A categorical, higher dimensional algebra and generalized topos framework for Łukasiewicz–Moisil Algebraic–Logic models of non-linear dynamics in complex functional genomes and cell interactomes is proposed. Łukasiewicz–Moisil Algebraic–Logic models of neural, genetic and neoplastic cell networks, as well as signaling pathways in cells are formulated in terms of non-linear dynamic systems with n-state components that allow for the generalization of previous logical models of both genetic activities and neural networks. An algebraic formulation of variable ‘next-state functions’ is (...) extended to a Łukasiewicz–Moisil Topos with an n-valued Łukasiewicz–Moisil Algebraic Logic subobject classifier description that represents non-random and non-linear network activities as well as their transformations in developmental processes and carcinogenesis. The unification of the theories of organismic sets, molecular sets and Robert Rosen’s (M,R)-systems is also considered here in terms of natural transformations of organismal structures which generate higher dimensional algebras based on consistent axioms, thus avoiding well known logical paradoxes occurring with sets. Quantum bionetworks, such as quantum neural nets and quantum genetic networks, are also discussed and their underlying, non-commutative quantum logics are considered in the context of an emerging Quantum Relational Biology. (shrink)

A categorical, higher dimensional algebra and generalized topos framework for Łukasiewicz–Moisil Algebraic–Logic models of non-linear dynamics in complex functional genomes and cell interactomes is proposed. Łukasiewicz–Moisil Algebraic–Logic models of neural, genetic and neoplastic cell networks, as well as signaling pathways in cells are formulated in terms of non-linear dynamic systems with n-state components that allow for the generalization of previous logical models of both genetic activities and neural networks. An algebraic formulation of variable ‘next-state functions’ is (...) extended to a Łukasiewicz–Moisil Topos with an n-valued Łukasiewicz–Moisil Algebraic Logic subobject classifier description that represents non-random and non-linear network activities as well as their transformations in developmental processes and carcinogenesis. The unification of the theories of organismic sets, molecular sets and Robert Rosen’s (M,R)-systems is also considered here in terms of natural transformations of organismal structures which generate higher dimensional algebras based on consistent axioms, thus avoiding well known logical paradoxes occurring with sets. Quantum bionetworks, such as quantum neural nets and quantum genetic networks, are also discussed and their underlying, non-commutative quantum logics are considered in the context of an emerging Quantum Relational Biology. (shrink)

In 1927 Louis de Broglie proposed an alternative approach to standard quantum mechanics known as the double solution program (DSP) where particles are represented as bunched fields or solitons guided by a base (weaker) wave. DSP evolved as the famous de Broglie-Bohm pilot wave interpretation (PWI) also known as Bohmian mechanics but the general idea to use solitons guided by a base wave to reproduce the dynamics of the PWI was abandoned. Here we propose a nonlinear scalar field theory (...) able to reproduce the PWI for the Schrödinger and Klein–Gordon guiding waves. Our model relies on a relativistic ‘phase harmony’ condition locking the phases of the solitonic particle and the guiding wave. We also discuss an extension of the theory for the N particles cases in presence of entanglement and external (classical) electromagnectic fields. (shrink)

It is often claimed (1) that levels of nature are related by supervenience, and (2) that processes occurring at particular levels of nature should be studied using dynamical systems theory. However, there has been little consideration of how these claims are related. To address the issue, I show how supervenience relations give rise to ‘supervenience functions’, and use these functions to show how dynamical systems at different levels are related to one another. I then use this analysis (...) to describe a graded approach to non-reductive physicalism, and to critically assess Davidson’s arguments for psychological anomaly. I also show how this approach can inform empirical research in cognitive science. (shrink)

In a series of recent papers, two of which appeared in this journal, a group of philosophers, physicists, and climate scientists have argued that something they call the `hawkmoth effect' poses insurmountable difficulties for those who would use non-linear models, including climate simulation models, to make quantitative predictions or to produce `decision-relevant probabilites.' Such a claim, if it were true, would undermine much of climate science, among other things. Here, we examine the two lines of argument the group has (...) used to support their claims. The first comes from a set of results in dynamical systems theory associated with the concept of `structural stability.' The second relies on a mathematical demonstration of their own, using the logistic equation, that they present using a hypothetical scenario involving two apprentices of Laplace's omniscient demon. We prove two theorems that are relevant to their claims, and conclude that both of these lines of argument fail. There is nothing out there that comes close to matching the charac. (shrink)

The acronym Developmental systems theory (DST) has been introduced into the literature on development in at least three different contexts in recent years – twice for DST, and before that, for Dynamical Systems Theory – and in all cases, to designate a new perspective for understanding development. Subtle but significant differences in argument and aims distinguish these uses, and confound the difficulty of saying just what DST is. My aim in this paper is to disambiguate these (...) different terms – both to call attention to the difference of perspectives, and to carve out a conceptual space for the concrete issues at stake. (shrink)

