization of a possibility. (shrink)

Esta reflexión propone que las Tecnologías de Mejoramiento Humano, en el siglo XXI, se erigen en un dispositivo biopolítico de poder molecular sobre la vida del individuo y de la especie humana, el cual está vertebrado tanto por los mecanismos de Infogeneración e Infogeneración como de líneas de visibilidad, enunciación, fuerza, objetivación y subjetivación. Esta incipiente biopolítica de poder molecular que tiene por blanco de intervención los entresijos de la vitalidad y como finalidad producir artificialmente la vida, genera al menos (...) tres efectos: sobre la subjetividad, el cuerpo y la salud, suscitando, así, interrogantes importantes para la bioética y el bioderecho. En un primer momento, esbozamos las notas características del Dispositivo biopolítico de mejoramiento humano. Después, abordamos el modo en que el DBMh construye inéditas formas de subjetividad, al mismo tiempo que establece nuevas y distintas concepciones del cuerpo humano y de la salud. En la parte final se esboza un modelo de estratigrafía para leer fenómenos asociados a las TMh en el que se articula la bioética, la biopolítica y el bioderecho en un modelo de geometría variable. (shrink)

El Centro para la Difusión de la Música Contemporánea nació en 1983 para dinamizar la vida musical contemporánea. Entre sus actividades dirige el Festival Internacional de Música Contemporánea de Alicante, una temporada de conciertos en Madrid y el Laboratorio de Informática y Electrónica Musical. En la temporada 2005/06, acaba de instalarse en el nuevo Auditorio de la ampliación del Museo Nacional Centro de Arte Reina Sofía, lo que ha permitido desplegar una serie concertística mucho más ambiciosa. Uno de los apartados (...) de esta programación, el ciclo “Residencias”, que consta de cuatro conciertos, se constituye en un modelo de organización que aglutina a varios grupos y solistas en un afán común. A través de este ciclo, se plantean propuestas de innovación en el ámbito de la organización de conciertos, como estructura de debate del cómo debe articularse el ensemble de músicos dedicados a la música contemporánea en el futuro. (shrink)

O caráter protocolar desempenhado pelas matemáticas na formulação do conceito cartesiano de ciência é amplamente difundido e frequentemente reinvocado na literatura especializada quando se trata de abordar a exigência apodítica inerente a este conceito. No entanto, pouco se explora o que a diversidade das disciplinas matemáticas bem como a relação entretida por elas permite trazer de elucidação à noção cartesiana de ciência. Nosso propósito consiste, aqui, em tomar posição quanto a um debate acerca do estatuto da álgebra e da geometria (...) como disciplinas que fixam os lineamentos da teoria cartesiana do conhecimento ao exibirem o que Descartes reputaria como a aplicação ideal do intelecto. Trata-se de insistir, por vias que assinalam uma decisão teórica em favor de uma concepção mais intelectualista e menos imaginativa da ciência, que não há hesitação quanto ao papel primitivo e fundacional da álgebra se comparada à geometria. (shrink)

El artículo documenta y analiza las vicisitudes en torno a la incorporación de Hilbert de su famoso axioma de completitud, en el sistema axiomático para la geometría euclídea. Esta tarea es emprendida sobre la base del material que aportan sus notas manuscritas para clases, correspondientes al período 1894–1905. Se argumenta que este análisis histórico y conceptual no sólo permite ganar claridad respecto de cómo Hilbert concibió originalmentela naturaleza y función del axioma de completitud en su versión geométrica, sino que (...) además permite disipar equívocos en cuanto a la relación de este axioma con la propiedad metalógica de completitud de un sistema axiomático, tal como fue concebida por Hilbert en esta etapa inicial.The paper reports and analyzes the vicissitudes around Hilbert’s inclusion of his famous axiom of completeness, into his axiomatic system for Euclidean geometry. This task is undertaken on the basis of his unpublished notes for lecture courses, corresponding to the period 1894–1905. It is argued that this historical and conceptual analysis not only sheds new light on how Hilbert conceived originally the nature of his geometrical axiom of completeness, but also it allows to clarify some misunderstandings regarding this axiom and the metalogical property of completeness of an axiomatic system, as it was understoodby Hilbert in this initial stage. (shrink)

