Since the 1980s chaos has been the subject of great interest both in scientific research and in public consciousness. Chaos as played roles in books and movies such as Jurassic Park and Bellwether and has been the subject of numerous popularizations. But what is chaos—better characterized as chaotic dynamics—really? How much of an impact does it have on everyday life? This book explores these questions and more, introducing you to the basics of chaos as mathematicians and scientists study it (...) and apply it. There are a lot of buzzwords surrounding chaotic dynamics such as “butterfly effect” and “strange attractors,” and much discussion about whether chaos has shattered scientific dreams of a predictable world. This book will help you understand these buzzwords and their excitement, what limitations there are for predictability, and the wisdom scientists have learned from studying chaos. You will come away with a deeper appreciation of the intricacy and surprising order of our world. (shrink)

Climatology is a paradigmatic complex systems science. Understanding the global climate involves tackling problems in physics, chemistry, economics, and many other disciplines. I argue that complex systems like the global climate are characterized by certain dynamical features that explain how those systems change over time. A complex system's dynamics are shaped by the interaction of many different components operating at many different temporal and spatial scales. Examining the multidisciplinary and holistic methods of climatology can help us better understand the nature (...) of complex systems in general. -/- Questions surrounding climate science can be divided into three rough categories: foundational, methodological, and evaluative questions. "How do we know that we can trust science?" is a paradigmatic foundational question (and a surprisingly difficult one to answer). Because the global climate is so complex, questions like "what makes a system complex?" also fall into this category. There are a number of existing definitions of `complexity,' and while all of them capture some aspects of what makes intuitively complex systems distinctive, none is entirely satisfactory. Most existing accounts of complexity have been developed to work with information-theoretic objects (signals, for instance) rather than the physical and social systems studied by scientists. -/- Dynamical complexity, a concept articulated in detail in the first third of the dissertation, is designed to bridge the gap between the mathematics of contemporary complexity theory (in particular the formalism of "effective complexity" developed by Gell-Mann and Lloyd [2003]) and a more general account of the structure of science generally. Dynamical complexity provides a physical interpretation of the formal tools of mathematical complexity theory, and thus can be used as a framework for thinking about general problems in the philosophy of science, including theories, explanation, and lawhood. -/- Methodological questions include questions about how climate science constructs its models, on what basis we trust those models, and how we might improve those models. In order to answer questions about climate modeling, it's important to understand what climate models look like and how they are constructed. Climate model families are significantly more diverse than are the model families of most other sciences (even sciences that study other complex systems). Existing climate models range from basic models that can be solved on paper to staggeringly complicated models that can only be analyzed using the most advanced supercomputers in the world. I introduce some of the central concepts in climatology by demonstrating how one of the most basic climate models might be constructed. I begin with the assumption that the Earth is a simple featureless blackbody which receives energy from the sun and releases it into space, and show how to model that assumption formally. I then gradually add other factors (e.g. albedo and the greenhouse effect) to the model, and show how each addition brings the model's prediction closer to agreement with observation. After constructing this basic model, I describe the so-called "complexity hierarchy" of the rest of climate models, and argue that the sense of "complexity" used in the climate modeling community is related to dynamical complexity. -/- With a clear understanding of the basics of climate modeling in hand, I then argue that foundational issues discussed early in the dissertation suggest that computation plays an irrevocably central role in climate modeling. "Science by simulation" is essential given the complexity of the global climate, but features of the climate system--the presence of non-linearities, feedback loops, and chaotic dynamics--put principled limits on the effectiveness of computational models. This tension is at the root of the staggering pluralism of the climate model hierarchy, and suggests that such pluralism is here to stay, rather than an artifact of our ignorance. Rather than attempting to converge on a single "best fit" climate model, we ought to embrace the diversity of climate models, and view each as a specialized tool designed to predict and explain a rather narrow range of phenomena. Understanding the climate system as a whole requires examining a number of different models, and correlating their outputs. This is the most significant methodological challenge of climatology. -/- Climatology's role contemporary political discourse raises an unusually high number of evaluative questions for a physical science. The two leading approaches to crafting policy surrounding climate change center on mitigation (i.e. stopping the changes from occurring) and adaptation (making post hoc changes to ameliorate the harm caused by those changes). Crafting an effective socio-political response to the threat of anthropogenic climate change, however, requires us to integrate multiple perspectives and values: the proper response will be just as diverse and pluralistic as the climate models themselves, and will incorporate aspects of both approaches. I conclude by offering some concrete recommendations about how to integrate this value pluralism into our socio-political decision making framework. (shrink)

