This work addresses a broad range of questions which belong to four fields: computation theory, general philosophy of science, philosophy of cognitive science, and philosophy of mind. Dynamical system theory provides the framework for a unified treatment of these questions. ;The main goal of this dissertation is to propose a new view of the aims and methods of cognitive science--the dynamical approach . According to this view, the object of cognitive science is a particular set of (...) class='Hi'>dynamical systems, which I call "cognitive systems". The goal of a cognitive study is to specify a dynamical model of a cognitive system, and then use this model to produce a detailed account of the specific cognitive abilities of that system. The dynamical approach does not limit a-priori the form of the dynamical models which cognitive science may consider. In particular, this approach is compatible with both computational and connectionist modeling, for both computational systems and connectionist networks are special types of dynamical systems. ;To substantiate these methodological claims about cognitive science, I deal first with two questions in two different fields: What is a computational system? What is a dynamical explanation of a deterministic process? ;Intuitively, a computational system is a deterministic system which evolves in discrete time steps, and which can be described in an effective way. In chapter 1, I give a formal definition of this concept which employs the notions of isomorphism between dynamical systems, and of Turing computable function. In chapter 2, I propose a more comprehensive analysis which is based on a natural generalization of the concept of Turing machine. ;The goal of chapter 3 is to develop a theory of the dynamical explanation of a deterministic process. By a "dynamical explanation" I mean the specification of a dynamical model of the system or process which we want to explain. I start from the analysis of a specific type of explanandum--dynamical phenomena--and I then use this analysis to shed light on the general form of a dynamical explanation. Finally, I analyze the structure of those theories which generate explanations of this form, namely dynamical theories. (shrink)

This study considers the problem of using approximate way for realizing the neural supervisor for nonlinear multivariable systems. The Nonlinear Autoregressive-Moving Average (NARMA) model is an exact transformation of the input-output behavior of finite-dimensional nonlinear discrete time dynamical organization in a hoodlum of the equilibrium state. However, it is not convenient for intention of adaptive control using neural networks due to its nonlinear dependence on the control input. Hence, quite often, approximate technique are used for realizing the neural (...) supervisor to overcome computational complexity. In this study, we introduce two classes of ideal which are approximations to the NARMA model and which are linear in the control input, namely NARMA-L1 and NARMA-L2. The latter fact substantially simplifies both the theoretical breakdown as well as the practical request of the controller. Extensive imitation studies have shown that the neural controller designed using the proposed approximate models perform very well and in dozens situation even better than an approximate controller designed using the exact NARMA Model. In view of their mathematical tractability as well as their fate in simulation studies, a matter is made in this study that such approximate input-output paragon warrants a detailed study in their own right. (shrink)

Advocates of dynamic systems have suggested that higher mental processes are based on continuous representations. In order to evaluate this claim, we first define the concept of representation, and rigorously distinguish between discrete representations and continuous representations. We also explore two important bases of representational content. Then, we present seven arguments that discrete representations are necessary for any system that must discriminate between two or more states. It follows that higher mental processes require discrete representations. We (...) also argue that discrete representations are more influenced by conceptual role than continuous representations. We end by arguing that the presence of discrete representations in cognitive systems entails that computationalism (i.e., the view that the mind is a computational device) is true, and that cognitive science should embrace representational pluralism. (shrink)

The paper analyzes dynamic epistemic logic from a topological perspective. The main contribution consists of a framework in which dynamic epistemic logic satisfies the requirements for being a topological dynamical system thus interfacing discrete dynamic logics with continuous mappings of dynamical systems. The setting is based on a notion of logical convergence, demonstratively equivalent with convergence in Stone topology. Presented is a flexible, parametrized family of metrics inducing the latter, used as an analytical aid. We show (...) maps induced by action model transformations continuous with respect to the Stone topology and present results on the recurrent behavior of said maps. (shrink)

We define emergence algebraically in the context of discrete dynamical systems modeled as transformation semigroups. Emergence happens when a quotient structure (coarse-grained dynamics) is not a substructure of the original system. We survey small groups to show that algebraic emergence is neither ubiquitous nor rare. Then, we describe connections with hierarchical decompositions and explore some of the philosophical implications of the algebraic constraints.

This work presents a post-positivist research framework to explain any surprising fact in the evolutionary path of a complex, dynamic and contingent social phenomenon. Primarily, it reconciles the ontological and epistemological assumptions of Critical Realism with the principles of American Pragmatism. Then, the research approach is presented: theoretical propositions about a social structure are translated into a set of grammar rules that acknowledges a pattern of sequences of events of either individual action or social interaction between actors within a real (...) social system. The result is a discrete mathematical model for a concrete category of social process based on these rules. Finally, data-grounded refinement of the theory is possible by the comparison between cases belonging to the same category, but differing about some contingent pattern of sequences of event outcomes. Consequently, their grammars differ in some pairs of context-sensitive rules that can explain this surprising fact, such that the derivation of this alternative historical trajectory of event outcomes becomes an extension to the early category of social process. In this sense, the proposed framework suggests there is a hierarchy of classes of grammars for middle-range explanations based upon the ontological assumption of the generative nature of social reality. (shrink)

Conscious states—state that there is something it is like to be in—seem both rich or full of detail and ineffable or hard to fully describe or recall. The problem of ineffability, in particular, is a longstanding issue in philosophy that partly motivates the explanatory gap: the belief that consciousness cannot be reduced to underlying physical processes. Here, we provide an information theoretic dynamical systems perspective on the richness and ineffability of consciousness. In our framework, the richness of conscious experience (...) corresponds to the amount of information in a conscious state and ineffability corresponds to the amount of information lost at different stages of processing. We describe how attractor dynamics in working memory would induce impoverished recollections of our original experiences, how the discrete symbolic nature of language is insufficient for describing the rich and high-dimensional structure of experiences, and how similarity in the cognitive function of two individuals relates to improved communicability of their experiences to each other. While our model may not settle all questions relating to the explanatory gap, it makes progress toward a fully physicalist explanation of the richness and ineffability of conscious experience—two important aspects that seem to be part of what makes qualitative character so puzzling. (shrink)