The ‘causal-constitution’ fallacy, the ‘cognitive bloat’ worry, and the persisting theoretical confusion about the fundamental difference between the hypotheses of embedded (HEMC) and extended (HEC) cognition are three interrelated worries, whose common point—and the problem they accentuate—is the lack of a principled criterion of constitution. Attempting to address the ‘causal-constitution’ fallacy, mathematically oriented philosophers of mind have previously suggested that the presence of non-linear relations between the inner and the outer contributions is sufficient for cognitive extension. The abstract idea (...) of non-linearity, however, can be easily misunderstood and has, in the past, led to incorrect and counterintuitive conclusions about what may count as part of one’s overall cognitive system. In order to prevent any further mistakes I revisit dynamical systems theory to study the nature of the continuous mutual interactions that give rise to the aforementioned non-linear relations. Moreover, focusing on these interactions will allow us to provide two distinct arguments in support of the ontological postulation of extended cognitive systems, as well as an objective criterion of constitution. Accordingly, I put forward a version of HEC that treats continuous mutual interactions (and the resultant non-linear relations) not just as sufficient but also as necessary for cognitive extension. Such a qualified version of HEC may exclude certain alleged cases of cognitive extension where the agent does not mutually interact with his artifacts (e.g., shopping lists and directory services), but it is immune both to the ‘causal-constitution’ fallacy and the ‘cognitive bloat’ worry, and it can be sharply distinguished from HEMC. (shrink)

This contribution discusses competencies needed for regulating systems with properties of multi-causality and non-linear dynamics (therapeutic, economical, organizational, socio-political, technical, ecological, etc.). Various research communities have contributed insights, but none has come forward with an inclusive framework. To advance the debate, I propose to draw from dynamic systems theory (DST) and “4E” (embodied, embedded, enactive, and extended), cognition approaches, which offer a set of perspectives to understand what expert regulators in real-life settings do. They define (...) the regulator's agency as skillfully imposing constraints on a target system and hereby creating context-sensitive openings for self-organizing dynamics, rather than “controlling” the system. Adept regulators apply multi-pronged and multi-timescale constraints to achieve nuanced effects. Among other things, their skill set includes scarcely noted enactive processual competencies for “emergence management”, which the intellectualistic and insufficiently ecologically situated accounts of the complex problem solving literature omit. To capture the nature of system regulation, I advocate treating regulation dynamics and target system dynamics “symmetrically” by grounding regulator competencies in concepts from complexity theory. (shrink)

For Merleau-Ponty,consciousness in skillful coping is a matter of prereflective ‘I can’ and not explicit ‘I think that.’ The body unifies many domain-specific capacities. There exists a direct link between the perceived possibilities for action in the situation (‘affordances’) and the organism’s capacities. From Merleau-Ponty’s descriptions it is clear that in a flow of skillful actions, the leading ‘I can’ may change from moment to moment without explicit deliberation. How these transitions occur, however, is less clear. Given that Merleau-Ponty suggested (...) that a better understanding of the self-organization of brain and behavior is important, I will re-read his descriptions of skillful coping in the light of recent ideas on neurodynamics. Affective processes play a crucial role in evaluating the motivational significance of objects and contribute to the individual’s prereflective responsiveness to relevant affordances. (shrink)

Here, for the first time, development studies encounters the set of ideas popularly known as 'Chaos Theory'. Samir Rihani applies to the processes of economic development, ideas from complex adaptive systems like uncertainty, complexity, and unpredictability. Rihani examines various aspects of the development process - including the World Bank, debt, and the struggle against poverty - and demonstrates the limitations of fundamentally linear thinking in an essentially non-linear world.

Magnetoencephalography (MEG) and electroencephalography (EEG) are invaluable neuroscientific tools for unveiling human neural dynamics in three dimensions (space, time, and frequency), which are associated with a wide variety of perceptions, cognition, and actions. MEG/EEG also provides different categories of neuronal indices including activity magnitude, connectivity, and network properties along the three dimensions. In the last 20 years, interest has increased in inter-regional connectivity and complex network properties assessed by various sophisticated scientific analyses. We herein review the definition, computation, short history, (...) and pros and cons of connectivity and complex network (graph-theory) analyses applied to MEG/EEG signals. We briefly describe recent developments in source reconstruction algorithms essential for source-space connectivity and network analyses. Furthermore, we discuss a relatively novel approach used in MEG/EEG studies to examine the complex dynamics represented by human brain activity. The correct and effective use of these neuronal metrics provides a new insight into the multi-dimensional dynamics of the neural representations of various functions in the complex human brain. (shrink)

We survey and clarify some recent appearances of the term ‘emergence’. We distinguish epistemological emergence, which is merely a limitation of descriptive apparatus, from ontological emergence, which should involve causal features of a whole system not reducible to the properties of its parts, thus implying the failure of part/whole reductionism and of mereological supervenience for that system. Are there actually any plausible cases of the latter among the numerous and various mentions of ‘emergence’ in the recent literature? Quantum mechanics seems (...) to offer one, in the Bell properties of entangled particles, but other apparently promising candidates, such as non‐linear dynamical systems investigated by complexity studies and chaos theory, seem on careful analysis to display only epistemological emergence. We examine the consequences for physicalism of admitting ontological emergence in the micro‐physical. (shrink)

