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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.
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
In most experiments using event-related brain potentials (ERPs), there is a straightforward way to define-on theoretical grounds-which of the conditions tested is the experimental condition and which is the control condition. It, however, theoretical assumptions do not give sufficient and unambiguous information to decide this question, then the interpretation of an ERP effect becomes difficult, especially if one takes into account that certain effects can be both a positivity or a negativity on the basis of the morphology of the pattern as well as with respect to peak latency (regard for example, N400 and P345). Exemplified with an ERP experiment on language processing, we present such a critical case and offer a possible solution on the basis of nonlinear data analysis. We show that a generalized polarity histogram, the word statistics of symbolic dynamics, is in principle able to distinguish negative going ERP components from positive ones when an appropriate encoding strategy, the half wave encoding is employed. We propose statistical criteria which allow to determine ERP components on purely methodological grounds
We apply the recently developed symbolic resonance analysis to electroencephalographic measurements of event- related brain potentials (ERPs) in a language processing experiment by using a three-symbol static encoding with varying thresholds for analyzing the ERP epochs, followed by a spin-flip transformation as a nonlinear filter. We compute an estimator of the signal-to-noise ratio (SNR) for the symbolic dynamics measuring the coherence of threshold-crossing events. Hence, we utilize the inherent noise of the EEG for sweeping the underlying ERP components beyond the encoding thresholds. Plotting the SNR computed within the time window of a particular ERP component (the N400) against the encoding thresholds, we find different resonance curves for the experimental conditions. The maximal differences of the SNR lead to the estimation of optimal encoding thresholds. We show that topographic brain maps of the optimal threshold voltages and of their associated coherence differences are able to dissociate the underlying physiological processes, while corresponding maps gained from the customary voltage averaging technique are unable to do so
We describe a part of the stimulus sentences of a German language processing ERP experiment using a context- free grammar and represent different processing preferences by its unambiguous partitions. The processing is modeled by deterministic pushdown automata. Using a theorem proven by Moore, we map these automata onto discrete time dynamical systems acting at the unit square, where the processing preferences are represented by a control parameter. The actual states of the automata are rectangles lying in the unit square that can be interpreted as cylinder sets in the context of symbolic dynamics theory. We show that applying a wrong processing preference to a certain input string leads to an unwanted invariant set in the parsers dynamics. Then, syntactic reanalysis and repair can be modeled by a switching of the control parameter - in analogy to phase transitions observed in brain dynamics. We argue that ERP components are indicators of these bifurcations and propose an ERP-like measure of the parsing model
Untitled
(2004)
Diagnosis and repair of negative polarity constructions in the light of symbolic resonance analysis
(2006)
in a post hoc analysis, we investigate differences in event-related potentials of two studies (Drenhaus et al., 2004, to appear; Saddy et al., 2004) by using the symbolic resonance analysis (Beim Graben & Kurths, 2003). The studies under discussion, examined the failure to license a negative polarity item (NPI) in German: Saddy et al. (2004a) reported an N400 component when the NPI was not accurately licensed by negation; Drenhaus et al. (2004, to appear) considered additionally the influence of constituency of the licensor in NPI constructions. A biphasic N400-P600 response was found for the two induced violations (the lack of licensor and the inaccessibility of negation in a relative clause). The symbolic resonance analysis (SRA) revealed an effect in the P600 time window for the data in Saddy et al., which was not found by using the averaging technique. The SRA of the ERPs in Drenhaus et al., showed that the P600 components are distinguishable concerning the amplitude and latency. It was smaller and earlier in the condition where the licensor is inaccessible, compared to the condition without negation in the string. Our findings suggest that the failure in licensing NPIs is not exclusively related to semantic integration costs (N400). The elicited P600 components reflect differences in syntactic processing. Our results confirm and replicate the effects of the traditional voltage average analysis and show that the SRA is a useful tool to reveal and pull apart ERP differences which are not evident using the traditional voltage average analysis.