Organisms live not as discrete entities on which an independent environment acts, but as members of a reproductive lineage in an ongoing series of interactions between that lineage and a dynamic ecological niche. These interactions continuously shape both systems in a reciprocal manner, resulting in the emergence of reliably co-occurring configurations within and between both systems. The enactive approach to cognition describes this relationship as the structural coupling between an organism and its environment; similarly, Developmental Systems Theory emphasizes the (...) reciprocal nature of structurally coupled systems in its analysis of organisms as developmental processes embedded within a developmental system. Through an enactive-developmental systems framing, this paper identifies the organizational features of cognizing systems in order to motivate a picture of how organism and environment co-determine and co-construct one another. I argue that organisms can be characterized as self-organizing, operationally closed, plastic systems ecologically embedded within a developmental system. In virtue of this organizational makeup, organisms actively engage in the modulation and assessment of their coupling with their environment: cognitive strategies that entail contextualized responses to variations across the web of interactions that comprises the developmental system. (shrink)

Building on theoretical insights and rich experimental data of our preprints, we present here new theoretical and experimental results in three interrelated approaches to the Collatz problem and its generalizations: algorithmic decidability, random behavior, and Diophantine representation of related discrete dynamical systems, and their cyclic and divergent properties.

An ideal constructor produces geometry from scratch, modelled through the bottom-up assembly of a graph-like lattice within a space that is defined, bootstrap-wise, by that lattice. Construction becomes the problem of assembling a homogeneous lattice in three-dimensional space; that becomes the problem of resolving geometrical frustration in quasicrystalline structure; achieved by reconceiving the lattice as a dynamical system. The resulting construction is presented as the introductory model sufficient to motivate the formal argument that it is a fundamental structure; (...) based on which, it is proposed that where mathematics’ numbers conventionally correspond to dimensionless points on the stateless number line, numbers more fundamentally correspond to an ordering of discrete objects constructed within the stateful number lattice. A second observation is that this fundamental lattice structure is helically configured with fractal character, which, as it relates to the geometry underlying spacetime, has relevance to questions in physics, particularly those involving wave-particle duality. (shrink)

With the advent of computers in the experimental labs, dynamic systems have become a new tool for research on problem solving and decision making. A short review of this research is given and the main features of these systems (connectivity and dynamics) are illustrated. To allow systematic approaches to the influential variables in this area, two formal frameworks (linear structural equations and finite state automata) are presented. Besides the formal background, the article sets out how the task demands of (...) class='Hi'>system identification and system control can be realised in these environments, and how psychometrically acceptable dependent variables can be derived. (shrink)

I examine explanations’ realist commitments in relation to dynamical systems theory. First I rebut an ‘explanatory indispensability argument’ for mathematical realism from the explanatory power of phase spaces (Lyon and Colyvan 2007). Then I critically consider a possible way of strengthening the indispensability argument by reference to attractors in dynamical systems theory. The take-home message is that understanding of the modal character of explanations (in dynamical systems theory) can undermine platonist arguments from explanatory indispensability.

It is argued that the theory of situated cognition together with dynamic systems theory can explain the core of artistic practice and aesthetic experience, and furthermore paves the way for an account of how artist and audience can meet via the artist's work. The production and consumption of art is an embodied practice, firmly based in perception and action, and supported by features of the local, agent-centered and global socio-cultural contexts. Artistic creativity and aesthetic experience equally result from the dynamic (...) interplay between agent and context, allowing for artist and viewer to relate to the artist's work in similar ways. (shrink)

Our approach aims at accounting for causal claims in terms of how the physical states of the underlying dynamical system evolve with time. Causal claims assert connections between two sets of physicals states—their truth depends on whether the two sets in question are genuinely connected by time evolution such that physical states from one set evolve with time into the states of the other set. We demonstrate the virtues of our approach by showing how it is able to (...) account for typical causes, causally relevant factors, being ‘the’ cause, and cases of overdetermination and causation by absences. (shrink)

Progress in the last few decades in what is widely known as “Chaos Theory” has plainly advanced understanding in the several sciences it has been applied to. But the manner in which such progress has been achieved raises important questions about scientific method and, indeed, about the very objectives and character of science. In this presentation, I hope to engage my audience in a discussion of several of these important new topics.

Traditionally, computational theory (CT) and dynamical systems theory (DST) have presented themselves as opposed and incompatible paradigms in cognitive science. There have been some efforts to reconcile these paradigms, mainly, by assimilating DST to CT at the expenses of its anti-representationalist commitments. In this paper, building on Piccinini’s mechanistic account of computation and the notion of functional closure, we explore an alternative conciliatory strategy. We try to assimilate CT to DST by dropping its representationalist commitments, and by inviting CT (...) to recognize the functionally closed nature of some computational systems. (shrink)

Efforts to bridge emotion theory with neurobiology can be facilitated by dynamic systems (DS) modeling. DS principles stipulate higher-order wholes emerging from lower-order constituents through bidirectional causal processes cognition relations. I then present a psychological model based on this reconceptualization, identifying trigger, self-amplification, and self-stabilization phases of emotion-appraisal states, leading to consolidating traits. The article goes on to describe neural structures and functions involved in appraisal and emotion, as well as DS mechanisms of integration by which they interact. These mechanisms (...) include nested feedback interactions, global effects of neuromodulation, vertical integration, action-monitoring, and synaptic plasticity, and they are modeled in terms of both functional integration and temporal synchronization. I end by elaborating the psychological model of emotion–appraisal states with reference to neural processes. (shrink)

