In everyday situations, and particularly in some sport and working contexts, humans face an inherently unpredictable and uncertain environment. All sorts of unpredictable and unexpected things happen but typically people are able to skillfully adapt. In this paper, we address two key questions in cognitive science. First, how is an agent able to bring its previously learned skill to bear on a novel situation? Second, how can an agent be both sensitive to the particularity of a given situation, while remaining (...) flexibly poised for many other possibilities for action? We will argue that both the sensitivity to novel situations and the sensitivity to a multiplicity of action possibilities are enabled by the property of skilled agency that we will call metastable attunement. We characterize a skilled agent’s flexible interactions with a dynamically changing environment in terms of metastable dynamics in agent-environment systems. What we find in metastability is the realization of two competing tendencies: the tendency of the agent to express their intrinsic dynamics and the tendency to search for new possibilities. Metastably attuned agents are ready to engage with a multiplicity of affordances, allowing for a balance between stability and flexibility. On the one hand, agents are able to exploit affordances they are attuned to, while at the same time being ready to flexibly explore for other affordances. Metastable attunement allows agents to smoothly transition between these possible configurations so as to adapt their behaviour to what the particular situation requires. We go on to describe the role metastability plays in learning of new skills, and in skilful behaviour more generally. Finally, drawing upon work in art, architecture and sports science, we develop a number of perspectives on how to investigate metastable attunement in real life situations. (shrink)

The brain displays both the anatomical features of a vast amount of interconnected topological mappings as well as the functional features of a nonlinear, metastable system at the edge of chaos, equipped with a phase space where mental random walks tend towards lower energetic basins. Nevertheless, with the exception of some advanced neuro-anatomic descriptions and present-day connectomic research, very few studies have been addressing the topological path of a brain embedded or embodied in its external and internal environment. Herein, by (...) using new formal tools derived from algebraic topology, we provide an account of the metastable brain, based on the neuro-scientific model of Operational Architectonics of brain-mind functioning. We introduce a “topodynamic” description that shows how the relationships among the countless intertwined spatio-temporal levels of brain functioning can be assessed in terms of projections and mappings that take place on abstract structures, equipped with different dimensions, curvatures and energetic constraints. Such a topodynamical approach, apart from providing a biologically plausible model of brain function that can be operationalized, is also able to tackle the issue of a long-standing dichotomy: it throws indeed a bridge between the subjective, immediate datum of the naïve complex of sensations and mentations and the objective, quantitative, data extracted from experimental neuro-scientific procedures. Importantly, it opens the door to a series of new predictions and future directions of advancement for neuroscientific research. (shrink)

The dominated convergence theorem implies that if is a sequence of functions on a probability space taking values in the interval [0, 1], and converges pointwise a.e., then converges to the integral of the pointwise limit. Tao [26] has proved a quantitative version of this theorem: given a uniform bound on the rates of metastable convergence in the hypothesis, there is a bound on the rate of metastable convergence in the conclusion that is independent of the sequence and the underlying (...) space. We prove a slight strengthening of Tao’s theorem which, moreover, provides an explicit description of the second bound in terms of the first. Specifically, we show that when the first bound is given by a continuous functional, the bound in the conclusion can be computed by a recursion along the tree of unsecured sequences. We also establish a quantitative version of Egorov’s theorem, and introduce a new mode of convergence related to these notions. (shrink)

According to the Furstenberg-Zimmer structure theorem, every measure-preserving system has a maximal distal factor, and is weak mixing relative to that factor. Furstenberg and Katznelson used this structural analysis of measure-preserving systems to provide a perspicuous proof of Szemer\'edi's theorem. Beleznay and Foreman showed that, in general, the transfinite construction of the maximal distal factor of a separable measure-preserving system can extend arbitrarily far into the countable ordinals. Here we show that the Furstenberg-Katznelson proof does not require the full strength (...) of the maximal distal factor, in the sense that the proof only depends on a combinatorial weakening of its properties. We show that this combinatorially weaker property obtains fairly low in the transfinite construction, namely, by the $\omega^{\omega^\omega}$th level. (shrink)

This article is arranged around two general claims and a thought experiment. I begin by suggesting that the genome should be studied as a developmental system, and that genes supervene on genomes (rather than the other way around). I move on to present a thought experiment that illustrates the implications a dynamic view of the genome has for central concepts in biology, in particular the information content of the genome, and the notion of responses to stress.