Recent years, active suspension system has been widely used in automobiles to improve the road holding ability and the riding comfort. This study presents a new fuzzy model predictive control for a nonlinear quarter car active suspension system. A nonlinear dynamical model of active suspension is established, where the nonlinear dynamical characteristic of the spring and damper are considered. Based on the proposed fuzzy model predictive control method is presented to stabilize the displacement of the active suspension (...) in the presence of different road profiles. Parameters of the model predictive and fuzzy logic control laws are designed to estimate the (Bump and Sinusoidal)road profile input in the active suspension. At last, the reliability of the fuzzy model predictive control method is evaluated by the MATLAB simulation tool. Simulation result shows that the fuzzy model predictive control method obtained the satisfactory control performance for the active suspension system. (shrink)

Whether the hands-on experience of creating inventions can promote Students’ interest in pursuing a science, technology, engineering, and mathematics (STEM) career has not been extensively studied. In a quantitative study, we drew on the attitude-behavior-outcome framework to explore the correlates between hands-on making attitude, epistemic curiosities, and career interest. This study targeted students who joined the selection competition for participating in the International Exhibition of Young Inventors (IEYI) in Taiwan. The objective of the invention exhibition is to encourage young students (...) to make innovative projects by applying STEM knowledge and collaborative design. We collected 220 valid data from participants in the 2021 Taiwan IEYI selection competition and conducted a confirmatory factor analysis and structural equation modeling to test the hypotheses. Results indicated that: (1) hands-on making attitude was positively related to two types of epistemic curiosity; (2) interest-type epistemic curiosity (IEC) and deprivation-type epistemic curiosity (DEC) were positively associated with STEM career interest; additionally, DEC had a higher coefficient on STEM career interest than IEC; (3) both types of EC had a mediating role between hands-on making attitude and STEM career interest. It is expected that encouraging students to participate in invention exhibition competitions can raise both types of EC and increase their interest in pursuing STEM careers. (shrink)

A dynamical system is called chaotic if small changes to its initial conditions can create large changes in its behavior. By analogy, we call a dynamical system structurally chaotic if small changes to the equations describing the evolution of the system produce large changes in its behavior. Although there are many definitions of “chaos,” there are few mathematically precise candidate definitions of “structural chaos.” I propose a definition, and I explain two new theorems that show that a set (...) of models is structurally chaotic if it contains a chaotic function. I conclude by discussing the relationship between structural chaos and structural stability. (shrink)

Recently, Rueger and Sharp (1996) and Koperski (1998) have been concerned to show that certain procedural accounts of model confirmation are compromised by non‐linear dynamics. We suggest that the issues raised are better approached by considering whether chaotic data analysis methods allow for reliable inference from data. We provide a framework and an example of this approach.

A model of consciousness and conscious experience is introduced. Starting with a non-Lipschitz Chaotic dynamics of neural activity, we propose that the synaptic transmission between adjacent as well as distant neurons should be regulated in brain dynamics through quantum tunneling. Further, based on various studies of different previous authors, we consider the emergence of very large quantum mechanical system representable by an abstract quantum net entirely based on quantum-like entities having in particular the important feature of expressing self-reference similar (...) to what occurs in consciousness. The properties of such quantum-like mind entities are discussed in detail. A quantum-like model of conscious experience is also discussed. It is shown that such quantum mechanical entities are able to arrange themselves alternatively on the basis of the subject story, memory, and pain-pleasure in response to an external stimulus, thus giving the subject the possibility to response to the stimulus on the basis of his emotion as well as cognitive state. Finally, we discuss the possible connections between the quantum-like model introduced in this paper and the chaotic behaviors often identified experimentally in studies on brain dynamics. Part I of this article contains: Introduction; 1. Non Lipschitz Terminal Dynamics of Single Neuron Activity; and References; 2. Quantum Mechanical Properties of Neuron Dynamics; and 3. A Quantum Model of Consciousness I. (shrink)