Clark and Chalmers (2002) advance two hypotheses that both cognition and the mind extend into the environment. Both hypotheses are grounded in active externalism about mental content and the Parity Principle. Active externalism proposes that the external features of the environment in the present directly influence our mental contents and behavior. The Parity Principle states that a process or state in the environment is cognitive if it is functionally equivalent to a comparable intracranial cognitive process. This paper reviews two of (...) the strongest replies to the hypotheses, namely that arguments for them commit the coupling-constitution fallacy and that the hypothesis of extended cognition is incompatible with any satisfactory criteria that distinguishes between cognitive and non-cognitive processes. This paper argues that a dynamical systems approach avoids both objections and offers a conceptual and methodological framework for an extended cognitive science. Lastly, an account of collective intentionality will be considered to show how groups of individuals can be the bearers of mental states. (shrink)

Dynamicism has provided cognitive science with important tools to understand some aspects of “how cognitive agents work” but the issue of “what makes something cognitive” has not been sufficiently addressed yet, and, we argue, the former will never be complete without the later. Behavioristic characterizations of cognitive properties are criticized in favor of an organizational approach focused on the internal dynamic relationships that constitute cognitive systems. A definition of cognition as adaptive-autonomy in the embodied and situated neurodynamic domain is provided: (...) the compensatory regulation of a web of stability dependencies between sensorimotor structures, is created and preserved during a historical/developmental process. We highlight the functional role of emotional embodiment: internal bioregulatory processes coupled to the formation and adaptive regulation of neurodynamic autonomy. Finally, we discuss a “minimally cognitive behavior program” in evolutionary simulation modelling suggesting that much is to be learned from a complementary “minimally cognitive organization program”. (shrink)

(This version was submitted to Behavioral and Brain Science. A revised version was published by Biological Theory) Estimates of autism’s incidence increased 5-10 fold in ten years, an increase which cannot be genetic. Though many mutations are associated with autism, no mutation seems directly to cause autism. We need to find the direct cause. Complexity science provides a new paradigm - confirmed in biology by extensive hard data. Both the body and the personality are complex dynamic systems which spontaneously self-organize (...) from simple dynamic systems. Autism may therefore be caused by the failure of a simple dynamic system. We know that infants who cannot track their mother’s face often become autistic, that eye-contact initiates intersubjectivity which is blocked in autism, and that the infant-mother pair seems designed to promote eye-contact, as does the eye’s appearance. This author earlier proposed that failure of eye-contact might directly cause autism and that early non-maternal childcare, including television/video, would therefore be statistically linked to autism. Waldman et al. (2008; 2006) recently proved that autism is strongly linked to precipitation (indoor activity) and to the introduction of cable. The most plausible explanation? Early exposure to television/video is linked to autism. Furthermore a normal developmental cascade (blocked in autism) has been deciphered: (a) Infant-mother eye-contact triggers increased maternal attention. (b) Early maternal attention permanently increases not only baseline vasopressin but also that oxytocin release which is triggered by subsequent maternal attention. (c) Vasopressin and oxytocin promote face recognition, gazing-at-the-eyes, emotion recognition, and social bonding. The eye-contact hypothesis suggests a clinical study addressing prevention: recruit prospective parents who agree to curtail television/video/computer/wi-fi in their families; measure autism’s incidence in their children. (shrink)

The new kid on the block in cognitive science these days is dynamic systems. This way of thinking about the mind is, as usual, radically opposed to computationalism - - the hypothesis that thinking is computing. The use of dynamic systems is just the latest in a series of attempts, from Searle's Chinese Room Argument, through the weirdnesses of postmodernism, to overthrown computationalism, which as we all know is a perfectly nice hypothesis about the mind that never hurt anyone.

From his earliest work forward, phenomenologist Maurice Merleau-Ponty attempted to develop a new ontology of nature that would avoid the antinomies of realism and idealism by showing that nature has its own intrinsic sense which is prior to reflection. The key to this new ontology was the concept of form, which he appropriated from Gestalt psychology. However, Merleau-Ponty struggled to give a positive characterization of the phenomenon of form which would clarify its ontological status. Evan Thompson has recently taken up (...) Merleau-Ponty’s ontology as the basis for a new, “enactive” approach to cognitive science, synthesizing it with concepts from dynamic systems theory and Francisco Varela’s theory of autopoiesis. However, Thompson does not quite succeed in resolving the ambiguities in Merleau-Ponty’s account of form. This article builds on an indication from Thompson in order to propose a new account of form as asymmetry, and of the genesis of form in nature as symmetry-breaking. These concepts help us to escape the antinomies of Modern thought by showing how nature is the autoproduction of a sense which can only be known by an embodied perceiver. (shrink)

So-called ‘distinctively mathematical explanations’ (DMEs) are said to explain physical phenomena, not in terms of contingent causal laws, but rather in terms of mathematical necessities that constrain the physical system in question. Lange argues that the existence of four or more equilibrium positions of any double pendulum has a DME. Here we refute both Lange’s claim itself and a strengthened and extended version of the claim that would pertain to any n-tuple pendulum system on the ground that such (...) explanations are actually causal explanations in disguise and their associated modal conditionals are not general enough to explain the said features of such dynamical systems. We argue and show that if circumscribing the antecedent for a necessarily true conditional in such explanations involves making a causal analysis of the problem, then the resulting explanation is not distinctively mathematical or non-causal. Our argument generalises to other dynamical systems that may have purported DMEs analogous to the one proposed by Lange, and even to some other counterfactual accounts of non-causal explanation given by Reutlinger and Rice. (shrink)