Given a convergence theorem in analysis, under very general conditions a model-theoretic compactness argument implies that there is a uniform bound on the rate of metastability. We illustrate with three examples from ergodic theory.

Human neural and behavioral activities have been reported to exhibit fractal dynamics known as 1/f noise, which is more aptly named 1/f scaling. Some argue that 1/f scaling is a general and pervasive property of the dynamical substrate from which cognitive functions are formed. Others argue that it is an idiosyncratic property of domain‐specific processes. An experiment was conducted to investigate whether 1/f scaling pervades the intrinsic fluctuations of a spoken word. Ten participants each repeated the word bucket over 1,000 (...) times, and fluctuations in acoustic measurements across repetitions generally followed the 1/f scaling relation, including numerous parallel yet distinct series of 1/f fluctuations. On the basis of work showing that 1/f scaling is a universal earmark of metastability, it is proposed that the observed pervasiveness of 1/f fluctuations in speech reflects the fact that cognitive functions are formed as metastable patterns of activity in brain, body, and environment. (shrink)

This paper discusses what kind of quantitative information one can extract under which circumstances from proofs of convergence statements in analysis. We show that from proofs using only a limited amount of the law-of-excluded-middle, one can extract functionals , where L is a learning procedure for a rate of convergence which succeeds after at most B-many mind changes. This -learnability provides quantitative information strictly in between a full rate of convergence and a rate of metastability in the sense of (...) Tao . In fact, it corresponds to rates of metastability of a particular simple form. Moreover, if a certain gap condition is satisfied, then B and L yield a bound on the number of possible fluctuations. We explain recent applications of proof mining to ergodic theory in terms of these results. (shrink)

It is shown that the stationary states of stochastic systems are stable. Therefore one cannot use the stationary probability distributions for describing the stochastic systems in metastable states. It is shown that the nonstationary stochastic processes can have sample paths with stationary parts. It is proposed to consider these stationary parts as the metastable states.

Arguably, emotion is always valenced—either pleasant or unpleasant—and dependent on the pleasure system. This system serves adaptive evolutionary functions; relying on separable wanting, liking, and learning neural mechanisms mediated by mesocorticolimbic networks driving pleasure cycles with appetitive, consummatory, and satiation phases. Liking is generated in a small set of discrete hedonic hotspots and coldspots, while wanting is linked to dopamine and to larger distributed brain networks. Breakdown of the pleasure system can lead to anhedonia and other features of affective disorders. (...) Eudaimonia and well-being are difficult to study empirically, yet whole-brain computational models could offer novel insights potentially linking eudaimonia to optimal metastability in the pleasure system. (shrink)

Crowd behaviour challenges our fundamental understanding of social phenomena. Involving complex interactions between multiple temporal and spatial scales of activity, its governing mechanisms defy conventional analysis. Using 1.5 million Twitter messages from the 15M movement in Spain as an example of multitudinous self-organization, we describe the coordination dynamics of the system measuring phase-locking statistics at different frequencies using wavelet transforms, identifying 8 frequency bands of entrained oscillations between 15 geographical nodes. Then we apply maximum entropy inference methods to describe Ising (...) models capturing transient synchrony in our data at each frequency band. The models show that all frequency bands of the system operate near critical points of their parameter space and while fast frequencies present only a few metastable states displaying all-or-none synchronization, slow frequencies present a diversity of metastable states of partial synchronization. Furthermore, describing the state at each frequency band using the energy of the corresponding Ising model, we compute transfer entropy to characterize cross-scale interactions between frequency bands, showing a cascade of upward information flows in which each frequency band influences its contiguous slower bands and downward information flows where slow frequencies modulate distant fast frequencies. (shrink)