Precision medicine and molecular systems medicine (MSM) are highly utilized and successful approaches to improve understanding, diagnosis, and treatment of many diseases from bench-to-bedside. Especially in the COVID-19 pandemic, molecular techniques and biotechnological innovation have proven to be of utmost importance for rapid developments in disease diagnostics and treatment, including DNA and RNA sequencing technology, treatment with drugs and natural products and vaccine development. The COVID-19 crisis, however, has also demonstrated the need for systemic thinking and transdisciplinarity and the (...) limits of MSM: the neglect of the bio-psycho-social systemic nature of humans and their context as the object of individual therapeutic and population-oriented interventions. COVID-19 illustrates how a medical problem requires a transdisciplinary approach in epidemiology, pathology, internal medicine, public health, environmental medicine, and socio-economic modeling. Regarding the need for conceptual integration of these different kinds of knowledge we suggest the application of general system theory (GST). This approach endorses an organism-centered view on health and disease, which according to Ludwig von Bertalanffy who was the founder of GST, we call Organismal Systems Medicine (OSM). We argue that systems science offers wider applications in the field of pathology and can contribute to an integrative systems medicine by (i) integration of evidence across functional and structural differentially scaled subsystems, (ii) conceptualization of complex multilevel systems, and (iii) suggesting mechanisms and non-linear relationships underlying the observed phenomena. We underline these points with a proposal on multi-level systems pathology including neurophysiology, endocrinology, immune system, genetics, and general metabolism. An integration of these areas is necessary to understand excess mortality rates and polypharmacological treatments. In the pandemic era this multi-level systems pathology is most important to assess potential vaccines, their effectiveness, short-, and long-time adverse effects. We further argue that these conceptual frameworks are not only valid in the COVID-19 era but also important to be integrated in a medicinal curriculum. (shrink)

Mental imagery is an important topic in classical and modern philosophy, as it is central to the study of knowledge; since subjects can recall features of perceptual experiences in different ways and times, even modifying their structure, in this brief essay we will focus on non-perceptive mental images and to this purpose we will analyse, on the one hand, the nature of perceptive mental images ; on the other hand, NPMI generation according to different strategic conditions and retrieval modalities and, (...) so, their structural relationships with PMI. Thus, we will clarify what NPMI amounts to and, to this purpose, we will address the issue of epistemic correlation and semantic reference. As regards the former, we will adopt the notion of ‘belief’, both to describe which attitude supports the use of an NPMI and to account for its relationship with a PMI. As regards the latter, we will talk about weak ontology between an NPMI and the world, to conceive ‘the way in which’ mental imagery, despite the absence of a sensorial modification, refers to physical objects. As the subject’s mental contents determine, but do not constrain, what NPMI is like, we will deal with the ‘involvement’ of prior knowledge and the notion of meaningful space to underline that its generation is always the result of a wide process which involves perceptive visual information already processed and stored together with further mental contents. So, though some Authors consider mental imagery to be a ‘percept-like’ image and, somehow, espouse the theory of reactivation, we will pose a challenge to this theory – i.e. to what we call mental imagery standard framework – describing an NPMI in terms of configurational setting and indeterminacy. Consequently, we will propose a non-linear dynamic framework of mental imagery generation , according to which an NPMI is not reducible to a mere recalling of figural features of a perceptive image. (shrink)

Any approach to the study of managerial situations undertaken without reflection on the underpinning philosophy is flawed because it limits our ability to question the validity of the knowledge claimed in the analysis. The paper considers this issue and presents a philosophical reflection on the use of a systems approach to the modelling of human enterprises. It draws on insights from systems thinking, cognitive science, autopoiesis, communication theory and non-linear dynamics. These are interpreted within the context (...) of social systems as networks of conversations that are generated in language. It is written to invite an exchange of ideas concerning the role of the generative dialogue. (shrink)

In this work we develop a time-symmetric soliton theory for quantum particles inspired from works by de Broglie and Bohm. We consider explicitly a non-linear Klein–Gordon theory leading to monopolar oscillating solitons. We show that the theory is able to reproduce the main results of the pilot-wave interpretation for non interacting particles in a external electromagnetic field. In this regime, using the time symmetry of the theory, we are also able to explain quantum entanglement between (...) several solitons and we reproduce the famous pilot-wave nonlocality associated with the de Broglie-Bohm theory. (shrink)

Tim van Gelder, following Brandom, Collins and others, uses the so‐called wide content of capacities which support social, norm governed activities, such as language, to argue for their anti‐natural, abstract, but socially instituted nature and thence for the failure of the entire traditional mind‐body discussion as ill‐posed. We argue that his former conclusion is wrong, that such properties are naturalisable, complicated organisational properties of the complexly organised, non‐linearly interactive systems that human beings are. This analysis also provides principled support, (...) but on other grounds, for van Gelder’s latter conclusion. We outline a new naturalist approach to the organisational capacities of such systems that is intended to ground their biological, cognitive and social characters. (shrink)

This paper rereads John Dewey's works in the light of complexity theory and self‐organising systems. Dewey's pragmatic inquiry is posited as inspirational for developing a logic of education and learning that would incorporate novelty and creativity, these artistic elements being part and parcel of the science of complexity. Dewey's philosophical concepts are explored against the background of such founders of dynamical systems theory as Ludwig von Bertalanffy, Ervin Laszlo, and Erich Jantsch. If, in this process, Dewey's (...) thought appears to undergo some transformation, this would only confirm Jim ) belief that Dewey would welcome, in accord with his own philosophical project, the reconstruction of his own ideas so as to better respond to contingencies and challenges of new times, places and contexts. The paper introduces some elements of non‐linear dynamics, relating them to the problematic of learning and the transformation of habits. Finally, the paper addresses a delicate balance between novelty and confirmation in a self‐organised system, positing it as an issue of pedagogical significance. (shrink)

