Primitive Vassiliev Invariants and Factorization in Chern-Simons Perturbation Theory

The general structure of the perturbative expansion of the vacuum expectation value of a Wilson line operator in Chern-Simons gauge field theory is analyzed. The expansion is organized according to the independent group structures that appear at each order. It is shown that the analysis is greatly simplified if the group factors are chosen in a certain way that we call canonical. This enables us to show that the logarithm of a polinomial knot invariant can be written in terms of primitive Vassiliev invariants only.Comment: 15 pages, latex, 2 figure

Means or end? On the Valuation of Logic Diagrams

From the beginning of the 16th century to the end of the 18th century, there were not less than ten philosophers who focused extensively on Venn’s ostensible analytical diagrams, as noted by modern historians of logic (Venn, Gardner, Baron, Coumet et al.). But what was the reason for early modern philosophers to use logic or analytical diagrams? Among modern historians of logic one can find two theses which are closely connected to each other: M. Gardner states that since the Middle Ages certain logic diagrams were used just in order to teach “dull-witted students”. Therefore, logic diagrams were just a means to an end. According to P. Bernhard, the appreciation of logic diagrams had not started prior to the 1960s, therefore the fact that logic diagrams become an end the point of research arose very late. The paper will focus on the question whether logic resp. analytical diagrams were just means in the history of (early) modern logic or not. In contrast to Gardner, I will argue that logic diagrams were not only used as a tool for “dull-witted students”, but rather as a tool used by didactic reformers in early modern logic. In predating Bernhard’s thesis, I will argue that in the 1820s logic diagrams had already become a value in themselves in Arthur Schopenhauer’s lectures on logic, especially in proof theory

How to Eat a Cake Without Having It: An Evaluation of the IFIP Working Group 8.1 Report on Information Systems Methodologies

This paper reviews some aspects of Olle et al. [1988]. After an analysis of the terms "method" and "methodology", it is concluded that the book is an exercise in information system (IS) development methodology. We then argue that the aim of the book, the provision of a framework which should help in understanding existing IS development methods, is only partly reached, and that much work towards this goal is still to be done. Finally, we indicate some of the improvements which can be made to the text with respect to the presentation of the material as well as to the attainment of the goal

A Prehistory of n-Categorical Physics

This paper traces the growing role of categories and n-categories in physics, starting with groups and their role in relativity, and leading up to more sophisticated concepts which manifest themselves in Feynman diagrams, spin networks, string theory, loop quantum gravity, and topological quantum field theory. Our chronology ends around 2000, with just a taste of later developments such as open-closed topological string theory, the categorification of quantum groups, Khovanov homology, and Lurie's work on the classification of topological quantum field theories.Comment: 129 pages, 8 eps figure

Causal Relationship: a new tool for the causal characterization of Lorentzian manifolds

We define and study a new kind of relation between two diffeomorphic Lorentzian manifolds called {\em causal relation}, which is any diffeomorphism characterized by mapping every causal vector of the first manifold onto a causal vector of the second. We perform a thorough study of the mathematical properties of causal relations and prove in particular that two given Lorentzian manifolds (say $V$ and $W$) may be causally related only in one direction (say from $V$ to $W$, but not from $W$ to $V$). This leads us to the concept of causally equivalent (or {\em isocausal} in short) Lorentzian manifolds as those mutually causally related. This concept is more general and of a more basic nature than the conformal relationship, because we prove the remarkable result that a conformal relation \f is characterized by the fact of being a causal relation of the {\em particular} kind in which both \f and \f^{-1} are causal relations. For isocausal Lorentzian manifolds there are one-to-one correspondences, which sometimes are non-trivial, between several classes of their respective future (and past) objects. A more important feature of isocausal Lorentzian manifolds is that they satisfy the same causality constraints. This indicates that the causal equivalence provides a possible characterization of the {\it basic causal structure}, in the sense of mutual causal compatibility, for Lorentzian manifolds. Thus, we introduce a partial order for the equivalence classes of isocausal Lorentzian manifolds providing a classification of spacetimes in terms of their causal properties, and a classification of all the causal structures that a given fixed manifold can have. A full abstract inside the paper.Comment: 47 pages, 10 figures. Version to appear in Classical and Quantum Gravit

Understanding as integration of heterogeneous representations

The search for understanding is a major aim of science. Traditionally, understanding has been undervalued in the philosophy of science because of its psychological underpinnings; nowadays, however, it is widely recognized that epistemology cannot be divorced from psychology as sharp as traditional epistemology required. This eliminates the main obstacle to give scientific understanding due attention in philosophy of science. My aim in this paper is to describe an account of scientific understanding as an emergent feature of our mastering of different (causal) explanatory frameworks that takes place through the mastering of scientific practices. Different practices lead to different kinds of representations. Such representations are often heterogeneous. The integration of such representations constitute understanding

The implementation of graphic organizers to teach reading comprehension skills to second graders of the sur oriental Boston Branch School

El propósito del siguiente proyecto fue seguir una secuencia didáctica y aplicar mapas mentales tal como un organizador gráfico como herramienta de entendimiento y al mismo tiempo mejorar las habilidades de lectura en el L2 con el fin de guiar los aprendices a localizar y clasificar información usando un mapa mental como un organizador gráfico para mejorar las habilidades de lectura