In this brief overview paper, we analyse information flow in the brain. Although Shannon’s information concept, in its pure algebraic form, has made a number of valuable contributions to neuroscience, information dynamics within the brain is not fully captured by its classical description. These additional dynamics consist of self-organisation, interplay of stability/instability, timing of sequential processing, coordination of multiple sequential streams, circular causality between bottom-up and top-down operations, and information creation. Importantly, all of these processes are dynamic, hierarchically nested and (...) correspond to continuous brain state change, even if the external environment remains constant. This is where metastable coordination comes into play. In a metastable regime of brain functioning, as a result of the simultaneous co-existence of tendencies for independence and cooperation, information is continuously created, preserved for some time and then dissipated through the formation of dynamical and nested spatio-temporal coalitions among simple neuronal assemblies and larger coupled conglomerates of them—so-called delocalised operational modules. (shrink)

This article provides a retrospective, current and prospective overview on developments in brain research and neuroscience. Both theoretical and empirical studies are considered, with emphasis in the concept of multivariability and metastability in the brain. In this new view on the human brain, the potential multivariability of the neuronal networks appears to be far from continuous in time, but confined by the dynamics of short-term local and global metastable brain states. The article closes by suggesting some of the implications (...) of this view in future multidisciplinary brain research. (shrink)

Supersaturated hcp f -Zr alloys containing 22-28 at.% N were prepared by nitriding sheets of Zr in an atmosphere of high-purity N 2 , followed by homogenization under high-purity Ar gas. Quenching and isothermal ageing of the alloys for various times between 500 and 650°C resulted in precipitation of a metastable phase, rather than the equilibrium phase ZrN. This investigation focused on determining the structure, orientation relationship, habit plane, morphology, growth kinetics and atomic growth mechanism of this non-equilibrium precipitate using (...) transmission electron microscopy imaging and diffraction techniques, high-resolution transmission electron microscopy, electron-energy-loss spectroscopy and various simulation programs. The precipitate, which was arbitrarily designated the  phase, has a monoclinic Bravais lattice. Its lattice parameters are a = 0.32 nm, b = 0.60 nm, c = 0.56 nm, f = g = 90° and n = 121.5°. Its orientation relationship with the f matrix is $$ _alpha /mskip-2/ _xiquad adquad [01bar 10] _alpha /mskip-2/ [001]_xi, $$ and the average habit plane of lenticularly shaped precipitates is $_alpha$ . Determination of the structure and other aspects of the phase transformation are discussed. (shrink)

In our contribution we will observe phenomenal architecture of a mind and operational architectonics of the brain and will show their intimate connectedness within a single integrated metastable continuum. The notion of operation of different complexity is the fundamental and central one in bridging the gap between brain and mind: it is precisely by means of this notion that it is possible to identify what at the same time belongs to the phenomenal conscious level and to the neurophysiological level of (...) brain activity organization, and what mediates between them. Implications for linguistic semantics, self-organized distributed computing algorithms, artificial machine consciousness, and diagnosis of dynamic brain diseases will be discussed briefly. (shrink)

By utilizing the topological concept of pseudocompactness, we simplify and improve a proof of Caicedo, Dueñez, and Iovino concerning Terence Tao's metastability. We also pinpoint the exact relationship between the Omitting Types Theorem and the Baire Category Theorem by developing a machine that turns topological spaces into abstract logics.

Intra-molecular connectivity (that is, chemical structure) does not emerge from computations based on fundamental quantum-mechanical principles. In order to compute molecular electronic energies (of C 3 H 4 hydrocarbons, for instance) quantum chemists must insert intra-molecular connectivity “by hand.” Some take this as an indication that chemistry cannot be reduced to physics: others consider it as evidence that quantum chemistry needs new logical foundations. Such discussions are generally synchronic rather than diachronic —that is, they neglect ‘historical’ aspects. However, systems of (...) interest to chemists generally are metastable . In many cases chemical systems of a given elemental composition may exist in any one of several different metastable states depending on the history of the system. Molecular structure generally depends on contingent historical circumstances of synthesis and separation, rather than solely or mainly on relative energies of alternative stable states, those energies in turn determined by relationships among components. Chemical structure is usually ‘kinetically-determined’ rather than ‘thermodynamically-determined.’ For instance, cyclical hydrocarbon ring-systems (as in cyclopropene) are produced only in special circumstances. Adequate theoretical treatments must take account of the persistent effects of such contingent historical events whenever they are relevant—as they generally are in chemistry. (shrink)