During the last two decades the role of quantitative genetics in evolutionary theory has expanded considerably. Quantitative genetic-based models addressing long term phenotypic evolution, evolution in multiple environments (phenotypic plasticity) and evolution of ontogenies (developmental trajectories) have been proposed. Yet, the mathematical foundations of quantitative genetics were laid with a very different set of problems in mind (mostly the prediction of short term responses to artificial selection), and at a time in which any details of the genetic machinery were virtually (...) unknown. In this paper we discuss what a model is in population biology, and what kind of model we need in order to address the complexities of phenotypic evolution. We review the assumptions of quantitative genetics and its most recent accomplishments, together with the limitations that such assumptions impose on the modelling of some aspects of phenotypic evolution. We also discuss three alternative appr oaches to the theoretical description of evolutionary trajectories (nonlinear dynamics, complexity theory and optimization theory), and their respective advantages and limitations. We conclude by calling for a new theoretical synthesis, including quantitative genetics and not necessarily limited to the other approaches here discussed. (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)

This summary of the original paradigm of the universal science of complexity starts with the discovered exact origin of the stagnating "end" of conventional, unitary science paradigm and development traditionally presented by its own estimates as the only and the best possible kind of scientific knowledge. Using a transparent generalisation of the exact mathematical formalism of arbitrary interaction process, we show that unitary science approach and description, including its imitations of complexity and chaoticity, correspond to artificial and ultimately strong reduction (...) of the natural plurality of unreduced interaction results called realisations to a single, "average" or "exact", realisation. This severe reduction of the natural world dynamics in unitary science underlies all its unsolvable "mysteries" and "paradoxes", persisting "difficult problems", and finally the modern "end" of the progress of just that, actually very special kind of knowledge, whose irreducible limits lead to the modern deep crisis of the global civilisation development. We show then how the rigorously substantiated restoration of the full richness of real-world dynamics within the intrinsically unified knowledge of the universal science of complexity provides not only the causally complete solution to the old and new problems of unitary science but opens practically unlimited possibilities for the new progress of science and civilisation as a result of this crucial extension, which we call complexity revolution. The unreduced analysis of the universal complexity science shows that at the current critical bifurcation point of development, we have only two incompatible possibilities and emerging tendencies, either the dangerously growing degradation within the dominating unitary science and thinking limits (irrespective of purely empirical technology power becoming even dangerous here) or the new golden age of scientific discoveries and civilisation progress with the qualitatively extended approach and results of unreduced complexity science and the new thinking it implies. (shrink)

The presented study introduces a new theoretical model of collapse for social, cultural, or political systems. Based on the current form of quantum anthropology conceptualized by Heidi Ann Russell, further development of this field is provided. The new theoretical model is called the spiral model of collapses, and is suggested to provide an analytical framework for collapses in social, cultural, and political systems. The main conclusions of this study are: 1) The individual crises in the period before a collapse of (...) social, cultural, and political systems form the trajectory of a conical helix similar to a vortex. 2) The occurrences of crises in the period before a collapse have the shape of the trajectory on the surface of the circular cone with a convex wall narrowing up to its peak. The shape of this cone is based on the Fibonacci sequence coiled into the three-dimensional space. 3) The constant circular movement along the trajectory of crises can occur in exceptional situations in the development of social, cultural, and political systems; however, such a state is always temporary. In such cases, the trajectory of the crisis does not follow the Fibonacci sequence, but the shape of a regular helix. Remaining on the trajectory of a regular helix in the long-term is highly improbable for social, cultural, and political systems. 4) The creation of new potentialities after the final collapse of a system is explained by the conception of topological inversion, when the heretofore embodied part of the energy-information field returns to the global, wave-particle energy-information potential. 5) The global, wave-particle energy-information potential is a source of energy-information for future embodiments in the sense of the future collapses of wave functions. (shrink)

Instead of postulated fixed structures and abstract principles of usual positivistic science, the unreduced diversity of living world reality is consistently derived as dynamically emerging results of unreduced interaction process development, starting from its simplest configuration of two coupled homogeneous protofields. The dynamically multivalued, or complex and intrinsically chaotic, nature of these real interaction results extends dramatically the artificially reduced, dynamically single-valued projection of standard theory and solves its stagnating old and accumulating new problems, “mysteries” and “paradoxes” within the (...) unified and causally complete picture of intrinsically evolving, dynamically complex reality. The permanently unfolding complexity progress thus revealed is fundamentally unlimited and does not need to stop at the directly observed diversity of usual matter complexity. The exciting, but rigorously substantiated and objectively inevitable prospects of further civilisation complexity development towards its superior levels of genuine sustainability and global Noosphere are outlined, with practically important conclusions for today’s critical problem solution. (shrink)