La concepción cartesiana del espacio representa la apertura de una nueva época, revolucionaria, en la concepción espacial de su tiempo, en vista del significado e impacto de la geometría de coordenadas de Descartes. La articulación de la aritmética y la geometría, resultado de la innovadora concepción del método —de las Regulæ ad Directionem Ingenii (1628)— conduce a entender el conocimiento como resultado de las relaciones entre los componentes de un sistema y la expresión de éstas en términos de (...) funciones matemáticas. El enfoque aquí propuesto para el estudio del espacio cartesiano —como sistemático o unitario— es una ruta de análisis que difiere, pero complementa, las perspectivas ontológica, física y teológica que habitualmente se han recorrido para el estudio del espacio en este filósofo y de este modo cubre un importante hueco. Este enfoque ubica las consecuencias epistemológicas fundamentales que se extraen de la concepción metódica cartesiana. (shrink)

In this paper we extend Neutro-Algebra and Anti-Algebra to geometric spaces, founding Neutro/Geometry and AntiGeometry. While Non-Euclidean Geometries resulted from the total negation of a specific axiom (Euclid's Fifth Postulate), AntiGeometry results from the total negation of any axiom or even more axioms of any geometric axiomatic system (Euclidean, Hilbert, etc. ) and of any type of geometry such as Geometry (Euclidean, Projective, Finite, Differential, Algebraic, Complex, Discrete, Computational, Molecular, Convex, etc.), and Neutro-Geometry results from the partial negation of one (...) or more axioms [and without total negation of any axiom] of any geometric axiomatic system and of any type of geometry. Generally, instead of a classical geometric Axiom, one can take any classical geometric Theorem of any axiomatic system and of any type of geometry, and transform it by Neutrosophication or Antisofication into a Neutro-Theorem or Anti-Theorem respectively to construct a Neutro-Geometry or Anti-Geometry. Therefore, Neutro-Geometry and Anti-Geometry are respectively alternatives and generalizations of Non-Euclidean Geometries. In the second part, the evolution from Paradoxism to Neutrosophy, then to NeutroAlgebra and Anti-Algebra, then to Neutro-Geometry and Anti-Geometry, and in general to Neutro-Structure and Anti-Structure that arise naturally in any field of knowledge is recalled. At the end, applications of many Neutro-Structures in our real world are presented. (shrink)

La propuesta fenomenológica de Husserl, aunque se inició con un estudio sobre la naturaleza del número y las funciones matemáticas, abarca mucho más que eso. Se conocen una serie de ensayos editados póstumamente en el tomo XXI de la serie Hussserliana que abarcan los años 1890-1908, y que se enfocan en comprender los avances de la geometría (euclidiana y no euclidiana) y el papel que desempeña en la constitución del espacio físico. Los estudios sobre geometría euclidiana y no (...) euclidiana continuarían así la investigación de Filosofía de la aritmética, ya que ambos comparten los Grundgedanken, es decir, el conjunto de herramientas y temas relacionados con la noción de representación simbólica. El objetivo de este artículo es presentar de manera general los principales problemas a los que Husserl se enfrenta en relación con temas geométricos y espaciales. Se intentará reconstruir, de manera histórico-crítica, aspectos esenciales sobre los temas y problemas de la filosofía de la geometría tal y como Husserl la desarrolla en sus primeras obras fenomenológicas. (shrink)

El Trabajo por Proyectos es una metodología muy apropiada para utilizarla en la enseñanza superior, por su carácter investigador. El aprendizaje es activo, involucra al alumno y trabaja otras capacidades cognitivas distintas a las que se desarrollan con la clase magistral. Con la implantación, este curso, del llamado Plan Bolonia, algunos profesores pertenecientes al Grupo de Innovación Educativa Didáctica de las Matemáticas de la UPM, nos planteamos introducir en la asignatura de primer curso del Grado de Arquitectura, denominada Geometría (...) Euclídea, Afín y Proyectiva algunos cambios dirigidos a este tipo de aprendizaje. (shrink)

