Artículos con la etiqueta ‘matemática’

Alan Turing and the Origins of Complexity

Por • 9 oct, 2011 • Category: Filosofía

The 75th anniversary of Turing’s seminal paper and his centennial year anniversary occur in 2011 and 2012, respectively. It is natural to review and assess Turing’s contributions in diverse fields in the light of new developments that his thoughts has triggered in many scientific communities. Here, the main idea is to discuss how the work of Turing allows us to change our views on the foundations of Mathematics, much like quantum mechanics changed our conception of the world of Physics. Basic notions like computability and universality are discussed in a broad context, making special emphasis on how the notion of complexity can be given a precise meaning after Turing, i.e., not just qualitative but also quantitative. Turing’s work is given some historical perspective with respect to some of his precursors, contemporaries and mathematicians who took up his ideas farther.



Constructibilidad relativizada y el Axioma de Elección

Por • 19 jun, 2011 • Category: Filosofía

El objetivo de este trabajo es presentar en un solo cuerpo tres maneras de relativizar (o generalizar) el concepto de conjunto constructible de Godel que no suelen aparecer juntas en la literatura especializada y que son importantes en la Teoría de Conjuntos, por ejemplo para resolver problemas de consistencia o independencia. Presentamos algunos modelos resultantes de las diferentes formas de relativizar el concepto de constructibilidad, sus propiedades basicas y algunas formas debiles del Axioma de Elección validas o no validas en ellas.



Time of Philosophers, Time of Physicists, Time of Mathematicians

Por • 26 abr, 2011 • Category: Filosofía

Is presentism compatible with relativity ? This question has been much debated since the argument first proposed by Rietdijk and Putnam. The goal of this text is to study the implications of relativity and quantum mechanics on presentism, possibilism, and eternalism. We put the emphasis on the implicit metaphysical preconceptions underlying each of these different approaches to the question of time. We show that there exists a unique version of presentism which is both non-trivial, in the sense that it does not reduce the present to a unique event, and compatible with special relativity and quantum mechanics: the one in which the present of an observer at a point is identified with the backward light cone of that point. However, this compatibility is achieved at the cost of a renouncement to the notion of an objective, observer-independent reality. We also argue that no non-trivial version of presentism survives in general relativity, except if some mechanism forbids the existence of closed timelike curves, in which case precisely one version of possibilism does survive.



The Monty Hall Problem: Switching is Forced by the Strategic Thinking

Por • 25 mar, 2011 • Category: Opinion

Game versions of the Monty Hall Problem are discussed. The focus is on the principle of eliminating the dominated strategies, both in the zero-sum and noncooperative formulations.



Towards an axiomatic system for Kolmogorov complexity

Por • 4 feb, 2011 • Category: Filosofía

In this paper, we try to extend this work, both by looking at alternative axiomatic systems for plain complexity and by considering potential axiomatic systems for other types of complexity.



Fundamental and Real-World Challenges in Economics

Por • 13 ene, 2011 • Category: Economía

In the same way as the Hilbert Program was a response to the foundational crisis of mathematics, this article tries to formulate a research program for the socio-economic sciences.



Ergodic directional switching in mobile insect groups – arxiv.org

Por • 10 ago, 2010 • Category: Ciencia y tecnología

Authors: Carlos Escudero, Christian A. Yates, Jerome Buhl, Iain D. Couzin, Radek Erban, Ioannis G. Kevrekidis, Philip K. Maini (Submitted on 1 Aug 2010) Abstract: We obtain a Fokker-Planck equation describing experimental data on the collective motion of locusts. The noise is of internal origin and due to the discrete character and finite number of […]