Inherent global stabilization of unstable local behavior in coupled map lattices

The behavior of two-dimensional coupled map lattices is studied with respect to the global stabilization of unstable local fixed points without external control. It is numerically shown under which circumstances such inherent global stabilization can be achieved for both synchronous and asynchronous updating. Two necessary conditions for inherent global stabilization are derived analytically.Comment: 17 pages, 10 figures, accepted for publication in Int.J.Bif.Chao

Epistemic and Ontic Quantum Realities

Quantum theory has provoked intense discussions about its interpretation since its pioneer days. One of the few scientists who have been continuously engaged in this development from both physical and philosophical perspectives is Carl Friedrich von Weizsaecker. The questions he posed were and are inspiring for many, including the authors of this contribution. Weizsaecker developed Bohr's view of quantum theory as a theory of knowledge. We show that such an epistemic perspective can be consistently complemented by Einstein's ontically oriented position

At home in the quantum world

One among many misleading quotations about the alleged mysteries of quantum theory is from Feynman (1965): "I think I can safely say that nobody understands quantum mechanics.” Today we know that quantum theory describes many aspects of our world in a fully intelligible fashion. Pothos & Busemeyer (P&B) propose ways in which this may include psychology and cognitive scienc

Epistemic Entanglement due to Non-Generating Partitions of Classical Dynamical Systems

Quantum entanglement relies on the fact that pure quantum states are dispersive and often inseparable. Since pure classical states are dispersion-free they are always separable and cannot be entangled. However, entanglement is possible for epistemic, dispersive classical states. We show how such epistemic entanglement arises for epistemic states of classical dynamical systems based on phase space partitions that are not generating. We compute epistemically entangled states for two coupled harmonic oscillators.Comment: 13 pages, no figures; International Journal of Theoretical Physics, 201

Complementarity in classical dynamical systems

The concept of complementarity, originally defined for non-commuting observables of quantum systems with states of non-vanishing dispersion, is extended to classical dynamical systems with a partitioned phase space. Interpreting partitions in terms of ensembles of epistemic states (symbols) with corresponding classical observables, it is shown that such observables are complementary to each other with respect to particular partitions unless those partitions are generating. This explains why symbolic descriptions based on an \emph{ad hoc} partition of an underlying phase space description should generally be expected to be incompatible. Related approaches with different background and different objectives are discussed.Comment: 18 pages, no figure

Mental states as macrostates emerging from brain electrical dynamics

Psychophysiological correlations form the basis for different medical and scientific disciplines, but the nature of this relation has not yet been fully understood. One conceptual option is to understand the mental as “emerging” from neural processes in the specific sense that psychology and physiology provide two different descriptions of the same system. Stating these descriptions in terms of coarser- and finer-grained system states (macro- and microstates), the two descriptions may be equally adequate if the coarse-graining preserves the possibility to obtain a dynamical rule for the system. To test the empirical viability of our approach, we describe an algorithm to obtain a specific form of such a coarse-graining from data, and illustrate its operation using a simulated dynamical system. We then apply the method to an electroencephalographic recording, where we are able to identify macrostates from the physiological data that correspond to mental states of the subject