Nearly all listeners consider the subjective aspects of music, such as its emotional tone, to have primary importance. But contemporary philosophers often downplay, ignore, or even deny such aspects of experience. Moreover, traditional philosophies of music try to decontextualize it. Using music as an example, this paper explores the structure of qualitative experience, demonstrating that it is multi-layer emergent, non-compositional, enacted, and situation dependent, among other non-Cartesian properties. Our explanations draw on recent work in cognitive science, including blending, image schemas, (...) and sensory memory, as well as on phenomenology. A hierarchical structure transformation based complexity theory is applied to obtain a non-linear dynamical systems explanation of qualia and emotion that respects phenomenological insights about time, including retention and protention. The complexity measure provides both a metric structure and a potential function, on spaces of pieces that are constructed using given elements and transformations, with weights that reflect their cognitive difficulty. However, the approach is not reductionist; using improvisation and the evolution of musical notation as data, we argue that situatedness, especially enactment and social context, are key aspects of musical consciousness. (shrink)

The dynamics of single populations up to ecosystems, are often described by one or a set of non-linear ordinary differential equations. In this paper we review the use of bifurcation theory to analyse these non-linear dynamical systems. Bifurcation analysis gives regimes in the parameter space with quantitatively different asymptotic dynamic behaviour of the system. In small-scale systems the underlying models for the populations and their interaction are simple Lotka-Volterra models or more elaborated models with (...) more biological detail. The latter ones are more difficult to analyse, especially when the number of populations is large. Therefore for large-scale systems the Lotka-Volterra equations are still popular despite the limited realism. Various approaches are discussed in which the different time-scale of ecological and evolutionary biological processes are considered together. (shrink)

The article illustrates an alternative topology by taking advantage of the possibilities for new forms of perception in the realm of online virtual worlds. It is based on the outcomes of the ‘Noetic Grace’ project that was held in Linden Lab’s Second Life™ (SL) platform as a part of Yoshikaze project, supported form Humlab, Umeå University. During three months of virtual residency in Yoshikaze studio, the author experimented with different kinds of spatiotemporal awareness formed from the notions of virtuality as (...) expressed during the times of late antiquity. Saint John of Damascus (c. 676–749) was speaking about ‘virtual vision’ when he referred to the concept of ‘noetic grace’. Such an approach raises some fundamental questions about whether virtual worlds can have the potential to alter visual mechanisms in the whole spectrum of imagery; both in its creation as well as in its vision. Technologies of computing can be considered as the most outstanding practice of Descartes’ theories. However even if Cartesian resonance can be regarded as an abstract Logos and as such it is clearly distinguished from the class of the world, its principal effect to western thought was that of its dualism as a deterministic organization. Hence, Euclidian plane with a chosen Cartesian system, the so-called Cartesian plane, became the standard spatial environment. In the dual process model of thinking the forward and backward reasoning can be used to express Euclidian transformations in which the points are detached. Their interaction exists solely to define themselves in relation to the other, rather than to embed themselves in an aggregate space. Nevertheless, scientific progress has demonstrated a source that spurts many kinds of phenomena that are by far distinct from those of a systematic space. Anisotropic and heterogeneous topologies, magnetic flux, non-linear, dynamic systems and emergence are some of the findings that can alter the whole spectrum of human awareness. Consequently, in order to create a being-to-be into virtual worlds, one has to overcome the notion of single-self objectiveness and its systematic space and act as a potential entity released from any references that may set barriers to a formation of a different perception and imagery. (shrink)

We observe that Schrödinger’s equation may be written as two real coupled Hamilton–Jacobi (HJ)-like equations, each involving a quantum potential. Developing our established programme of representing the quantum state through exact free-standing deterministic trajectory models, it is shown how quantum evolution may be treated as the autonomous propagation of two coupled congruences. The wavefunction at a point is derived from two action functions, each generated by a single trajectory. The model shows that conservation as expressed through a continuity equation is (...) not a necessary component of a trajectory theory of state. Probability is determined by the difference in the action functions, not by the congruence densities. The theory also illustrates how time-reversal symmetry may be implemented through the collective behaviour of elements that individually disobey the conventional transformation (T\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathrm{T}$$\end{document}) of displacement (scalar) and velocity (reversal). We prove that an integral curve of the linear superposition of two vectors can be derived algebraically from the integral curves of one of the constituent vectors labelled by integral curves associated with the other constituent. A corollary establishes relations between displacement functions in diverse trajectory models, including where the functions obey different symmetry transformations. This is illustrated by showing that a (T\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathrm{T}$$\end{document}-obeying) de Broglie-Bohm trajectory is a sequence of points on the (non-T\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathrm{T}$$\end{document}) HJ trajectories, and vice versa. (shrink)

