Artículos con la etiqueta ‘complejidad’

On coordinatization of mathematics

Por • 10 jun, 2013 • Category: Educacion

The problem of advancing coordinatization of mathematics is considered. The need to develop a theory for measuring value and complexity of mathematical implications and proofs is discussed. Arguments advocating such an advance related to mathematical research guidance, publication standards and education are given.



Kolmogorov complexity as a hidden factor of scientific discourse: from Newton’s law to data mining

Por • 3 ene, 2013 • Category: Ciencia y tecnología

The word «complexity» is most often used as a meta–linguistic expression referring to certain intuitive characteristics of a natural system and/or its scientific description. These characteristics may include: sheer amount of data that must be taken into account; visible «chaotic» character of these data and/or space distribution/time evolution of a system etc. This talk is centered around the precise mathematical notion of «Kolmogorov complexity», originated in the early theoretical computer science and measuring the degree to which an available information can be compressed. In the first part, I will argue that a characteristic feature of basic scientific theories, from Ptolemy’s epicycles to the Standard Model of elementary particles, is their splitting into two very distinct parts: the part of relatively small Kolmogorov complexity («laws», «basic equations», «periodic table», «natural selection, genotypes, mutations») and another part, of indefinitely large Kolmogorov complexity («initial and boundary conditions», «phenotypes», «populations»). The data constituting this latter part are obtained by planned observations, focussed experiments, and afterwards collected in growing databases (formerly known as «books», «tables», «encyclopaedias» etc). In this discussion Kolomogorov complexity plays a role of the central metaphor. The second part and Appendix 1 are dedicated to more precise definitions and examples of complexity.



Randomness, Information, and Complexity

Por • 23 ago, 2012 • Category: Ciencia y tecnología

We review possible measures of complexity which might in particular be applicable to situations where the complexity seems to arise spontaneously. We point out that not all of them correspond to the intuitive (or «naive») notion, and that one should not expect a unique observable of complexity. One of the main problems is to distinguish complex from disordered systems. This and the fact that complexity is closely related to information requires that we also give a review of information measures. We finally concentrate on quantities which measure in some way or other the difficulty of classifying and forecasting sequences of discrete symbols, and study them in simple examples.



Knowledge epidemics and population dynamics models for describing idea diffusion

Por • 6 ene, 2012 • Category: Opinion

The diffusion of ideas is often closely connected to the creation and diffusion of knowledge and to the technological evolution of society. Because of this, knowledge creation, exchange and its subsequent transformation into innovations for improved welfare and economic growth is briefly described from a historical point of view. Next, three approaches are discussed for modeling the diffusion of ideas in the areas of science and technology, through (i) deterministic, (ii) stochastic, and (iii) statistical approaches. These are illustrated through their corresponding population dynamics and epidemic models relative to the spreading of ideas, knowledge and innovations. The deterministic dynamical models are considered to be appropriate for analyzing the evolution of large and small societal, scientific and technological systems when the influence of fluctuations is insignificant. Stochastic models are appropriate when the system of interest is small but when the fluctuations become significant for its evolution. Finally statistical approaches and models based on the laws and distributions of Lotka, Bradford, Yule, Zipf-Mandelbrot, and others, provide much useful information for the analysis of the evolution of systems in which development is closely connected to the process of idea diffusion.



Complexity

Por • 10 oct, 2011 • Category: sociologia

The term complexity derives etymologically from the Latin plexus, which means interwoven. Intuitively, this implies that something complex is composed by elements that are difficult to separate. This difficulty arises from the relevant interactions that take place between components. This lack of separability is at odds with the classical scientific method – which has been used since the times of Galileo, Newton, Descartes, and Laplace – and has also influenced philosophy and engineering. In recent decades, the scientific study of complexity and complex systems has proposed a paradigm shift in science and philosophy, proposing novel methods that take into account relevant interactions.



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.



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.



Evidence of strategic periodicities in collective conflict dynamics

Por • 17 ene, 2011 • Category: Leyes

We demonstrate the existence of periodicities that are not directly coupled to environmental cycles or known ultraridian mechanisms.