Can stable regularities be explained without appealing to governing laws or any other modal notion? In this paper, I consider what I will call a ‘Humean system’—a generic dynamical system without guiding laws—and assess whether it could display stable regularities. First, I present what can be interpreted as an account of the rise of stable regularities, following from Strevens [2003], which has been applied to explain the patterns of complex systems (such as those from meteorology and statistical mechanics). Second, since (...) this account presupposes that the underlying dynamics displays deterministic chaos, I assess whether it can be adapted to cases where the underlying dynamics is not chaotic but truly random—that is, cases where there is no dynamics guiding the time evolution of the system. If this is so, the resulting stable, apparently non-accidental regularities are the fruit of what can be called statistical necessity rather than of a primitive physical necessity. (shrink)

Can we conceive of disorder in a positive sense? We organize our desks, we discipline our children, we govern our polities--all with the aim of reducing disorder, of temporarily reversing the entropy that inevitably asserts itself in our lives. Going all the way back to Hesiod, we see chaos as a cosmogonic state of utter confusion inevitably reigned in by laws of regularity, in a transition from fearful unpredictability to calm stability. In contrast to a similar early Chinese notion of (...) chaotic disorder (luan), early Daoists posit a type of chaos that is to be cultivated rather than feared. This chaos is a primal disorder, akin to Hesiod's, but rather than threatening disruption, it is replete with creative potential and through spontaneous action yields orderly processes that proceed from the concretion of things to their dissolution and back, in a complex web of relations. This processional activity, although taken in one sense as cosmogonic, in a more important sense is immanent at every moment of activity. This article identifies terms of chaos, such as dun dun 沌 沌, hundun 渾 沌, and xingming 涬 溟 in Laozi and Zhuangzi and examines the passages in which they occur. Analyzing these passages brings us to a better understanding of "chaos" in a Chinese sense and to a familiarity with related terms in its semantic field, such as xuan 玄 (dark, mysterious), miao 妙 (subtle/profound), wei 微 (minute/inchoate), xiao 小 (small/minute), and pu 樸 (uncarved block). We see that the Daoist ideal is to return to a chaotic inchoateness by melding with the cosmos and there finding a repository of creative potential. This notion of chaos as the inchoate is used a springboard into understanding the origins of Daoist spontaneity. (shrink)

Magnetic levitation system is operated primarily based at the principle of magnetic attraction and repulsion to levitate the passengers and the train. However, magnetic levitation trains are rather nonlinear and open loop unstable which makes it hard to govern. In this paper, investigation, design and control of a nonlinear Maglev train based on NARMA-L2, model reference and predictive controllers. The response of the Maglev train with the proposed controllers for the precise role of a Magnetic levitation machine have (...) been as compared for a step input signal. The simulation consequences prove that the Maglev teach system with NARMA-L2 controller suggests the quality performance in adjusting the precise function of the system and the device improves the experience consolation and street managing criteria. (shrink)

Life expectancy prediction, a pivotal facet of public health and policy formulation, has witnessed remarkable advancements owing to the integration of neural network models and comprehensive datasets. In this research, we present an innovative approach to forecasting life expectancy in diverse countries. Leveraging a neural network architecture, our model was trained on a dataset comprising 22 distinct features, acquired from Kaggle, and encompassing key health indicators, socioeconomic metrics, and cultural attributes. The model demonstrated exceptional predictive accuracy, attaining an impressive 99.27% (...) and an average error of 0.0034, underscoring the potency of deep learning in tackling complex, real-world challenges. Furthermore, our study delved into feature importance analysis, identifying critical determinants such as HIV/AIDS prevalence, income composition of resources, and socioeconomic status that significantly influence life expectancy. These findings provide actionable insights for healthcare policymakers and practitioners, emphasizing the importance of addressing health disparities, promoting economic development, and implementing targeted interventions. This research bridges the gap between data-driven methodologies and global health, offering a robust predictive tool and enriching our understanding of the multifaceted dynamics that shape life expectancy across nations. (shrink)