Introduction The article is focused on theoretical and methodological analysis of a number of social dynamics models that appeared on the basis of non-classical science. They are “challenge — response”, self-organization, a cycle of phase transitions “birth — life — death”, and “zone model”. The author reveals heuristic potential of each model, its strengths and weaknesses in the methodological aspect. The aim of the study is to consider the models of social dynamics that appeared on the basis of non-classical science (...) in social cognition, identify their methodological foundations; compare these theoretical constructs with each other, and to improve these structures in theoretical and methodological aspects. Methods The following general scientific methods were used in the study: modeling, structural-functional, systemic and comparative analysis. The scientific novelty of the study. The author traces evolution of how the models under consideration have been forming in the framework of social cognition, and points out the epistemological foundations of their occurrence. In the “challenge-response” model, the author identifies its basic ideas and classifies the sources that generate historical “challenges” and the entities that form “answers” to them. The author specifies that the model of self-organization appeared long before the 20th century, but only thanks to the systematic approach and synergetics it acquires the necessary theoretical level. The author also points out positive aspects and limitations of the self-organization model in relation to social cognition. The author specifies the full structure of the “zone model” in social cognition, which includes the following elements: the center, the middle part, the intermediate space, and the periphery. Modifications of this model are shown in the framework of the world-system approach and other social theories. Results. The study demonstrates that in relation to each model, empirical material was first accumulated, and only then it was theoretically generalized on the basis of non-classical science. It is shown that the main merit of the world-system analysis is creating a “zone” model of social dynamics. The author recognizes that the zone model to the maximum extent includes other theoretical constructions: “challenge - answer”, self-organization, the cycle of phase transitions “birth - life - death”. It is assumed that in the future, theoretical approaches in the humanities are more likely to include new methodological tools. Conclusions. The author reveals continuity of intellectual instruments among various non-classical models of social dynamics, shows separate stages of the models evolution. It is stated that in the framework of the non-classical methodology of social cognition, there is a place for the approaches generated by classical science (for example, the assumption of linearity as a way of developing society). (shrink)

It is well known that infinite minimal sets for continuous functions on the interval are Cantor sets; that is, compact zero dimensional metrizable sets without isolated points. On the other hand, it was proved in Alcaraz and Sanchis (Bifurcat Chaos 13:1665–1671, 2003) that infinite minimal sets for continuous functions on connected linearly ordered spaces enjoy the same properties as Cantor sets except that they can fail to be metrizable. However, no examples of such subsets have been known. In this note (...) we construct, in ZFC, ${2^{\mathfrak{c}}}$ non-metrizable infinite pairwise non-homeomorphic minimal sets on compact connected linearly ordered spaces. (shrink)

The dynamics of calcium in the cortical cytoplasm of plant cells has been modeled by Goodwin & Trainor (1985) using a mechanochemical field theory based on the interaction between calcium ions and the cytoskeleton. The resulting mathematical model is a system of two non-linear partial differential equations which rule the evolution of the free calcium concentration and of the cytogel strain field in the cytoplasm. According to the values of parameters such as: calcium diffusion coefficient, strength of the (...) calcium-strain coupling, gel elasticity or total calcium concentration, this system may be stable or unstable around an homogeneous equilibrium state. With the aid of numerical simulations, various kinds of solutions have been observed. When inertial forces ar neglected or for low values of the gel density, most of the solutions are asymptotically stable and are reached after a more or less complex transient. But for higher values of the volumetric density more complex solutions may exist, periodic in time and space or eventually chaotic. (shrink)

Ecologists are challenged by the need to bridge and synthesize different approaches and theories to obtain a coherent understanding of ecosystems in a changing world. Both food web theory and regime shift theory shine light on mechanisms that confer stability to ecosystems, but from different angles. Empirical food web models are developed to analyze how equilibria in real multi-trophic ecosystems are shaped by species interactions, and often include linear functional response terms for simple estimation of interaction strengths (...) from observations. Models of regime shifts focus on qualitative changes of equilibrium points in a slowly changing environment, and typically include non-linear functional response terms. Currently, it is unclear how the stability of an empirical food web model, expressed as the rate of system recovery after a small perturbation, relates to the vulnerability of the ecosystem to collapse. Here, we conduct structural sensitivity analyses of classical consumer-resource models in equilibrium along an environmental gradient. Specifically, we change non-proportional interaction terms into proportional ones, while maintaining the equilibrium biomass densities and material flux rates, to analyze how alternative model formulations shape the stability properties of the equilibria. The results reveal no consistent relationship between the stability of the original models and the proportionalized versions, even though they describe the same biomass values and material flows. We use these findings to critically discuss whether stability analysis of observed equilibria by empirical food web models can provide insight into regime shift dynamics, and highlight the challenge of bridging alternative modelling approaches in ecology and beyond. (shrink)

Teachers' adaptive expertise has received increasing attention in the current English as foreign language teaching field, however, it has seldom been examined with adaptive practices by teachers in on-going classes among existing literature. Adopting a mixed-method design with data triangulation, this study was conducted to explore the complexity of teachers' adaptive expertise and adaptive teaching practices that an EAP writing teacher demonstrated in academic writing courses, from a Complex Dynamic Systems Theory perspective. Semi-structured interviews, classroom observations, and (...) questionnaires were arranged to collect qualitative and quantitative data from an EAP writing teacher and 43 EFL learners in a Chinese university. Thematic analysis and SPSS were mainly used in the current work for data analysis. Our findings confirmed the complexity of TAE and ATP with specific features of non-linearity, interconnectedness, and self-organization, which are classic CDST characteristics; the TAE evolved with meta-cognitive, cognitive, affective and social components that are intertwined and contributed to the teacher's adaptive teaching practices in her academic writing course; being facilitated by TAE, the teacher's adaptive teaching practices significantly enhanced EFL learners, learning motivation of academic writing and their learning efficiency. Findings of the current work pave the way for future studies in researching TAE and ATP with a thorough consideration of language teachers, students and contexts from the CDST perspective. Moreover, pedagogical contributions are highlighted through the detailed examinations of the EAP writing teacher's ATP, including the class design, teaching plans, and methods, which would be fruitful for the development of tertiary EAP writing research. (shrink)