This article is devoted to describing results of conceptualization of the idea of mind at the stage of maturity. Delineated the acquisition by the energy system (mind) of stable morphological characteristics, which associated with such a pivotal formation as the discourse. A qualitative structural and ontological sign of the system transition to this stage is the transformation of the verbal morphology of the mind into a discursive one. The analysis of the poststructuralist understanding of discourse in the context (...) of the dispersion of meanings (Foucault) made it possible to formulate a notion of it as a meaning that is constituted by the relation between the discursive practice and the worldview, regarded as a meta-discourse or a global discursive formation. In consequence of this relationship, a discrete and simultaneous scattering of meanings arises, the procedural side of which is a concrete discourse, and its productive aspect is linked with the creation of a local discursive formation. Based on this view it is proposed a logical formula of discourse, which takes into account the entropy of the language and the entropy of the worldview, as a particular manifestation of the mind entropy. Using this formula and considering the reactive nature of discourse, it was developed a classification, which included such types of discourses as reactive, suggestive, synthetic and creative. In turn, the proposed types of discourses are correlated with the specific characteristics of certain activities, as a psychological category. Also, it was considered the translation of the structure of discourse dissipation from the cognitive plan into the affective sphere because of which it is formed a hierarchy of significances, which performs the sense-forming function. It was analyzed the inverse influence of the hierarchy of significances on the structure of meanings dispersion and for respective account it was introduced a conditional coefficient of the value deviation of the significance of the meanings. This parameter reflects the sense correction of the meaning that occurs in the process of the emergence of discourse from discursive practice. Thus, the discourse is presented as a complex dynamic formation of the mind arising at the maturity stage of the system as a result of the combined effect of entropic dispersion of meanings and the value deviation of their significances. (shrink)

This paper reviews some major episodes in the history of the spatial isomorphism problem of dynamical systems theory. In particular, by analysing, both systematically and in historical context, a hitherto unpublished letter written in 1941 by John von Neumann to Stanislaw Ulam, this paper clarifies von Neumann's contribution to discovering the relationship between spatial isomorphism and spectral isomorphism. The main message of the paper is that von Neumann's argument described in his letter to Ulam is the very first proof (...) that spatial isomorphism and spectral isomorphism are not equivalent because spectral isomorphism is weaker than spatial isomorphism: von Neumann shows that spectrally isomorphic ergodic dynamical systems with mixed spectra need not be spatially isomorphic. (shrink)

The received view about emergence and reduction is that they are incompatible categories. I argue in this paper that, contrary to the received view, emergence and reduction can hold together. To support this thesis, I focus attention on dynamical systems and, on the basis of a general representation theorem, I argue that, as far as these systems are concerned, the emulation relationship is sufficient for reduction (intuitively, a dynamical system DS1 emulates a second dynamical system (...) DS2 when DS1 exactly reproduces the whole dynamics of DS2). This representational view of reduction, contrary to the standard deductivist one, is compatible with the existence of structural properties of the reduced system that are not also properties of the reducing one. Therefore, under this view, by no means are reduction and emergence incompatible categories but, rather, complementary ones. (shrink)

Culture as a dynamic system of meaningful relations can naturally accommodate a hermeneutic analysis. In this essay, the notion of Gadamer’s hermeneutics as involving interpretable meaning throughout experiential reality permits a natural concordance with an understanding of culture as meaningful. The Gadamerian idea that prejudices inform the horizons that make our experiences intelligible is applied to the view that culture is both a self-enclosed structure that is given by one’s horizon and one that continuously points past this horizon in (...) genuine dialogue. Nevertheless, in seeing culture as a coherent system that transcends itself, we are consequently faced with a dilemma regarding the evolution of one’s cultural horizons: whether past horizons can survive the creation of novel ones through dialogue. However, this may be resolved through Gadamer’s understanding of the functions of sameness and difference within horizonal evolution, and how these functions feature in the distinction between a shared ontological ground and the horizons through which the ground is interpreted. Ultimately, we showcase how it is noncontradictory to suppose that culture is both self- and other-referential. (shrink)

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)

Achieving Coherence introduces a transformative framework for understanding and managing the complexities of dynamic systems. In a world where uncertainty and interconnected challenges define the landscape, the SPARC framework (Spectrum of Possibility and Recursive Choice) offers a unified model to address these issues, bridging the gap between theory and application across disciplines. This work explores the principles of coherence, constraint satisfaction, and recursive feedback, shedding light on how systems maintain stability and adapt in the face of evolving constraints and environmental (...) noise. By integrating dimensional transitions, multi-constraint optimization, and resilience to stochastic influences, SPARC provides a novel approach to modeling systems that are inherently complex and interdependent. Applications range from stabilizing critical infrastructure and managing ecosystems under stress to advancing artificial intelligence and optimizing multi-agent systems. By demonstrating how local behaviors interact with global dynamics and how systems can thrive under variability, Achieving Coherence presents a compelling vision for navigating complexity and driving innovation in an interconnected world. (shrink)