The enormous scale of the available information and products on the Internet has necessitated the development of algorithms that intermediate between options and human users. These algorithms attempt to provide the user with relevant information. In doing so, the algorithms may incur potential negative consequences stemming from the need to select items about which it is uncertain to obtain information about users versus the need to select items about which it is certain to secure high ratings. This tension is an (...) instance of the exploration–exploitation trade‐off in the context of recommender systems. Because humans are in this interaction loop, the long‐term trade‐off behavior depends on human variability. Our goal is to characterize the trade‐off behavior as a function of human variability fundamental to such human–algorithm interaction. To tackle the characterization, we first introduce a unifying model that smoothly transitions between active learning and recommending relevant information. The unifying model gives us access to a continuum of algorithms along the exploration–exploitation trade‐off. We then present two experiments to measure the trade‐off behavior under two very different levels of human variability. The experimental results inform a thorough simulation study in which we modeled and varied human variability systematically over a wide rage. The main result is that exploration–exploitation trade‐off grows in severity as human variability increases, but there exists a regime of low variability where algorithms balanced in exploration and exploitation can largely overcome the trade‐off. (shrink)

Gottlob Frege abandoned his logicist program after Bertrand Russell had discovered that some assumptions of Frege’s system lead to contradiction (so called Russell’s paradox). Nevertheless, he proposed a new attempt for the foundations of mathematics in two last years of his life. According to this new program, the whole of mathematics is based on the geometrical source of knowledge. By the geometrical source of cognition Frege meant intuition which is the source of an infinite number of objects in arithmetic. In (...) this article, I describe this final attempt of Frege to provide the foundations of mathematics. Furthermore, I compare Frege’s views of intuition from The Foundations of Arithmetic (and his later views) with the Kantian conception of pure intuition as the source of geometrical axioms. In the conclusion of the essay, I examine some implications for the debate between Hans Sluga and Michael Dummett concerning the realistic and idealistic interpretations of Frege’s philosophy. (shrink)

This paper will focus on a philosophically significant construction whose semantics brings together two important notions in Kit Fine’s philosophy, the notion of truthmaking and the notion of a variable embodiment, or its extension, namely what I call a ‘variable object’. This is the construction of definite NPs like 'the number of people that can fit into the bus', 'the book John needs to write', and 'the gifted mathematician John claims to be'. Such NPs are analysed as standing (...) for variable objects, which are part of the 'shallow', construction-driven ontology of natural language, yet are real. (shrink)

This study of the history and contents of a hitherto unedited work on geometry by Vincenzo Viviani seeks to present a picture of the scientific environment in Italy in the second half of the 17th century, with particular emphasis on Tuscany and the impact the condemnation of Galileo had on ongoing scholarship. Information derived from unedited or less well-known material serves to illuminate a range of prominent and marginal figures who adopted different strategies for the dissemination of Galileo’s thought and (...) the application of its principles. A selection of texts, edited here for the first time, is presented in two appendices, while in a third decidedly unusual methods are used to elucidate the mathematical aspects. (shrink)

A presentation of Spinoza's theory of affections and concept of conatus aimed at a psychoanalyst audience.

This article sheds light on Hobbes’s concept of the state of nature through a reading of his conception of knowledge, which makes it possible to relate him with the ‘New Science’ or the Scientific Revolution. In consequence, this article describes Hobbes with some problems and traditions of the Scientific Revolution through a fresh reading of his theory of knowledge, whence the concept of the state of nature is redefined in terms of integral cause; this makes it possible to argue the (...) need for Commonwealth, excluding the anthropological pessimism traditionally attributed to Hobbes. (shrink)

BackgroundTo investigate the factors related to approval after review by an Institutional Review Board, the structure equation model was used to analyze the latent variables ‘investigators’, ‘vulnerability’ and ‘review process’ for 221 proposals submitted to our IRB.MethodsThe vulnerability factor included vulnerable cases, and studies that involved drug tests and genetic analyses. The principal investigator factor included the license level of the PI and whether they belonged to our institution. The review factor included administration time, total review time, and revision frequency. (...) The revision frequency and total review time influenced the efficiency of review.ResultsThe latent variable of reviewing was the most important factor mediating the PIs and vulnerability to IRB review approval. The local PIs moderated with genetic study and revision frequency had an impact on the review process and mediated non-approval.ConclusionsBetter guidance of the investigators and reviewers might improve the efficiency with which IRBs function. (shrink)