If quantum mechanics is interpreted as an objective, complete, physical theory, applying to macroscopic as well as microscopic systems, then the linearity of quantum dynamics gives rise to the measurement problem and related problems, which cannot be solved without modifying the dynamics. Eight desiderata are proposed for a reasonable modified theory. They favor a stochastic modification rather than a deterministic non-linear one, but the spontaneous localization theories of Ghirardi et al. and Pearle are criticized. The intermittent (...) fluorescence of a trapped atom irradiated by two laser beams suggests a stochastic theory in which the locus of stochasticity is interaction between a material system and the electromagnetic vacuum. (shrink)

We present a technique for the analysis of pattern formation by a class of models for the formation of ocular dominance stripes in the striate cortex of some mammals. The method, which employs the adiabatic approximation to derive a set of ordinary differential equations for patterning modes, has been successfully applied to reaction-diffusion models for striped patterns [1]. Models of ocular dominance stripes have been studied [2,3] by computation, or by linearization of the model equations. These techniques do not provide (...) a rationale for the origin of the stripes. We show here that stripe formation is a non-linear property of the models. Our analysis indicates that stripe selection is closely linked to a property in the dynamics of the models which arises from a symmetry between ipsilateral and contralateral synapses to the visual cortex of a given hemisphere. (shrink)

Economic logic impinges on contemporary political theory through both economic reductionism and economic methodology applied to political decision-making (through game theory). The authors argue that the sort of models used are based on mechanistic and linear methodologies that have now been found wanting in physics. They further argue that complexity based self-organization methods are better suited to model the complexities of economy and polity and their interactions with the overall social system.

A critical re-examination of the history of the concepts of space (including spacetime of general relativity and relativistic quantum field theory) reveals a basic ontological elusiveness of spatial extension, while, at the same time, highlighting the fact that its epistemic primacy seems to be unavoidably imposed on us (as stated by A.Einstein “giving up the extensional continuum … is like to breathe in airless space”). On the other hand, Planck’s discovery of the atomization of action leads to the fundamental (...) recognition of an ontology of non-spatial, abstract entities (Quine) for the quantum level of reality (QT), as distinguished from the necessarily spatio-temporal, experimental revelations (measurements). The elementary quantum act (measured by Planck’s constant) has neither duration nor extension, and any genuinely quantum process literally does not belong in the Raum and time of our experience. As Heisenberg stresses: “Während also die klassische Physik ein objectives Geschehen in Raum and Zeit zum Gegenstand hat, für dessen Existenz seine Beobachtung völlig irrelevant war, behandelt die Quantentheorie Vorgänge, die sozusagen nur in den Momenten der Beobachtung als raumzeitliche Phänomene aufleuchten, und über die in der zwischenzeit anschaulische physikalische Aussagen sinloss sind”. An admittedly speculative, hazardous conjecture is then advanced concerning the relation of such quantum ontology with the role of the pre-phenomenal continuum (Husserl) in the perception of macroscopically distinguishable objects in the Raum and time of our experience. Although rather venturesome, it brings together important philosophical issues. Coherently with recent general results in works on the foundations of QT, it is assumed that the linearity of quantum dynamical evolution does not apply to the central nervous system of living beings at a certain level of the evolutionary ramification and at the pre-conscious stage of subjectivity. Accordingly, corresponding to the onset of a non-linear dynamic evolution, a ‘primary spatial’ reduction is ‘continually’ taking place, thereby constituting the neural precondition for the experience of distinguishable macroscopic objects in the continuous spatial extension. While preventing the theoretically possible quantum superpositions of macroscopic objects from being perceivable by living beings, the ‘primary reduction’ has no effect on the standard processes concerning quantum level entities involved in laboratory man-made experiments. In this connection, an experimental check which might falsify the conjecture is briefly discussed. The approach suggested here, if sound, leads to a naturalization of that part of Kant’s Transcendental Aesthetics than can survive the Euclidean catastrophe. According to such naturalized transcendentalism, “space can well be transcendental without the axioms being so”, in agreement with a well-known statement by Boltzman. Finally, as far as QT is concerned, the conjecture entails that a scheme for quantum measurement of the von Neumann type cannot even ‘leave the ground’, vindicating Bohr’s viewpoint. A quantum theory of measurement, in a proper sense, turns out to be unnecessary and in fact impossible. (shrink)