In this work we study dimensional theoretical properties of some a±ne dynamical systems. By dimensional theoretical properties we mean Hausdor® dimension and box- counting dimension of invariant sets and ergodic measures on theses sets. Especially we are interested in two problems. First we ask whether the Hausdor® and box- counting dimension of invariant sets coincide. Second we ask whether there exists an ergodic measure of full Hausdor® dimension on these invariant sets. If this is not the case we ask (...) the question, whether at least the variational principle for Haus- dor® dimension holds, which means that there is a sequence of ergodic measures such that their Hausdor® dimension approximates the Hausdor® dimension of the invariant set. It seems to be well accepted by experts that these questions are of great importance in developing a dimension theory of dynamical systems (see the book of Pesin about dimension theory of dynamical systems [PE2]). Dimensional theoretical properties of conformal dynamical systems are fairly well understood today. For example there are general theorems about conformal repellers and hyperbolic sets for conformal di®eomorphisms (see chapter 7 of [PE2]). On the other hand the existence of two di®erent rates of expansion or contraction forces problems that are not captured by a general theory this days. At this stage of de- velopment of the dimension theory of dynamical systems it seems natural to study non conformal examples. This is the ¯rst step to understand the mechanisms that determine dimensional theoretical properties of non conformal dynamical systems. A±ne dynamical systems represent simple examples of non conformal systems. They are easy to de¯ne, but studying their dimensional theoretical properties does never- theless provide challenging mathematical problems and exemplify interesting phe- nomena. We consider here a special class of self-a±ne repellers in dimension two, depending on four parameters (see 2.1.). Furthermore we study a class of attractors of piecewise a±ne maps in dimension three depending on four parameters as well. The last object of our work are projections of these maps that are known as gener- alized Baker's transformations (see 2.2.). The contents of our work is the following: In chapter two we give an overview about some main results in the area of di- mension theory of a±ne dynamical systems and de¯ne the systems we study in this work. We will explain, what is known about the dimensional theoretical properties of these systems and describe what our new results are. In chapter three we then apply symbolic dynamics to our systems. We will introduce explicit shift codings 4 and ¯nd representations of all ergodic measures for our systems using these codings. From chapter four to chapter eight we study dimensional theoretical properties, which our systems generally or generically have. In chapter four we will prove a formula for the box-counting dimension of the repellers and the attractors (see the- orem 4.1.). Then in chapter ¯ve we apply general dimensional theoretical results for ergodic measures found by Ledrappier and Young [LY] and Barreira, Schmeling and Pesin [BPS] to our systems. These results relate the dimension of ergodic measures to metric entropy and Lyapunov exponents. Using this approach we will be able to reduce questions about the dimension of ergodic measures in our context to ques- tions about certain overlapping and especially overlapping self-similar measures on the line. These overlapping self-similar measures are studied in chapter six. Our main theorem extends a result of Peres and Solomyak [PS2] concerning the absolute continuity resp. singularity of symmetric self-similar measures to asymmetric ones (see theorem 6.1.3.). In chapter seven we bring our results together. We prove that we generically (in the sense of Lebesgue measure on a part of the parameter space) have the iden- tity of box-counting and Hausdor® dimension for the repellers and the attractors. (see theorem 7.1.1. and corollary 7.1.2.). This result suggest that one can expect that the identity of box-counting dimension and Hausdor® dimension holds at least generically in some natural classes of non conformal dynamical systems. Furthermore we will see in chapter seven that there generically exists an ergodic measure of full Hausdor® dimension for the repellers. On the other hand the vari- ational principle for Hausdor® dimension is not generic for the attractors. It holds only if we assume a certain symmetry (see theorem 7.1.1.). For generalized Baker's transformations we will ¯nd a part of the parameter space where there generically is an ergodic measure of full dimension and a part where the variational principle for Hausdor® dimension does not hold (see theorem 7.1.3.). Roughly speaking the reason why the variational principle does not hold here is, that if there exists both a stable and an unstable direction one can not generically maximize the dimension in the stable and in the unstable direction at the same time. In an other setting this phenomenon was observed before by Manning and McCluskey [MM]. In chapter eight we extend some results of the last section to invariant sets that correspond to special Markov chains instead of full shifts (see theorem 8.1.1.). In the last two chapters of our work we are interested in number theoretical excep- tions to our generic results. The starting point of our considerations in section nine are results of ErdÄos [ER1] and Alexander and Yorke [AY] that establish singularity and a decrease of dimension for in¯nite convolved Bernoulli measures under special conditions. Using a generalized notion of the Garsia entropy ([GA1/2]) we are able 5 to understand the consequences of number theoretical peculiarities in broader class of overlapping measures (see theorem 9.1.1.). In chapter ten we then analyze number theoretical peculiarities in the context of our dynamical systems. We restrict our attention to a symmetric situation where we generically have the existence of a Bernoulli measure of full dimension and the identity of Hausdor® and box-counting dimension for all of our systems. In the ¯rst section of chapter ten we ¯nd parameter values such that the variational principle for Hausdor® dimension does not hold for the attractors and for the Fat Baker's transformations (see theorem 10.1.1.). These are the ¯rst known examples of dynamical systems for which the variational principle for Hausdor® dimension does not hold because of number theoretical peculiarities of parameter values. For the repellers we have been able to show that under certain number theoretical conditions there is at least no Bernoulli measure of full Hausdor® dimension; the question if the variational principle for Hausdor® dimension holds remains open in this situation. In the second section of chapter ten we will show that the identity for Hausdor® and box-counting dimension can drops because there are number theoretical pecu- liarities. In the context of Weierstrass-like functions this phenomenon was observed by Przytycki and Urbanski [PU]. Our theorem extends this result to a larger class of sets, invariant under dynamical systems (see theorem 10.2.1). At the end of this work the reader will ¯nd two appendices, a list of notations and the list of references. In appendix A we introduce the notions of dimension we use in this work and collect some general facts in dimension theory. In appendix B we state the facts about Pisot-Vijayarghavan number, we need in our analysis of number theoretical peculiarities. The list of notations contains general notations and a table with a summary of notations we use to describe the dynamical systems that we study. Acknowledgments I wish to thank my supervisor JÄorg Schmeling for a lot of valuable discussion and all his help. Also thanks to Luis Barreira for his great hospitality in Lisboa and many interesting comments. This work was done while I was supported by "Promotionstipendium gem. NaFÄoG der Freien UniversitÄat Berlin". (shrink)

