A heurística da representação na ciência : os mecanismos e os princípios matemáticos na física de Descartes e Fermat

O objetivo deste artigo, que faz parte de um programa de pesquisa desenvolvido pelos autores sobre o papel da representação na ciência e no ensino de ciências, é destacar o uso de mecanismos e princípios matemáticos como heurísticas representacionais dos fenômenos físicos e utilizada, respectivamente, por Descartes e Fermat em suas investigações no campo da óptica, mais especificamente em suas análises do fenômeno da refração da luz. Com exemplos extraídos da obra dos referidos autores, buscamos explicitar compromissos e concepções distintas, mas não excludentes, acerca da dinâmica de construção e desenvolvimento de teorias científicas. Do ponto de vista heurístico, levantamos a tese da complementaridade e convergência entre ambas as representações, sob o argumento de que caberia aos mecanismos capturar o princípio material constitutivo do fenômeno, enquanto os princípios matemáticos abstratos se encarregariam da sua organização formal. Ao enfatizar aspectos relacionados à dinâmica de construção e desenvolvimento de teorias científicas, elementos heurísticos essenciais a uma compreensão da Natureza da Ciência e, portanto, relevantes ao processo de ensino e aprendizagem da Física, surgirão.The objective of this article, which is part of the research program developed by the authors on the role of representation in science and science education, is to highlight the use of mechanisms and mathematical principles as representational heuristics of physical phenomena. They have been used by Descartes and Fermat in their respective investigations in the field of optics, more specifically in their analysis of the light refraction phenomenon. With examples drawn from the works of the cited authors, we sought to reveal the distinct, but not exclusive commitments and conceptions about the dynamics involved in building and developing scientific theories. From the heuristic point of view, we raise the hypothesis of the complementarity and convergence between both representations, with the argument it's up to the mechanisms to capture the constituting material principle of the phenomenon, while the abstract mathematical principles should take care of its formal organization. By emphasizing aspects related to the dynamics of the construction and development of scientific theories, heuristic elements essential to an understanding of the Nature of Science (NOS) and therefore relevant to the Descartes, Fermat, Epistemology of physics, Heuristics, Physics Education teaching and learning process of physics will emerge

Dynamic instabilities induced by asymmetric influence: Prisoners' dilemma game on small-world networks

A two-dimensional small-world type network, subject to spatial prisoners' dilemma dynamics and containing an influential node defined as a special node with a finite density of directed random links to the other nodes in the network, is numerically investigated. It is shown that the degree of cooperation does not remain at a steady state level but displays a punctuated equilibrium type behavior manifested by the existence of sudden breakdowns of cooperation. The breakdown of cooperation is linked to an imitation of a successful selfish strategy of the influential node. It is also found that while the breakdown of cooperation occurs suddenly, the recovery of it requires longer time. This recovery time may, depending on the degree of steady state cooperation, either increase or decrease with an increasing number of long range connections.Comment: 5 pages, 6 figure

EXPERIMENTO MENTAL I: A CONCEPCAO CONTRATUALISTA CLASSICA, O MODELO DA TRAGEDIA DOS COMUNS E AS CONDICOES DE EMERGENCIA E ESTABILIDADE DA COOPERACAO HOBBES

The goal is to represent the problem of the conditions of the emergence and stability of cooperation among interacting individuals, as we interpret the classical contractualist approach of the problem of the origins of civil and political rights, in terms of the model of commons tragedy. This is pursued in order to show that the formation of the civil and political rights follows a process with two stages: privatization and statization or subjectivity and objectivity. The privatization process is related to the emergence of the individual as individual throughout the emergence of the property rights as dimensions of his individuality. In this case, each individual is himself a scarce resource still it is a common property from the point of view of the others individuals. The process of statization is related to the emergence and stability of the cooperation among the individuals. The social cooperation is the next stage and it is a strategy that results necessarily from each rational individual in order to make objective the recognition by the others of his property rights that was subjectively constructed in the process of individualization or privatization. The social cooperation, by its turn, requires the design of a contract among the individuals looking for recognition in which each of the property rights is specified and also its amount. Besides, it must specify the design of a mechanism, the State, to which is attributed the task of being in charge of the enforcement of the contract. The characteristics of the design as of the contract as of the mechanism of the state depend upon certain axiological elements of the classical contractualist conception. Hobbes chooses as the main axiological element the property right to life and states the main problem is that of the preservation of the life. This means that here the goal is to make the property right of life objective or, in other words, that must be a mutual recognition of this property right. In order to reach this goal it will be acceptable a trade-off between others property rights such as freedom, equality and also the right to defend each one with all means, among them the life of the others