Hemeroteca de la sección ‘Ciencia y tecnología’

On the mathematical and foundational significance of the uncountable

Por • 29 nov, 2017 • Category: Ciencia y tecnología

For various historical, practical, and foundational reasons, large parts of mathematics are studied indirectly via countable approximations, also called codes. It is a natural question whether this indirect study of codes is faithful to the original development in mathematics, or whether approximations somehow distort the latter. Another natural question is which parts of basic mathematics can(not) be studied via these representations. In this paper, we formulate new answers to these old questions. Our answers stem both from mathematics itself (via the study of the gauge integral) and its foundations (via Hilbert-Bernays’ Grundlagen der Mathematik and its spiritual successor Reverse Mathematics). We identify a number of basic theorems from (uncountable) mathematics for which the logical and computational properties are completely (and even maximally) distorted upon introducing countable approximations. In a nutshell, while countable approximations are interesting and important, even extremely basic ‘uncountable’ mathematics is infinitely more complicated than the ‘countable picture’ involving codes suggests.



El I+D+ i y el Observatorio Tecnológico de Defensa

Por • 3 nov, 2017 • Category: Ciencia y tecnología

Este artículo ofrece una visión sobre cómo el mundo de la defensa se adapta a la evolución existente en su entorno, tanto a la evolución de las tecnologías como a las necesidades y oportunidades de aplicación de estas a los intereses de defensa. Así, se destaca cómo el futuro ya no pasa tanto por el descubrimiento y desarrollo de nuevas tecnologías, sino por el aprovechamiento y aplicación de los desarrollos civiles para defensa. Es labor del Ministerio de Defensa, no solo anticiparse a los riesgos y amenazas, sino contribuir a la mejora de las capacidades tecnológicas e industriales para la defensa y de uso dual. Un ejemplo de mecanismo para esta adaptación es el Sistema de Vigilancia y Prospectiva Tecnológica (SOPT) ubicado en la SDGTECIN.



Reconsidering Experiments

Por • 17 oct, 2017 • Category: Ciencia y tecnología

Experiments may not reveal their full import at the time that they are performed. The scientists who perform them usually are testing a specific hypothesis and quite often have specific expectations limiting the possible inferences that can be drawn from the experiment. Nonetheless, as Hacking has said, experiments have lives of their own. Those lives do not end with the initial report of the results and consequences of the experiment. Going back and rethinking the consequences of the experiment in a new context, theoretical or empirical, has great merit as a strategy for investigation and for scientific problem analysis. I apply this analysis to the interplay between Fizeau’s classic optical experiments and the building of special relativity. Einstein’s understanding of the problems facing classical electrodynamics and optics, in part, was informed by Fizeau’s 1851 experiments. However, between 1851 and 1905, Fizeau’s experiments were duplicated and reinterpreted by a succession of scientists, including Hertz, Lorentz, and Michelson



Open problems in mathematical physics

Por • 13 oct, 2017 • Category: Ciencia y tecnología

We present a list of open questions in mathematical physics. After a historical introduction, a number of problems in a variety of different fields are discussed, with the intention of giving an overall impression of the current status of mathematical physics, particularly in the topical fields of classical general relativity, cosmology and the quantum realm. This list is motivated by the recent article proposing 42 fundamental questions (in physics) which must be answered on the road to full enlightenment. But paraphrasing a famous quote by the British football manager Bill Shankly, in response to the question of whether mathematics can answer the Ultimate Question of Life, the Universe, and Everything, mathematics is, of course, much more important than that.



Charles Peirce on the Classification of Dyadic Relations and the Implications for Mathematical Logic

Por • 3 oct, 2017 • Category: Ciencia y tecnología

Charles Peirce develops a scheme for classifying different kinds of monadic, dyadic and triadic relations. His account of these different classes of relations figures prominently in the development of his algebraic and diagrammatic systems of mathematical logic. Our aim in this essay is to reconstruct and examine central features of the classificatory system that he develops. Given the complexity of the system, we will focus our attention on the classification and explanation of of degenerate and genuine dyadic relations, and we will take up the discussion of triadic relations elsewhere. One of our reasons for wanting to explore this account of relations is to better understand how it informed the later development of relations as they figure in the history of mathematical logic. The earlier work of Peirce on dyadic relations influenced the development of the account of dyadic logical relations in works of Ernst Schroder, Leopold Lowenheim, Thoralf Skolem and Alfred Tarski. As such, our primary aim in this essay is to trace the early development of these ideas about the formal relation of the dyad for the sake of better understanding how it might have influenced these later developments.