The current assessment of behaviors in the inventories to diagnose autism spectrum disorders (ASD) focus on observation and discrete categorizations. Behaviors require movements, yet measurements of physical movements are seldom included. Their inclusion however, could provide an objective characterization of behavior to help unveil interactions between the peripheral and the central nervous systems. Such interactions are critical for the development and maintenance of spontaneous autonomy, self-regulation and voluntary control. At present, current approaches cannot deal with the heterogeneous, dynamic and (...) stochastic nature of development. Accordingly, they leave no avenues for real-time or longitudinal assessments of change in a coping system continuously adapting and developing compensatory mechanisms. We offer a new unifying statistical framework to reveal re-afferent kinesthetic features of the individual with ASD. The new methodology is based on the non-stationary stochastic patterns of minute fluctuations (micro-movements) inherent to our natural actions. Such patterns of behavioral variability provide re-entrant sensory feedback contributing to the autonomous regulation and coordination of the motor output. From an early age, this feedback supports centrally driven volitional control and fluid, flexible transitions between intentional and spontaneous behaviors. We show that in ASD there is a disruption in the maturation of this form of proprioception. Despite this disturbance, each individual has unique adaptive compensatory capabilities that we can unveil and exploit to evoke faster and more accurate decisions. Measuring the kinesthetic re-afference in tandem with stimuli variations we can detect changes in their micro-movements indicative of a more predictive and reliable kinesthetic percept. Our methods address the heterogeneity of ASD with a personalized approach grounded in the inherent sensory-motor abilities that the individual has already developed. (shrink)

This paper presents a theoretical study of the binary oppositions underlying the mechanisms of natural computation understood as dynamical processes on natural information morphologies. Of special interest are the oppositions of discrete vs. continuous, structure vs. process, and differentiation vs. integration. The framework used is that of computing nature, where all natural processes at different levels of organisation are computations over informational structures. The interactions at different levels of granularity/organisation in nature, and the character of the phenomena that (...) unfold through those interactions, are modeled from the perspective of an observing agent. This brings us to the movement from binary oppositions to dynamic networks built upon mutually related binary oppositions, where each node has several properties. (shrink)

“There’s Plenty of Room at the Bottom”, said the title of Richard Feynman’s 1959 seminal conference at the California Institute of Technology. Fifty years on, nanotechnologies have led computer scientists to pay close attention to the links between physical reality and information processing. Not all the physical requirements of optimal computation are captured by traditional models—one still largely missing is reversibility. The dynamic laws of physics are reversible at microphysical level, distinct initial states of a system leading to distinct (...) final states. On the other hand, as von Neumann already conjectured, irreversible information processing is expensive: to erase a single bit of information costs ~3 × 10−21 joules at room temperature. Information entropy is a thermodynamic cost, to be paid in non-computational energy dissipation. This paper addresses the problem drawing on Edward Fredkin’s Finite Nature hypothesis: the ultimate nature of the universe is discrete and finite, satisfying the axioms of classical, atomistic mereology. The chosen model is a cellular automaton with reversible dynamics, capable of retaining memory of the information present at the beginning of the universe. Such a CA can implement the Boolean logical operations and the other building bricks of computation: it can develop and host all-purpose computers. The model is a candidate for the realization of computational systems, capable of exploiting the resources of the physical world in an efficient way, for they can host logical circuits with negligible internal energy dissipation. (shrink)

The paper argues that digital ontology (the ultimate nature of reality is digital, and the universe is a computational system equivalent to a Turing Machine) should be carefully distinguished from informational ontology (the ultimate nature of reality is structural), in order to abandon the former and retain only the latter as a promising line of research. Digital vs. analogue is a Boolean dichotomy typical of our computational paradigm, but digital and analogue are only “modes of presentation” of Being (to (...) paraphrase Kant), that is, ways in which reality is experienced or conceptualised by an epistemic agent at a given level of abstraction. A preferable alternative is provided by an informational approach to structural realism, according to which knowledge of the world is knowledge of its structures. The most reasonable ontological commitment turns out to be in favour of an interpretation of reality as the totality of structures dynamically interacting with each other. The paper is the first part (the pars destruens) of a two-part piece of research. The pars construens, entitled “A Defence of Informational Structural Realism”, is developed in a separate article, also published in this journal. (shrink)

The work is an attempt to transfer a structure from Euclidean plane (pure geometrical) under the physical observation limit (resolving power) to a physical space (observable space). The transformation from the mathematical space to physical space passes through the observation condition. The mathematical modelling is adopted. The project is based on two stapes: (1) Looking for a simple mathematical model satisfies the definition of Euclidian plane; (2)That model is examined against three observation resolution conditions (resolved, unresolved and partially resolved). The (...) simplest mechanical model satisfies the definition of Euclidian plane is a planetary gear. The interesting examination of the mechanical model is that is under partial resolution. That examination shows analogous equation for Euler’s formula. The derived complex formula contains the resolved (observable) quantities of the mechanical system and satisfies the linear wave equation. The interpretation of this complex formula is: it is a function related to the position vector of a point in the small wheel of the partially resolved planetary gear system. The function is in terms of the observable quantities only. The work shows the possibility of transformation from real to complex space. The work is purely classical but the result of the partial resolution shows a function similar to the Quantum mechanics wave function. (shrink)

