Daylight and Architectural Simulation of the Egebjerg School (Denmark): Sustainable Features of a New Type of Skylight

This article discusses the performance of a new skylight for standard classrooms at the Egebjerg School (Denmark), which was built ca. 1970. This building underwent important reforms under a European project to which the authors contributed. This research aimed to create a new skylight prototype that is useful for several schools in the vicinity, since there is a lack of educational facilities. The former skylights consisted of plastic pyramids that presented serious disadvantages in terms of sustainability matters. During the design process, the priority changed to studying the factors that correlate daylighting with energy and other environmental aspects in a holistic and evocative approach. Accordingly, the new skylight features promote the admittance and di usion of solar energy through adroit guidance systems. In order to simulate di erent scenarios, we employed our own simulation tool, Diana X. This research-oriented software works with the e ects of direct solar energy that are mostly avoided in conventional programs. By virtue of Lambert’s reciprocity theorem, our procedure, which was based on innovative equations of radiative transfer, converts the energy received by di usive surfaces into luminous exitance for all types of architectural elements. Upon completion of the skylights, we recorded onsite measurements, which roughly coincided with the simulation data. Thus, conditions throughout the year improved

Applying stress-testing on value at risk (VaR) methodologies

In recent years, Value at Risk (VaR) methodologies, i. e., Parametric VaR, Historical Simulation and the Monte Carlo Simulation have experienced spectacular growth within the new regulatory framework which is Basle II. Moreover, complementary analyses such a Stress-testing and Back-testing have also demonstrated their usefulness for financial risk managers. In this paper, we develop an empirical Stress-Testing exercise by using two historical scenarios of crisis. In particular, we analyze the impact of the 11-S attacks (2001) and the Latin America crisis (2002) on the level of risk, previously calculated by different statistical methods. Consequently, we have selected a Spanish stock portfolio in order to focus on market risk

The great antinomy

Se plantea y discute una “gran antinomia” entre concepciones teoreticistas o fundacionistas, y concepciones pragmatistas, en relación con una amplia diversidad de enfoques científicos y/o filosóficos. Ilustramos este contraste de manera especial con el concepto de tiempo y algunas consideraciones en torno a los ‘negacionistas’ del tiempo, guiados por visiones teoreticistas.We formulate and discuss a “great antinomy” between theoreticist/foundationist conceptions and pragmatist conceptions, in relation to a wide diversity of scientific and/or philosophical approaches. The contrast is illustrated in particular with the concept of time, considering the ‘timelessness crowd’ that has been guided by a theoreticist vision

O surgimento da abordagem conjuntista em matemática

This paper reviews some of the central ideas that the author has offered in an attempt to analyze the rise of the set-theoretical approach in mathematics, from the 1850s to the 1920s. We focus on viewpoints that may be regarded as representative of new directions in the recent historiography of mathematics, such as emphasis on research schools and attention to the institutional contexts. To complement the rather well-known history of the work of Cantor and Dedekind, we discuss mainly the pioneering contribution of Riemann, and the guiding role played by Hilbert at the turn of the century

Mathematical logic: a discipline in search of a frame

Se ofrece un análisis de las transformaciones disciplinares que ha experimentado la lógica matemática o simbólica desde su surgimiento a fines del siglo XIX. Examinaremos sus orígenes como un híbrido de filosofía y matemáticas, su madurez e institucionalización bajo la rúbrica de “lógica y fundamentos”, una segunda ola de institucionalización durante la Posguerra, y los desarrollos institucionales desde 1975 en conexión con las ciencias de la computación y con el estudio de lenguaje e informática. Aunque se comenta algo de la “historia interna”, nos centraremos en la emergencia, consolidación y convoluciones de la lógica como disciplina, a través de varias asociaciones profesionales y revistas, en centros como Turín, Gotinga, Varsovia, Berkeley, Princeton, Carnegie Mellon, Stanford y Amsterdam.We offer an analysis of the disciplinary transformations underwent by mathematical or symbolic logic since its emergence in the late 19th century. Examined are its origins as a hybrid of philosophy and mathematics, the maturity and institutionalization attained under the label “logic and foundations”, a second wave of institutionalization in the Postwar period, and the institutional developments since 1975 in connection with computer science and with the study of language and informatics. Although some “internal history” is discussed, the main focus is on the emergence, consolidation and convolutions of logic as a discipline, through various professional associations and journals, in centers such as Torino, Göttingen, Warsaw, Berkeley, Princeton, Carnegie Mellon, Stanford, and Amsterdam.Ministerio de Ciencia y Tecnología BFF2003-09579-C03-02Junta de Andalucía P07-HUM-0259