A novel conceptual framework is introduced for the Complexity Levels Theory in a Categorical Ontology of Space and Time. This conceptual and formal construction is intended for ontological studies of Emergent Biosystems, Super-complex Dynamics, Evolution and Human Consciousness. A claim is defended concerning the universal representation of an item’s essence in categorical terms. As an essential example, relational structures of living organisms are well represented by applying the important categorical concept of natural transformations to biomolecular reactions and relational structures (...) that emerge from the latter in living systems. Thus, several relational theories of living systems can be represented by natural transformations of organismic, relational structures. The ascent of man and other living organisms through adaptation, is viewed in novel categorical terms, such as variable biogroupoid representations of evolving species. Such precise but flexible evolutionary concepts will allow the further development of the unifying theme of local-to-global approaches to highly complex systems in order to represent novel patterns of relations that emerge in super- and ultra-complex systems in terms of compositions of local procedures. Solutions to such local-to-global problems in highly complex systems with ‘broken symmetry’ might be possible to be reached with the help of higher homotopy theorems in algebraic topology such as the generalized van Kampen theorems (HHvKT). Categories of many-valued, Łukasiewicz-Moisil (LM) logic algebras provide useful concepts for representing the intrinsic dynamic ‘asymmetry’ of genetic networks in organismic development and evolution, as well as to derive novel results for (non-commutative) Quantum Logics. Furthermore, as recently pointed out by Baianu and Poli (Theory and applications of ontology, vol 1. Springer, Berlin, in press), LM-logic algebras may also provide the appropriate framework for future developments of the ontological theory of levels with its complex/entangled/intertwined ramifications in psychology, sociology and ecology. As shown in the preceding two papers in this issue, a paradigm shift towards non-commutative, or non-Abelian, theories of highly complex dynamics—which is presently unfolding in physics, mathematics, life and cognitive sciences—may be implemented through realizations of higher dimensional algebras in neurosciences and psychology, as well as in human genomics, bioinformatics and interactomics. (shrink)

Cellular automata (henceforth: CA) are discrete, abstract computational systems that have proved useful both as general models of complexity and as more specific representations of non-linear dynamics in a variety of scientific fields. Firstly, CA are (typically) spatially and temporally discrete: they are composed of a finite or denumerable set of homogeneous, simple units, the atoms or cells. At each time unit, the cells instantiate one of a finite set of states. They evolve in parallel at discrete time (...) steps, following state update functions or dynamical transition rules: the update of a cell state obtains by taking into account the states of cells in its local neighborhood (there are, therefore, no actions at a distance). Secondly, CA are abstract, as they can be specified in purely mathematical terms and implemented in physical structures. Thirdly, CA are computational systems: they can compute functions and solve algorithmic problems. Despite functioning in a different way from traditional, Turing machine-like devices, CA with suitable rules can emulate a universal Turing machine, and therefore compute, given Turing's Thesis, anything computable.... (shrink)

A novel conceptual framework is introduced for the Complexity Levels Theory in a Categorical Ontology of Space and Time. This conceptual and formal construction is intended for ontological studies of Emergent Biosystems, Super-complex Dynamics, Evolution and Human Consciousness. A claim is defended concerning the universal representation of an item’s essence in categorical terms. As an essential example, relational structures of living organisms are well represented by applying the important categorical concept of natural transformations to biomolecular reactions and relational structures (...) that emerge from the latter in living systems. Thus, several relational theories of living systems can be represented by natural transformations of organismic, relational structures. The ascent of man and other living organisms through adaptation, is viewed in novel categorical terms, such as variable biogroupoid representations of evolving species. Such precise but flexible evolutionary concepts will allow the further development of the unifying theme of local-to-global approaches to highly complex systems in order to represent novel patterns of relations that emerge in super- and ultra-complex systems in terms of compositions of local procedures. Solutions to such local-to-global problems in highly complex systems with ‘broken symmetry’ might be possible to be reached with the help of higher homotopy theorems in algebraic topology such as the generalized van Kampen theorems (HHvKT). Categories of many-valued, Łukasiewicz-Moisil (LM) logic algebras provide useful concepts for representing the intrinsic dynamic ‘asymmetry’ of genetic networks in organismic development and evolution, as well as to derive novel results for (non-commutative) Quantum Logics. Furthermore, as recently pointed out by Baianu and Poli (Theory and applications of ontology, vol 1. Springer, Berlin, in press), LM-logic algebras may also provide the appropriate framework for future developments of the ontological theory of levels with its complex/entangled/intertwined ramifications in psychology, sociology and ecology. As shown in the preceding two papers in this issue, a paradigm shift towards non-commutative, or non-Abelian, theories of highly complex dynamics—which is presently unfolding in physics, mathematics, life and cognitive sciences—may be implemented through realizations of higher dimensional algebras in neurosciences and psychology, as well as in human genomics, bioinformatics and interactomics. (shrink)

This paper explores whether human proactivity can be considered an expression of free will. The discussion involves two paradigms, which are mutually complementary and encompass psychological proactivity and reactivity. Both paradigms raise the question of linear and non-linear determinism, which inevitably leads to the issue of free will. The analysis attempts to find a compromise between linear and non-linear determinism through the approach of human dialectical complexity (Lebed & Bar-Eli, 2013). This refers to the relationships of (...) two types of complex subsystems within a human: the perceptual-motor dynamic system (PMDS), which is mostly determined by linear impacts and expressed through reactive behavior, and the “free-will”11. The authors employ the term “free will” in a metaphorical sense and do not put forth philosophical arguments for this consideration. complex system (FCS), which is mostly determined by non-linear redundant determinism and expressed through proactive dynamics. In summary, it is concluded that there cannot be a categorical assertion of the permanent existence of free will in human functioning. The human dialectical complexity expressed by both proactivity and reactivity causes the “floating” presence of free will depending on the prevalence of proactive control factors and the non-linear determination of a living human system. (shrink)