Years ago, when I was an undergraduate math major at the University of Wyoming, I came across an interesting book in our library. It was a book of counterexamples t o propositions in real analysis (the mathematics of the real numbers). Mathematicians work more or less like the rest of us. They consider propositions. If one seems to them to be plausibly true, then they set about to prove it, to establish the proposition as a theorem. Instead o f setting (...) out to prove propositions, the psychologists, neuroscientists, and other empirical types among us, set out to show that a proposition is supported by the data, and that it is the best such proposition so supported. The philosophers among us, when they are not causing trouble by arguing that AI is a dead end or that cognitive science can get along without representations, work pretty much like the mathematicians: we set out to prove certain propositions true on the basis of logic, first principles, plausible assumptions, and others' data. But, back to the book of real analysis counterexamples. If some mathematician happened t o think that some proposition about continuity, say, was plausibly true, he or she would then set out to prove it. If the proposition was in fact not a theorem, then a lot of precious time would be wasted trying to prove it. Wouldn't it be great to have a book that listed plausibly true propositions that were in fact not true, and listed with each such proposition a counterexample to it? Of course it would. (shrink)

According to Discrete Emotion Theory, a number of emotions are distinguishable on the basis of neural, physiological, behavioral and expressive features. Critics of this view emphasize the variability and context-sensitivity of emotions. This paper discusses some of these criticisms, and argues that they do not undermine the claim that emotions are discrete. This paper also presents some works in dynamical affective science, and argues that to conceive of discrete emotions as self-organizing and softly assembled patterns of (...) various processes accounts more naturally than traditional Discrete Emotion Theory for the variability and context-sensitivity of emotions. (shrink)

The Genetic Ranking Optimization Algorithm (GROA) is used to rank phishing content based on multiple features by optimizing the ranking system through iterative selection and weighting. Dynamic weighting further enhances the process by adjusting the weights of features based on their importance in real-time. This hybrid approach enables the model to learn from the data, improving classification over time.

Our universe shows to be local and non-local. The concept is confusing because in daily live we are not aware of the non-locality of our universe. Actually, in daily live local reality seems to be quite orderly and understandable. But we don’t know why everything is in motion and all our theories in physics are still approximations of physical reality. At least that is what they supposed to be.

This paper is an original attempt to understand the foundations of economic reasoning. It endeavors to rigorously define the relationship between subjective interpretations and objective valuations of such interpretations in the context of theoretical economics. This analysis is substantially expanded through a dynamic approach, where the truth of a valuation results in an updated interpretation or changes in the agent's subjective belief regarding the effectiveness of the selected action as well as the objective reality of the effectiveness of all other (...) possible actions (i.e. consequence realization). Complications arise when the economic agent is presented with a set of actions that render ambiguous preference, or when the effectiveness of an action cannot be perceived upon its selection, thereby necessitating a different theory of choice and consequence realization. (shrink)

Mechanistic explanations are often said to explain because they reveal the causal structure of the world. Conversely, dynamical models supposedly lack explanatory power because they do not describe causal structure. The only way for dynamical models to produce causal explanations is via the 3M criterion: the model must be mapped onto a mechanism. This framing of the situation has become the received view around the viability of dynamical explanation. In this paper, I argue against this position and (...) show that dynamical models can themselves reveal causal structure and consequently produce nonmechanistic, dynamical explanations. Taking the example of cell fates from systems biology, I show how dynamical models, and specifically the attractor landscapes they describe, identify the causes of cell differentiation and explain why cells select particular fates. These dynamical features of the system better fit Woodward’s (2010, 2018) criteria of specificity and proportionality and make them the best candidate causes of cell fates than mechanisms. I also show how these causes are irreducible and inaccessible to mechanistic models, making 3M unworkable and counterproductive in this case. Dynamical models can reveal dynamical causes and thereby provide causal explanations. (shrink)

Physical systems without time and dynamics have been considered. The principle of how to construct spacetime in a physical system without time and dynamics has been proposed. It has been found what can be objects in such a spacetime, and what can be an interaction between such objects. Within the framework of the considered class of systems, answers to the following problems of philosophy and physics have been found: the nature of consciousness and the connection of body and consciousness (...) (mind-body problem), the nature of time, the anthropic principle and the problem of fine-tuning the universe, the effectiveness of mathematics in describing physical phenomena, the limits of knowledge. There are a number of indications that our Universe is not based on one of the systems of the class considered. The considered class of systems makes it possible to find answers to questions that cannot be answered for our Universe. This shows that it is fundamentally possible to find answers to these questions for our Universe as well. (shrink)

The distinction between the discrete and the continuous lies at the heart of mathematics. Discrete mathematics (arithmetic, algebra, combinatorics, graph theory, cryptography, logic) has a set of concepts, techniques, and application areas largely distinct from continuous mathematics (traditional geometry, calculus, most of functional analysis, differential equations, topology). The interaction between the two – for example in computer models of continuous systems such as fluid flow – is a central issue in the applicable mathematics of the last hundred years. (...) This article explains the distinction and why it has proved to be one of the great organizing themes of mathematics. (shrink)

In this field questions arise which are certainly difficult; but as I listened last time to members of the group, I felt that the main difficulty perhaps lay in determining precisely what questions we are trying to answer. I have the conviction that if we could only say clearly what the questions are, the answers to them might not appear so elusive. So I have begun with a simple list of questions about discretion which in one form or another were, (...) as it seemed to me, expressed by the group last time. I may indeed have omitted something and inserted something useless: if so, no doubt I shall be informed of this later. The central questions then seem to me to be the following: 1. What is discretion, or what is the exercise of discretion? 2. Under what conditions and why do we in fact accept or tolerate discretion in a legal system? 3. Must we accept discretion or tolerate discretion, and if so, why? 4. What values does the use of discretion menace, and what values does it maintain or promote? 5. What can be done to maximize the beneficial operation of the use of discretion and to minimize any harm that it does? (shrink)