A commonly deployed signifier to render the political event of a riot intelligible, ‘chaos’ describes an affective condition of disorder and disarray. For some theorists of affect, such a condition of chaotic unpredictability suggests emancipatory potential. Recounting the 2018 May Day / May 1st protests in Paris, that both politicians and media declared to be a riot, this paper argues that to consider the riot as chaotic is to think and feel like a state. Critically interrogating the analytical (...) purchase of ‘chaos’ to describe a riotous assembly of bodies, this paper contends that ‘chaos’ is not only a theoretically impoverished concept to understand such political events, but also that sovereignty mobilizes ‘chaos’ as an affective infrastructure of governance to shore up attachment to the security state. Repudiating the sovereign logic of chaos, this paper presents a first-person encounter with a protest-declared-riot in order to explore the various affects that materialize around such events. Through ethnographic reflection, this paper outlines a series of affects that accompanied the day’s events, such as speculative optimism, fragility, suspicion, fear, boldness, and joy. In so doing, the paper develops an affective approach to theorize relations of political antagonism in the street, arguing that whereas the state weaponizes terror as a form of governance, the rioters weaponize joy as an affective means of resistance. (shrink)

Recently, active suspension system will become important to the vehicle industries because of its advantages in improving road managing and ride comfort. This paper offers the development of mathematical modelling and design of a neural network control approach. The paper will begin with a mathematical model designing primarily based at the parameters of the active suspension system. A nonlinear three by four-way valve-piston hydraulic actuator became advanced which will make the suspension system under the active condition. Then, the model (...) can be analyzed thru MATLAB/Simulink software program. Finally, the NARMA-L2, model reference and predictive controllers are designed for the active suspension system. The results are acquired after designing the simulation of the quarter-car nonlinear active suspension system. From the simulation end result using MATLAB/Simulink, the response of the system might be as compared between the nonlinear active suspension system with NARMA-L2, model reference and predictive controllers. Besides that, the evaluation has been made between the proposed controllers thru the characteristics of the manage objectives suspension deflection, body acceleration and body travel of the active suspension system. . As a conclusion, designing a nonlinear active suspension system with a nonlinear hydraulic actuator for quarter car model has improved the car performance by using a NARMA-L2 controller. The improvements in performance will improve road handling and ride comfort performance of the active suspension system. (shrink)

In non‐literal uses of language, the content an utterance communicates differs from its literal truth conditions. Loose talk is one example of non‐literal language use (amongst many others). For example, what a loose utterance of (1) communicates differs from what it literally expresses: (1) Lena arrived at 9 o'clock. Loose talk is interesting (or so I will argue). It has certain distinctive features which raise important questions about the connection between literal and non‐literal language use. This paper aims to (i.) (...) introduce a range of novel data demonstrating certain overlooked features of loose talk, and (ii.) develop a new theory of the phenomenon which accounts for these data. In particular, this theory is motivated by the need to explain minimal pairs such as (2)-(3): (2) Lena arrived at 9 o'clock, but she did not arrive at 9 o'clock exactly. (3) ?? Lena did not arrive at 9 o'clock exactly, but she arrived at 9 o'clock. (2) and (3) agree in their truth conditions. Yet they differ in felicity. As such, they constitute a problem for any account which hopes to predict the acceptability of the loose use of a sentence from its truth conditions and the context of utterance alone. Instead, it will be argued, to explain loose talk phenomena we must posit an additional layer of meaning outstripping truth conditions. This layer of meaning is shown to exhibit a range of properties, all of which point to its being semantically encoded. Thus, if correct, the theory provides a new example of how semantic meaning must extend beyond literal, truth‐conditional content. (shrink)

Do scientific theories limit human knowledge? In other words, are there physical variables hidden by essence forever? We argue for negative answers and illustrate our point on chaotic classical dynamical systems. We emphasize parallels with quantum theory and conclude that the common real numbers are, de facto, the hidden variables of classical physics. Consequently, real numbers should not be considered as ``physically real" and classical mechanics, like quantum physics, is indeterministic.

