@article{TrollBeimGraben1998, author = {Troll, G{\"u}nter and Beim Graben, Peter}, title = {Zipfs law is not a consequence of the central limit theorem}, year = {1998}, language = {en} } @phdthesis{BeimGraben2000, author = {Beim Graben, Peter}, title = {Symbolische Dynamik ereigniskorrelierter Gehirnpotentiale in der Sprachverarbeitung}, pages = {112 S.}, year = {2000}, language = {de} } @article{BeimGraben2014, author = {Beim Graben, Peter}, title = {Contextual emergence of intentionality}, series = {Journal of consciousness studies : controversies in science \& the humanities ; an international multi-disciplinary journal}, volume = {21}, journal = {Journal of consciousness studies : controversies in science \& the humanities ; an international multi-disciplinary journal}, number = {5-6}, publisher = {Imprint Academic}, address = {Exeter}, issn = {1355-8250}, pages = {75 -- 96}, year = {2014}, abstract = {By means of an intriguing physical example, magnetic surface swimmers, that can be described in terms of Dennett's intentional stance, I reconstruct a hierarchy of necessary and sufficient conditions for the applicability of the intentional strategy. It turns out that the different levels of the intentional hierarchy are contextually emergent from their respective subjacent levels by imposing stability constraints upon them. At the lowest level of the hierarchy, phenomenal physical laws emerge for the coarse-grained description of open, nonlinear, and dissipative non-equilibrium systems in critical states. One level higher, dynamic patterns, such as, for example, magnetic surface swimmers, are contextually emergent as they are invariant under certain symmetry operations. Again one level up, these patterns behave apparently rationally by selecting optimal pathways for the dissipation of energy that is delivered by external gradients. This is in accordance with the restated Second Law of thermodynamics as a stability criterion. At the highest level, true believers are intentional systems that are stable under exchanging their observation conditions.}, language = {en} } @article{BeimGrabenAtmanspacher2006, author = {Beim Graben, Peter and Atmanspacher, Harald}, title = {Complementarity in classical dynamical systems}, issn = {0015-9018}, doi = {10.1007/s10701-005-9013-0}, year = {2006}, abstract = {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 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}, language = {en} }