Hemeroteca del mes mayo, 2014

Herbrand’s Fundamental Theorem: The Historical Facts and their Streamlining

Por • 31 may, 2014 • Category: Ambiente

Using Heijenoort’s unpublished generalized rules of quantification, we discuss the proof of Herbrand’s Fundamental Theorem in the form of Heijenoort’s correction of Herbrand’s “False Lemma” and present a didactic example. Although we are mainly concerned with the inner structure of Herbrand’s Fundamental Theorem and the questions of its quality and its depth, we also discuss the outer questions of its historical context and why Bernays called it “the central theorem of predicate logic” and considered the form of its expression to be “concise and felicitous”.

A formally verified proof of the Central Limit Theorem

Por • 31 may, 2014 • Category: Educacion

We describe a formally verified proof of the Central Limit Theorem in the Isabelle proof assistant.

Networks of Military Alliances, Wars, and International Trade

Por • 31 may, 2014 • Category: sociologia

We investigate the role of networks of military alliances in preventing or encouraging wars between groups of countries. A country is vulnerable to attack if some allied group of countries can defeat the defending country and its (remaining) allies based on their collective military strengths. We show that there do not exist any networks which contain no vulnerable countries and that are stable against the pairwise addition of a new alliance as well as against the unilateral deletion of any existing alliance. We then show that economic benefits from international trade provide incentives to form alliances in ways that restore stability and prevent wars, both by increasing the density of alliances so that countries are less vulnerable and by removing the incentives of countries to attack their allies.

Canciller Patiño dijo que Senado de EEUU busca patrocinar a la oposición

Por • 30 may, 2014 • Category: Nacionales

El canciller ecuatoriano, Ricardo Patiño, rechazó los “intentos injerencistas” de otros gobiernos en las políticas y asuntos internos de Venezuela que buscan crear “desestabilización en el país”. Esto lo declaró desde Ecuador, luego de la reunión de cancilleres que se desarrolló en ese país.

Rusia se opone a sanciones de Estados Unidos contra Venezuela

Por • 30 may, 2014 • Category: Nacionales

El jefe de la diplomacia rusa señaló que “todos los problemas [de un país] deben resolverse de forma constitucional, sin ninguna injerencia externa, ni siquiera bajo forma de sanciones o amenazas de sanciones”.

The Anthyphairetic Revolutions of the Platonic Ideas

Por • 30 may, 2014 • Category: Filosofía

In the present work it is shown, by an examination of the Platonic dialogues Theaetetus, Sophistes, Politicus, and Philebus, that (a) a Platonic Idea is the philosophic analogue of a pair of lines incommensurable in length only, (b) the Division and Collection, the method by which humans obtain knowledge of a Platonic Idea, is the philosophic analogue of the palindromically periodic anthyphairesis of this pair, and (c) a Platonic Idea is One in the sense of the self-similarity induced by periodic anthyphairesis. A byproduct of the above analysis is that (d) Theaetetus had obtained a proof of the Proposition: The anthyphairesis of a dyad of lines incommensurable in length only is palindromically periodic. It is further verified that the concepts and tools contained in the Theaetetean Book X of the Elements suffice for the proof of the Proposition.

Algorithmic identification of probabilities is hard

Por • 30 may, 2014 • Category: Educacion

Suppose that we are given an infinite binary sequence which is random for a Bernoulli measure of parameter p . By the law of large numbers, the frequency of zeros in the sequence tends to ~p , and thus we can get better and better approximations of p as we read the sequence. We study in this paper a similar question, but from the viewpoint of inductive inference. We suppose now that p is a computable real, but one asks for more: as we are reading more and more bits of our random sequence, we have to eventually guess the exact parameter p (in the form of a Turing code). Can one do such a thing uniformly on all sequences that are random for computable Bernoulli measures, or even on a `large enough’ fraction of them? In this paper, we give a negative answer to this question. In fact, we prove a very general negative result which extends far beyond the class of Bernoulli measures.

Bohm’s approach to Quantum Mechanics and Individuality

Por • 30 may, 2014 • Category: Ciencia y tecnología

In this paper we discuss the role of the individual in the Bohm theory, according to which a particle does appear to have an individuality, but one that is significantly different from a classical particle. In contrast however, Ladyman and Ross (2007) interpret an in-depth discussion by Brown, Elby and Weingard (1996) as implying that the properties normally associated with particles (mass, charge, etc.) are inherent only in the quantum field and not in the particles. Brown, Sjoqvist and Bacciagaluppi (1999) themselves are somewhat ambivalent suggesting that it might not be unreasonable to assume that in the Bohm theory properties such as mass and charge also reside in the particles (cf. French 2011 and French and Krause 2006). This suggests that whether or not particles are individuals in non-relativistic quantum theory is a genuinely open question in a stronger sense than Ladyman and Ross imply. After an appraisal of this discussion we go on to discuss the nature of Bohmian individuals in more detail, by considering the issue in the light of new developments in the underlying mathematical structures, due to de Gosson and Hiley.

A quantum-information-theoretic complement to a general-relativistic implementation of a beyond-Turing computer

Por • 30 may, 2014 • Category: Leyes

There exists a growing literature on the so-called physical Church-Turing thesis in a relativistic spacetime setting. The physical Church-Turing thesis is the conjecture that no computing device that is physically realizable (even in principle) can exceed the computational barriers of a Turing machine. By suggesting a concrete implementation of a beyond-Turing computer in a spacetime setting, Istvan Nemeti and Gyula David (2006) have shown how an appreciation of the physical Church-Turing thesis necessitates the confluence of mathematical, computational, physical, and indeed cosmological ideas. In this essay, I will honour Istvan’s seventieth birthday, as well as his longstanding interest in, and his seminal contributions to, this field going back to as early as 1987 by modestly proposing how the concrete implementation in Nemeti and David (2006) might be complemented by a quantum-information-theoretic communication protocol between the computing device and the logician who sets the beyond-Turing computer a task such as determining the consistency of Zermelo-Fraenkel set theory. This suggests that even the foundations of quantum theory and, ultimately, quantum gravity may play an important role in determining the validity of the physical Church-Turing thesis.

Maduro en su laberinto

Por • 30 may, 2014 • Category: Nacionales

Hay momentos en que los opositores le dan mejores consejos al presidente que sus mismos colaboradores. Maduro debe ponerse las pilas porque tiempo es lo que no tiene.