Five stages of accepting constructive mathematics

Por • 27 sep, 2017 • Category: Ciencia y tecnología

On the odd day, a mathematician might wonder what constructive mathematics is all about. They may have heard arguments in favor of constructivism but are not at all convinced by them, and in any case they may care little about philosophy. A typical introductory text about constructivism spends a great deal of time explaining the principles and contains only trivial mathematics, while advanced constructive texts are impenetrable, like all unfamiliar mathematics. How then can a mathematician find out what constructive mathematics feels like? What new and relevant ideas does constructive mathematics have to offer, if any? I shall attempt to answer these questions.



The “go-stop-go” of Italian civil nuclear programs, beset by lack of strategic planning, exploitation for personal gain and unscrupulous political conspiracies: 1946-1987

Por • 19 sep, 2017 • Category: Ciencia y tecnología

The Italian civil nuclear projects had a very early origin, with the first ideas originating as far back as 1945. The construction of the first three plants dated back to the period 1956-1964, and at that time Italy ranked third in the world for installed power. However, the very ambitious projects were immediately after thwarted in the early 1960s by the “Ippolito trial”. Actually, a whole range of advanced programmes for the development of the country went to a stop, since they clashed with national and international major powers. Italy was relegated to a second rank power. The fourth nuclear plan was designed in 1970, and its commercial operation began in 1981. In the meantime, a strong anti-nuclear movement grew, and the position of the pro-nuclear Italian Communist Party began to change. After the Chernobyl accident, a national referendum was held, which in 1987 put an end to the Italian nuclear programmes.



Winning Investment Strategies Based on Financial Crisis Indicators

Por • 17 sep, 2017 • Category: Ciencia y tecnología

The aim of this work is to create systematic trading strategies built upon several financial crisis indicators based on the spectral properties of market dynamics. Within the limitations of our framework and data, we will demonstrate that our systematic trading strategies are able to make money, not as a result of pure luck but, in a reproducible way and while avoiding the pitfall of over fitting, as a result of the skill of the operators and their understanding and knowledge of the financial market. Using singular value decomposition (SVD) techniques in order to compute all spectra in an efficient way, we have built two kinds of financial crisis indicators with a demonstrable power of prediction. Firstly, there are those that compare at every date the distribution of the eigenvalues of a covariance or correlation matrix to a distribution of reference representing either a calm or agitated market reference. Secondly, we have those that merely compute at every date a chosen spectral property (trace, spectral radius or Frobenius norm) of a covariance or correlation matrix. Aggregating the signals provided by all the indicators in order to minimize false positive errors, we then build systematic trading strategies based on a discrete set of rules governing the investment decisions of the investor.



Information Theory and the Length Distribution of all Discrete Systems

Por • 9 sep, 2017 • Category: Ciencia y tecnología

We begin with the extraordinary observation that the length distribution of 80 million proteins in UniProt, the Universal Protein Resource, measured in amino acids, is qualitatively identical to the length distribution of large collections of computer functions measured in programming language tokens, at all scales. That two such disparate discrete systems share important structural properties suggests that yet other apparently unrelated discrete systems might share the same properties, and certainly invites an explanation.



Network Analysis of Particles and Grains

Por • 3 sep, 2017 • Category: Ciencia y tecnología

The arrangements of particles and forces in granular materials and particulate matter have a complex organization on multiple spatial scales that range from local structures to mesoscale and system-wide ones. This multiscale organization can affect how a material responds or reconfigures when exposed to external perturbations or loading. The theoretical study of particle-level, force-chain, domain, and bulk properties requires the development and application of appropriate mathematical, statistical, physical, and computational frameworks. Traditionally, granular materials have been investigated using particulate or continuum models, each of which tends to be implicitly agnostic to multiscale organization. Recently, tools from network science have emerged as powerful approaches for probing and characterizing heterogeneous architectures in complex systems, and a diverse set of methods have yielded fascinating insights into granular materials.