The Motives behind Cantor's Set Theory – Physical, Biological, and Philosophical Questions

The celebrated “creation” of transfinite set theory by Georg Cantor has been studied in detail by historians of mathematics. However, it has generally been overlooked that his research program cannot be adequately explained as an outgrowth of the mainstream mathematics of his day. We review the main extra-mathematical motivations behind Cantor’s very novel research, giving particular attention to a key contribution, the Grundlagen (Foundations of a general theory of sets) of 1883, where those motives are articulated in some detail. Evidence from other publications and correspondence is pulled out to provide clarification and a detailed interpretation of those ideas and their impact upon Cantor’s research. Throughout the paper, a special effort is made to place Cantor’s scientific undertakings within the context of developments in German science and philosophy at the time (philosophers such as Trendelenburg and Lotze, scientists like Weber, Riemann, Vogt, Haeckel), and to reflect on the German intellectual atmosphere during the nineteenth century

Hilbert, logicism, and mathematical existence

David Hilbert’s early foundational views, especially those corresponding to the 1890s, are analysed here. I consider strong evidence for the fact that Hilbert was a logicist at that time, following upon Dedekind’s footsteps in his understanding of pure mathematics. This insight makes it possible to throw new light on the evolution of Hilbert’s foundational ideas, including his early contributions to the foundations of geometry and the real number system. The context of Dedekind-style logicism makes it possible to offer a new analysis of the emergence of Hilbert’s famous ideas on mathematical existence, now seen as a revision of basic principles of the “naive logic” of sets. At the same time, careful scrutiny of his published and unpublished work around the turn of the century uncovers deep differences between his ideas about consistency proofs before and after 1904. Along the way, we cover topics such as the role of sets and of the dichotomic conception of set theory in Hilbert’s early axiomatics, and offer detailed analyses of Hilbert’s paradox and of his completeness axiom (Vollständigkeitsaxiom)

On arbitrary sets and ZFC

Set theory deals with the most fundamental existence questions in mathematics– questions which affect other areas of mathematics, from the real numbers to structures of all kinds, but which are posed as dealing with the existence of sets. Especially noteworthy are principles establishing the existence of some infinite sets, the so-called “arbitrary sets.” This paper is devoted to an analysis of the motivating goal of studying arbitrary sets, usually referred to under the labels of quasi-combinatorialism or combinatorial maximalist. After explaining what is meant by definability and by “arbitrariness”, a first historical part discusses the strong motives why set theory was conceived as a theory of arbitrary sets, emphasizing connections with analysis and particularly with the continuum of real numbers. Judged from this perspective, the axiom of choice stands out as a most central and natural set-theoretic principle (in the sense of quasi-combinatorialism). A second part starts by considering the potential mismatch between the formal systems of mathematics and their motivating conceptions, and proceeds too fferan elementary discussion of how far the Zermelo–Fraenkel system goes in laying out principles that capture the idea of “arbitrary sets”. We argue that the theory is rather poor in this respect.Junta de Andalucía P07-HUM-02594Ministerio de Ciencia y Tecnología BFF2003-09579-C0

A double bind? Reflections on history, science and culture

El objetivo de este trabajo es explorar el doble vínculo entre ciencia y cultura a través de un repaso, desde la historia y la filosofía de la ciencia, de las actividades científicas, en particular las asociadas al conocimiento matemático, en tanto que conjuntos de saberes y prácticas pertenecientes a un contexto intelectual, social y político más amplio y complejo.The aim of this paper is to explore the double bind between science and culture through the analysis, from the history and philosophy of science perspective, of various scientific activities, in particular those linked to mathematical knowledge, described as knowledge-making practices belonging to a much wider and complex intellectual, social and political context