Under the putative influence of dietary selection pressure, the subcellular distribution of alanine:glyoxylate aminotransferase 1 (AGT) has changed on many occasions during the evolution of mammals. Depending on the particular species, AGT can be found either in peroxisomes or mitochondria, or in both peroxisomes and mitochondria. This variable localization depends on the differential expression of N‐terminal mitochondrial and C‐terminal peroxisomal targeting sequences by the use of alternative transcription and translation initiation sites. AGT is peroxisomal in most humans, but it (...) is mistargeted to the mitochondria in a subset of patients suffering from the rare herediatry disease primary hyperoxaluria type 1. Mistargeting is due to the unlikely combination of a normally occurring polymorphism that generates a functionally weak mitochondrial targeting sequence and a disease‐specific mutation which, in combination with the polymorphism, inhibits AGT dimerization. The mechanisms by which AGT can be targeted differentially to peroxisomes and/or mitochondria highlight the different molecular requirements for protein import into these two organelles. (shrink)

In this paper we find an algebraic equivalent of the Hallden property in modal logics, namely, we prove that the Hallden-completeness in any normal modal logic is equivalent to the so-called super-embedding property of a suitable class of modal algebras. The joint embedding property of a class of algebras is equivalent to the Pseudo-Relevance Property. We consider connections of the above-mentioned properties with interpolation and amalgamation. Also an algebraic equivalent of of the principle of variable separation in superintuitionistic logics (...) will be found. (shrink)

In the previous paper (Filozofia Nauki No 3-4, 1994, pp. 7-17) we have shown how the initial and final singularities in the closed Friedman world model can be analysed in terms of the structured spaces in spite of the fact that these singularities constitute the single point in the b-boundary of space-time. In the present paper we generalize our approach by using methods of noncommutative geometry. We construct a noncommutative algebra in terms of which geometry of space-time with singularities can (...) be developed. This algebra admits a representation in the space of operators on a Hilbert space, and the initial and final singularities in the closed Friedman model are given by its two distinct representations. The striking feature of this approach is its analogy with the mathematical formalism of quantum mechanics. (shrink)

We consider the Geometria Practica of Christopher Clavius, S.J., a surprisingly eclectic and comprehensive practical geometry text, whose first edition appeared in 1604. Our focus is on four particular sections from Books IV and VI where Clavius has either used his sources in an interesting way or where he has been uncharacteristically reticent about them. These include the treatments of Heron’s Formula, Archimedes’ Measurement of the Circle, four methods for constructing two mean proportionals between two lines, and finally an algorithm (...) for computing nth roots of numbers. (shrink)

Este ensaio introdutório faz uma breve apresentação do tratado de óptica atribuído a Euclides de Alexandria, inserindo-o no contexto das teorias sobre a visão formuladas pelas doutrinas filosóficas antigas. Ressalta-se o antagonismo entre a análise geométrica da visão, empreendida por Euclides, e as considerações filosóficas acerca dos processos físicos subjacentes à sensação visual. Pretende-se mostrar que o objeto da óptica euclidiana é a percepção visual daquilo que Aristóteles denomina "sensível comum". This introductory essay provides an abridged presentation of the optical (...) treatise attributed to Euclid of Alexandria, placing it in the context of theories about vision formulated by the ancient philosophical doctrines. I emphasize the antagonism between the geometric analysis of vision, undertaken by Euclid, and the philosophical considerations about the physical processes underlying visual sensation. In addition, I aim to show that the object of Euclidean optics is the visual perception of what Aristotle calls "common sensible". (shrink)

Autor wskazuje na analogie pomiędzy kartezjańskim układem współrzędnych, a kartezjańską koncepcją bytu psychofi zycznego. Jak się okazuje, rozważania z zakresu geometrii stanowią uzasadnienie dla wielu założeń i hipotez poczynionych przez Kartezjusza na użytek budowy przez niego jego koncepcji ontologicznej.