Human participants and recurrent (“connectionist”) neural networks were both trained on a categorization system abstractly similar to natural language systems involving irregular (“strong”) classes and a default class. Both the humans and the networks exhibited staged learning and a generalization pattern reminiscent of the Elsewhere Condition (Kiparsky, 1973). Previous connectionist accounts of related phenomena have often been vague about the nature of the networks’ encoding systems. We analyzed our network using dynamical systems theory, revealing topological and (...) geometric properties that can be directly compared with the mechanisms of non-connectionist, rule-based accounts. The results reveal that the networks “contain” structures related to mechanisms posited by rule-based models, partly vindicating the insights of these models. On the other hand, they support the one mechanism (OM), as opposed to the more than one mechanism (MOM), view of symbolic abstraction by showing how the appearance of MOM behavior can arise emergently from one underlying set of principles. The key new contribution of this study is to show that dynamical systems theory can allow us to explicitly characterize the relationship between the two perspectives in implemented models. (shrink)

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. (shrink)

How significant is social evolution theory for the maintenance of virulence in natural populations? We assume that secreted, distantly acting virulence factors are highly likely to be cooperative public goods. Using this assumption, we discuss and critically assess the potential importance of social interactions for understanding the evolution, diversity and distribution of virulence in the Bacillus cereus group, a novel study system for microbial social biology. We conclude that dynamic equilibria in Cry toxin production, as well as strong (...) spatial structure and population bottlenecks in hosts are the main ecological factors maintaining the cooperative secretion of virulence factors and argue that collective action has contributed to the evolution of narrow host range. Non‐linearities in the benefits associated with public goods, as well as the lack of private secretion systems in the Firmicutes may also explain the prevalence and importance of distantly acting virulence factors in B. cereus and its relatives. (shrink)

Organizations in changing environments need to become flexible, responsive and participative. We develop an understanding of governance in these organizations by drawing analogies between organization theory and theories of non-linear dynamics. We identify freedom and creativity as driving principles in 'chaotic' participative organizations, and explore the ethics of their exercise within organizational communities of practice, communities of discernment and communities of commitment.

This article attempts to re-think the notion of reflexivity in terms of non-linearity. It tries to understand the second modernity as a non-linear modernity. This second modernity is understood as much in terms of communications as social norms. It is a modernity that is thoroughly monist. It features non-linear socio-technical systems.

The meaning of the wave function and its evolution are investigated. First, we argue that the wave function in quantum mechanics is a description of random discontinuous motion of particles, and the modulus square of the wave function gives the probability density of the particles being in certain locations in space. Next, we show that the linear non-relativistic evolution of the wave function of an isolated system obeys the free Schrödinger equation due to the requirements of spacetime translation invariance (...) and relativistic invariance. Thirdly, we argue that the random discontinuous motion of particles may lead to a stochastic, nonlinear collapse evolution of the wave function. A discrete model of energy-conserved wavefunction collapse is proposed and shown consistent with existing experiments and our macroscopic experience. Besides, we also give a critical analysis of the de Broglie-Bohm theory, the many-worlds interpretation and other dynamical collapse theories, and briefly discuss the issues of unifying quantum mechanics and relativity. (shrink)

In philosophy of action, we typically aim to explain action by appealing to conative attitudes whose contents are either logically consistent propositions or can be rendered as such. Call this “the logical criterion.” This is especially difficult to do with clear-minded, intentional incontinence since we have to explain how two judgments can have non-contradicting contents yet still aim at contradictory outcomes. Davidson devises an innovative way of doing this but compromises his ability to explain how our better judgments can cause (...) our continent behaviors. In this essay, I preserve Davidson’s approach to the logical criterion but deviate from his broader theory of action by developing a default-interventionist dual systems theory of action. To do this, I focus on the dynamical relationship between System 1 and System 2: the logical construction of value judgments in System 2 from System 1 and the imaginative construction of non-propositional conative attitudes in System 1 from System 2. I draw on Street’s Humean constructivism and Peacocke’s theory of imagination for logical and imaginative construction, respectively. Within this framework, I provide a new definition of continence and incontinence that satisfies the logical criterion and explains how our better judgments can cause our continent behaviors. (shrink)

This book brings together in a single coherent framework a research programme begun by the author in the forties. The main model around which the analysis is built is Hicksian in character, having been drawn in large part from John Hicks's Value and Capital. The model is extended so as to include money and securities. In respect of the theory of the firm the model focuses on demand and supply plans, on inputs and outputs, on inventories, and on dependencies (...) between them. The stability of temporary equilibrium is discussed for linear and non-linear cases. Because the concept of structural stability is important for understanding non-linear cases, it is defined and applied to the case of economic motion generated from the temporary equilibrium analysis. The addenda focus on developments in economic theory following the publication of the main model. (shrink)

Systems Theory is best understood in its dual nature as an episode in the generic development of human understanding of the world, and as the specific product of its social history. On the one hand it is a "moment" in the investigation of complex systems, the place between the formulation of a problem and the interpretation of its solution where mathematical modeling can make the obscure obvious. On the other hand it is the attempt of a reductionist (...) scientific tradition to come to terms with complexity, non-linearity and change through sophisticated mathematical and computational techniques, a groping toward a more dialectical understanding that is held back both by its philosophical biases and by the institutional and economic contexts of its development. (shrink)