Complex Systems Biology approaches are here considered from the viewpoint of Robert Rosen’s (M,R)-systems, Relational Biology and Quantum theory, as well as from the standpoint of computer modeling. Realizability and Entailment of (M,R)-systems are two key aspects that relate the abstract, mathematical world of organizational structure introduced by Rosen to the various physicochemical structures of complex biological systems. Their importance for understanding biological function and life itself, as well as for designing new strategies for treating diseases such as cancers, is (...) pointed out. The roles played by multiple metastable states in the “continuous uphill flow of Life” supported through internal bioenergetic processes that are coupled to essential inflows are also discussed in relation to dynamic realizations of (M,R)-systems. Furthermore, the roles played by the underlying, many-valued, quantum logics and symbolic computations for ultra-complex biological systems are also briefly discussed. (shrink)

In this paper we aim to show that phenomenal consciousness is realized by a particular level of brain operational organization and that understanding human consciousness requires a description of the laws of the immediately underlying neural collective phenomena, the nested hierarchy of electromagnetic fields of brain activity – operational architectonics. We argue that the subjective mental reality and the objective neurobiological reality, although seemingly worlds apart, are intimately connected along a unified metastable continuum and are both guided by the universal (...) laws of the physical world such as criticality, self-organization and emergence. (shrink)

The understanding of the interrelationship between brain and mind remains far from clear. It is well established that the brain's capacity to integrate information from numerous sources forms the basis for cognitive abilities. However, the core unresolved question is how information about the "objective" physical entities of the external world can be integrated, and how unifiedand coherent mental states (or Gestalts) can be established in the internal entities of distributed neuronal systems. The present paper offers a unified methodological and conceptual (...) basis for a possible mechanism of how the transient synchronization of brain operations may construct the unified and relatively stable neural states, which underlie mental states. It was shown that the sequence of metastable spatial EEG mosaics does exist and probably reflects the rapid stabilization periods of the interrelation of large neuron systems. At the EEG level this is reflected in the stabilization of quasi-stationary segments on corresponding channels. Within the introduced framework, physical brain processes and psychological processes are considered as two basic aspects of a single whole informational brain state. The relations between operational process of the brain, mental states and consciousness are discussed. (shrink)

In this paper, we set out to develop a theoretical and conceptual framework for the new field of Radical Embodied Cognitive Neuroscience. This framework should be able to integrate insights from several relevant disciplines: theory on embodied cognition, ecological psychology, phenomenology, dynamical systems theory, and neurodynamics. We suggest that the main task of Radical Embodied Cognitive Neuroscience is to investigate the phenomenon of skilled intentionality from the perspective of the self-organization of the brain-body-environment system, while doing justice to the phenomenology (...) of skilled action. In previous work, we have characterized skilled intentionality as the organism's tendency toward an optimal grip on multiple relevant affordances simultaneously. Affordances are possibilities for action provided by the environment. In the first part of this paper, we introduce the notion of skilled intentionality and the phenomenon of responsiveness to a field of relevant affordances. Second, we use Friston's work on neurodynamics, but embed a very minimal version of his Free Energy Principle in the ecological niche of the animal. Thus amended, this principle is helpful for understanding the embeddedness of neurodynamics within the dynamics of the system “brain-body-landscape of affordances.” Next, we show how we can use this adjusted principle to understand the neurodynamics of selective openness to the environment: interacting action-readiness patterns at multiple timescales contribute to the organism's selective openness to relevant affordances. In the final part of the paper, we emphasize the important role of metastable dynamics in both the brain and the brain-body-environment system for adequate affordance-responsiveness. We exemplify our integrative approach by presenting research on the impact of Deep Brain Stimulation on affordance responsiveness of OCD patients. (shrink)

Quantum entanglement lies at the foundation of quantum mechanics. Witness Schrödinger highlighting entanglement with his puzzling cat thought experiment and Einstein deriding it as “spooky action at a distance.” Nonetheless, quantum entanglement has been verified experimentally and is essential for quantum information and quantum computing. The quantum superposition principle, together with entanglement, dramatically contrasts the quantum from the classical description of reality. We attempt to integrate physical reality with a Christian worldview.