Recognition of the plasticity of development — from gene expression to neuroplasticity — is increasingly undermining the traditional distinction between structure and function, or anatomy and behavior. At the same time, dynamic systems theory — a set of tools and concepts drawn from the physical sciences — has emerged as a way of describing what Maurice Merleau-Ponty calls the “dynamic anatomy” of the living organism. This article surveys and synthesizes dynamic systems models of development from biology, neuroscience, and psychology in (...) order to propose an integrated account of growth, learning, and behavior. Key to this account is the concept of self-differentiation or symmetry-breaking. I argue that development can be understood as a cascade of symmetry-breaking events brought about by the ongoing interactions of multiple, nested, nonlinear dynamic systems whose self-organizing behaviors gradually alter their own anatomical conditions. I begin by introducing the concept of symmetry-breaking as a way of understanding anatomical development. I then extend this approach to motor development by arguing that the organism’s behavior grows along with its body, like a new organ. Finally, I argue that the organism’s behavior and its world grow together dialectically, each driving the other to become more complex and asymmetrical through its own increasing asymmetry. Thus development turns out to be a form of cognition or sense-making, and cognition a form of development. (shrink)

It has become a fact that fluency and competency in utilizing the advancement of technology, specifically the computer and the internet is one way that could help in facilitating learning in mathematics. This study investigated the effects of Dynamic Geometry Software (DGS) and Computer Algebra Systems (CAS) in teaching Mathematics. This was conducted in Zamboanga del Sur National High School (ZSNHS) during the third grading period of the school year 2015-2016. The study compared the achievement and attitude towards Mathematics between (...) those students taught with DGS and CAS and those students who were taught without DGS and CAS. A quasi-experimental pretest-posttest control group design was used with two groups which was matched according to their mathematical level. An achievement test was developed and administered to assess the students’ achievement in Mathematics. Aiken’s attitude scale was also used to assess the students’ attitude towards Mathematics. The data were treated with One-Way Analysis of Covariance (ANCOVA) and t-test at 0.05 level of significance. The study revealed a significant difference between the mathematics achievement between students taught with DGS and CAS and those who were taught without it. The integration of DGS and CAS in Mathematics lessons leads to better academic achievement result compared with that of the conventional method of teaching. Moreover, there was no significant difference on the attitude level of the students between the two groups. (shrink)

We propose an axiomatic approach to constructing the dynamics of systems, in which one the main elements 9e8 is the consciousness of a subject. The main axiom is the statements that the state of consciousness is completely determined by the results of measurements performed on it. In case of economic systems we propose to consider an offer of transaction as a fundamental measurement. Transactions with delayed choice, discussed in this paper, represent a logical generalization of incomplete transactions and allow for (...) a more rigorous approach to studying the properties of the algebra of economic measurements. Considering the behavior of an object as a sequence of actions and choices allows extending the obtained results to random systems, which include the subject's consciousness as one of its elements. The specifics, on which the description of fundamental measurements is based, allows easily transferring the formalism of Schwinger's theory of selective measurements (and the consequent quantum-mechanical formalism) to the economic and social systems. (shrink)

A computational theory of consciousness should include a quantitative measure of consciousness, or MoC, that (i) would reveal to what extent a given system is conscious, (ii) would make it possible to compare not only different systems, but also the same system at different times, and (iii) would be graded, because so is consciousness. However, unless its design is properly constrained, such an MoC gives rise to what we call the boundary problem: an MoC that labels a (...) class='Hi'>system as conscious will do so for some – perhaps most – of its subsystems, as well as for irrelevantly extended systems (e.g., the original system augmented with physical appendages that contribute nothing to the properties supposedly supporting consciousness), and for aggregates of individually conscious systems (e.g., groups of people). This problem suggests that the properties that are being measured are epiphenomenal to consciousness, or else it implies a bizarre proliferation of minds. We propose that a solution to the boundary problem can be found by identifying properties that are intrinsic or systemic: properties that clearly differentiate between systems whose existence is a matter of fact, as opposed to those whose existence is a matter of interpretation (in the eye of the beholder). We argue that if a putative MoC can be shown to be systemic, this ipso facto resolves any associated boundary issues. As test cases, we analyze two recent theories of consciousness in light of our definitions: the Integrated Information Theory and the Geometric Theory of consciousness. (shrink)

Real-world economies are open-ended dynamic systems consisting of heterogeneous interacting participants. Human participants are decision-makers who strategically take into account the past actions and potential future actions of other participants. All participants are forced to be locally constructive, meaning their actions at any given time must be based on their local states; and participant actions at any given time affect future local states. Taken together, these essential properties imply real-world economies are locally-constructive sequential games. This paper discusses a modeling approach, (...) Agent-based Computational Economics, that permits researchers to study economic systems from this point of view. ACE modeling principles and objectives are first concisely presented and explained. The remainder of the paper then highlights challenging issues and edgier explorations that ACE researchers are currently pursuing. (shrink)

In recent decades, plural logic has established itself as a well-respected member of the extensions of first-order classical logic. In the present paper, I draw attention to the fact that among the examples that are commonly given in order to motivate the need for this new logical system, there are some in which the elements of the plurality in question are internally singularized (e.g. ‘Whitehead and Russell wrote Principia Mathematica’), while in others they are not (e.g. ‘Some philosophers wrote (...) Principia Mathematica’). Then, building on previous work, I point to a subsystem of plural logic in which inferences concerning examples of the first type can be adequately dealt with. I notice that such a subsystem (here called ‘discrete plural logic’) is in reality a mere variant of first-order logic as standardly formulated, and highlight the fact that it is axiomatizable while full plural logic is not. Finally, I urge that greater attention be paid to discrete plural logic and that discrete plurals are not used in order to motivate the introduction of full-fledged plural logic—or, at least, not without remarking that they can also be adequately dealt with in a considerably simpler system. (shrink)