Nowhere dense graph classes, stability, and the independence property

A class of graphs is nowhere dense if for every integer r there is a finite upper bound on the size of cliques that occur as (topological) r-minors. We observe that this tameness notion from algorithmic graph theory is essentially the earlier stability theoretic notion of superflatness. For subgraph-closed classes of graphs we prove equivalence to stability and to not having the independence property.Comment: 9 page

Was heißt Fortschritt im Wissen? Gnoseoto­pi­sche Überlegungen zur Auf­klä­rung und ihren Folgen

This article focuses on the question of what “progress in knowledge” (Fortschritt im Wissen) since the Enlightenment could mean. The answer is rooted in a shift in perspective in our understanding of the Enlightenment, and in an awareness of the gnoseotope at the center of this perspectival shift. Given the fact that human knowledge has always been considered li­mited, the axiom called gnoseotope (from Greek gnōsis: cognition, know­ledge and topos: place, area, field) can be defined as the area of re­latively secure knowledge, which is subject to both quantitative (cumulative) and qualitative (paradigmatic) histo­rical changes. Considering the further fact that human ignorance has been acknowledged since Antiquity and taken for granted for millennia of human history, the awareness of this ignorance becomes parti­cularly problematic during the Enlightenment when irreducible yet systematically repressed elements of human ignorance were integrated into the epistemology of 18th-century rationalism. This article discusses the development in the shift from ignorance as a given to ignorance as a systematically reflected part of the conditions of human knowledge from a historical point of view through the examples of Christian Wolff, Alexander Gottlieb Baumgarten, and Johann Georg Sulzer. The argument does not focus on the ‘completion’ of the rationalist system of 18th-century philosophy, but rather on the subversive quality of the introduction of subrational elements into that system, resul­ting in the ultimate breakdown of the system and in the expansion of the horizon of the Enlightenment gnoseotope. In this sense, the Enlightenment can be seen as expanding from from an age (“Enlightenment” with an upper-case “E”) to a method (“enlightenment” with a lower-case “e”). The article concludes with recent debates (as initiated by Ulrich Beck, Rainer Specht, and contemporary natural scientists) about the effects that a gnoseotopical perspective has on globalization and ecological politics, and more broadly with reflections on the current need for core Enlightenment ideas in their full complexity

Teaching It In A Knowledge Economy Raising Tacit Productivity

The growth of interactions represents a broad shift in the nature of economic activity. Interactions are defined as the searching, coordinating, and monitoring that people and firms do when they exchange goods, services, or ideas, for many employees today, collaborative, complex problem solving is the essence of their work, these “tacit” activates -- involving the exchange of information, the making of judgments, and a need to draw on multifaceted forms of knowledge in exchanges with coworkers, customers, and suppliers – are increasingly a part of the standard model for companies in the developed world

An approach to popular medicine in Ubrique (1996-1997)

La necesidad de curar una enfermedad es consustancial a la evolución de la especie humana. En el proceso de desarrollo como civilización, los mecanismos empleados para conseguir este fin han ido parejos con el aumento de conocimientos en diferentes ramas del saber. Conforme iba avanzando la técnica, otros mecanismos más antiguos quedaban relegados en segundo término o, incluso, eran definitivamente dados de lado en beneficio del saber emergente. En Medicina, en cambio, la esencia de la enfermedad, no bien conocida o asimilada por las personas enfermas y sanas, ha permitido que técnicas, remedios y formas de actuar que se podría creer quedaron superadas por otra Medicina más tecnificada hayan perdurado y sean incluso ampliamente utilizadas en la actualidad. El lugar escogido para la realización del trabajo es Ubrique, donde se han entrevistado 43 personas que han aportado información diversa tanto sobre enfermedades o problemas de salud como sobre los remedios más útiles.The need to cure illness is inherent to evolution of human mankind. In its developmental process as a civilization, the means for this aim have accompanied the increasing knowledge in all areas of wisdom. As technique improved, ancient methods were forgotten or relegated by the emergent knowledge. Regarding Medicine, on the contrary, the essence of illness having not been known or accepted by healthy and sick has allowed techniques, remedies and methods to live through modern Medicine and be used nowadays. The chosen setting for this work is Ubrique, where 43 interviewed people have furnished us with information on disorders or health problems and useful remedies

The Attractor and the Quantum States

The dissipative dynamics anticipated in the proof of 't Hooft's existence theorem -- "For any quantum system there exists at least one deterministic model that reproduces all its dynamics after prequantization" -- is constructed here explicitly. We propose a generalization of Liouville's classical phase space equation, incorporating dissipation and diffusion, and demonstrate that it describes the emergence of quantum states and their dynamics in the Schroedinger picture. Asymptotically, there is a stable ground state and two decoupled sets of degrees of freedom, which transform into each other under the energy-parity symmetry of Kaplan and Sundrum. They recover the familiar Hilbert space and its dual. Expectations of observables are shown to agree with the Born rule, which is not imposed a priori. This attractor mechanism is applicable in the presence of interactions, to few-body or field theories in particular.Comment: 14 pages; based on invited talk at 4th Workshop ad memoriam of Carlo Novero "Advances in Foundations of Quantum Mechanics and Quantum Information with Atoms and Photons", Torino, May 2008; submitted to Int J Qu Inf

A path integral for classical dynamics, entanglement, and Jaynes-Cummings model at the quantum-classical divide

The Liouville equation differs from the von Neumann equation 'only' by a characteristic superoperator. We demonstrate this for Hamiltonian dynamics, in general, and for the Jaynes-Cummings model, in particular. -- Employing superspace (instead of Hilbert space), we describe time evolution of density matrices in terms of path integrals which are formally identical for quantum and classical mechanics. They only differ by the interaction contributing to the action. This allows to import tools developed for Feynman path integrals, in order to deal with superoperators instead of quantum mechanical commutators in real time evolution. Perturbation theory is derived. Besides applications in classical statistical physics, the "classical path integral" and the parallel study of classical and quantum evolution indicate new aspects of (dynamically assisted) entanglement (generation). Our findings suggest to distinguish 'intra'- from 'inter-space' entanglement.Comment: 22 pages; based on invited talk at Quantum 2010 - Advances in Foundations of Quantum mechanics and Quantum Information with Atoms and Photons (Torino, May 2010). To appear in Int. J. Qu. Inf

Interpreting nowhere dense graph classes as a classical notion of model theory

A class of graphs is nowhere dense if for every integer r there is a finite upper bound on the size of complete graphs that occur as r-minors. We observe that this recent tameness notion from (algorithmic) graph theory is essentially the earlier stability theoretic notion of superflatness. For subgraph-closed classes of graphs we prove equivalence to stability and to not having the independence property. Expressed in terms of PAC learning, the concept classes definable in first-order logic in a subgraph-closed graph class have bounded sample complexity, if and only if the class is nowhere dense