Limits of Computation

Analizamos un conjunto de oraciones y fórmulas que se niegan a sí mismas: Desde la paradoja del mentiroso, la de la Ínsula de “El Quijote”, hasta el teorema de Gödel o los límites computacionales propuestos por Turing. Partiendo de dos diferencias cruciales: limitación por atribución versus limitación absoluta; y no saber versus saber que es paradójico, mostramos como resolver estas situaciones mediante un nuevo valor de verdad “G=paradójico”; de modo que pueda ser posible conocer el valor de verdad de cualquier oración o proceso computacional.

Mostramos como las limitaciones que supuso el Teorema de Gödel a la creación de sistemas consistentes y completos; o los análisis de Turing a los límites computacionales, se pueden superar usando un nuevo valor lógico, “G”, “paradójico”. Veremos que en el fondo está la viaja paradoja del mentiroso, como solo afecta a unas pocas “Islas Gödelianas de Incertidumbre” y cómo es posible asignar un tratamiento distinto del de las frases verdaderas o falsas (o producibles o no producibles), de modo sea posible “conocer” la veracidad de la frase.

Children and the media - kids and Technology combo
Today, technology for kids is a source of learning and entertainment, and in a pinch when parents have to get dinner made or take a few minutes to answer emails, a terrific babysitter.
For school-age kids, technology can be a double-edged sword. There are countless benefits that can be garnered from using technology: Computers can be used to do research, play online math games, and improve language skills. Television (and DVDs) can offer educational programming such as documentaries and other educational materials. And even video games can encourage developmental skills such as hand-eye coordination (and some motion-controlled active games on the Wii or Xbox with Kinect can promote physical activity such as dancing). But all these electronic devices can also have some distinct disadvantages as well. Here are some reasons why technology should be limited for kids and how to do it.
Reasons for Limiting Kids’ Exposure to Technology

The behavior of some systems is noncomputable in a precise new sense.  One infamous problem is that of the stability of the solar system:  Given the initial positions and velocities of several mutually gravitating bodies, will any eventually collide or be thrown off to infinity?  Many have made vague suggestions that this and similar problems are undecidable:  No finite procedure can reliably determine whether a given configuration will eventually prove unstable.  But taken in the most natural way, this is trivial.  The state of a system corresponds to a point in a continuous space, and virtually no set of points in space is strictly decidable.  A new, more pragmatic concept is therefore introduced:  A set is decidable up to measure zero (d.m.z.) if there is a procedure to decide whether a point is in that set and it only fails on some points that form a set of zero volume.  This is motivated by the intuitive correspondence between volume and probability:  We can ignore a zero-volume set of states because the state of an arbitrary system almost certainly will not fall in that set.  D.m.z. is also closer to the intuition of decidability than other notions in the literature, which are either less strict or apply only to special sets, like closed sets.  Certain complicated sets are not d.m.z., most remarkably including the set of know stable orbits for planetary systems (the KAM tori).  This suggests that the stability problem is indeed undecidable in the precise sense of d.m.z.  Carefully extending decidability concepts from idealized models to actual systems, we see that even deterministic aspects of physical behaviour can be undecidable in a clear and significant sense.

Computer science is winning the ground that was the traditional domain of physics. Answer to the question what ultimately matters nowadays belongs more to computer science than to physics. Search for answers to questions about truth, meaning, mind, subjectivity, consciousness etc. lies among others within AI. A brief skeptic argument against Penrose's neo-vitalism is presented. The next question is if we can claim understanding the phenomena on the ground of their experimental reproducibility?