Neuroscientists have in recent years turned to building models that aim to generate predictions rather than explanations. This “predictive turn” has swept across domains including law, marketing, and neuropsychiatry. Yet the norms of prediction remain undertheorized relative to those of explanation. I examine two styles of predictive modeling and show how they exemplify the normative dynamics at work in prediction. I propose an account of how predictive models, conceived of as technological devices for aiding decision-making, can come to be adequate (...) for purposes that are defined by both their guiding research questions and their larger social context of application. (shrink)

Main principles of the complex nonlinear thinking which are based on the notions of the modern theory of evolution and self-organization of complex systems called also synergetics are under discussion in this article. The principles are transdisciplinary, holistic, and oriented to a human being. The notions of system complexity, nonlinearity of evolution, creative chaos, space-time definiteness of structure-attractors of evolution, resonant influences, nonlinear and soft management are here of great importance. In this connection, a prominent contribution made to (...) system analysis and to a necessary reform of education and thinking by Edgar Morin is considered. (shrink)

Abstract: This study introduces a machine learning-based model for predicting student performance using a comprehensive dataset derived from educational sources, encompassing 15 key features and comprising 62,631 student samples. Our five-layer neural network demonstrated remarkable performance, achieving an accuracy of 89.14% and an average error of 0.000715, underscoring its effectiveness in predicting student outcomes. Crucially, this research identifies pivotal determinants of student success, including factors such as socio-economic background, prior academic history, study habits, and attendance patterns, shedding light on the (...) nuanced dynamics of student performance. The key influential features identified in this study offer valuable insights into the complex factors shaping student achievement. These insights are vital for educators, policymakers, and institutions seeking to enhance educational outcomes and promote equitable access to quality education. This research provides a data-driven foundation for proactive interventions, personalized learning strategies, and support systems, ultimately contributing to improved student performance and academic success. The high accuracy of the predictive model and the feature analysis it provides empower decision-makers in the education sector. This model holds significant potential for applications in student performance monitoring, early intervention, and tailored educational strategies. By adopting a data-driven approach, this work advances the field of educational analytics and contributes to the goal of fostering student success and educational equity. (shrink)

This chapter explores to what extent some core ideas of predictive processing can be applied to the phenomenology of time consciousness. The focus is on the experienced continuity of consciously perceived, temporally extended phenomena (such as enduring processes and successions of events). The main claim is that the hierarchy of representations posited by hierarchical predictive processing models can contribute to a deepened understanding of the continuity of consciousness. Computationally, such models show that sequences of events can be represented as states (...) of a hierarchy of dynamical systems. Phenomenologically, they suggest a more fine-grained analysis of the perceptual contents of the specious present, in terms of a hierarchy of temporal wholes. Visual perception of static scenes not only contains perceived objects and regions but also spatial gist; similarly, auditory perception of temporal sequences, such as melodies, involves not only perceiving individual notes but also slightly more abstract features (temporal gist), which have longer temporal durations (e.g., emotional character or rhythm). Further investigations into these elusive contents of conscious perception may be facilitated by findings regarding its neural underpinnings. Predictive processing models suggest that sensorimotor areas may influence these contents. (shrink)

It is usual to identify initial conditions of classical dynamical systems with mathematical real numbers. However, almost all real numbers contain an infinite amount of information. I argue that a finite volume of space can’t contain more than a finite amount of information, hence that the mathematical real numbers are not physically relevant. Moreover, a better terminology for the so-called real numbers is “random numbers”, as their series of bits are truly random. I propose an alternative classical mechanics, which is (...) empirically equivalent to classical mechanics, but uses only finite-information numbers. This alternative classical mechanics is non-deterministic, despite the use of deterministic equations, in a way similar to quantum theory. Interestingly, both alternative classical mechanics and quantum theories can be supplemented by additional variables in such a way that the supplemented theory is deterministic. Most physicists straightforwardly supplement classical theory with real numbers to which they attribute physical existence, while most physicists reject Bohmian mechanics as supplemented quantum theory, arguing that Bohmian positions have no physical reality. (shrink)

When dissimilar images are presented to the two eyes, binocular rivalry (BR) occurs, and perception alternates spontaneously between the images. Although neural correlates of the oscillating perception during BR have been found in multiple sites along the visual pathway, the source of BR dynamics is unclear. Psychophysical and modeling studies suggest that both low- and high-level cortical processes underlie BR dynamics. Previous neuroimaging studies have demonstrated the involvement of high-level regions by showing that frontal and parietal cortices responded time locked (...) to spontaneous perceptual alternation in BR. However, a potential contribution of early visual areas to BR dynamics has been overlooked, because these areas also responded to the physical stimulus alternation mimicking BR. In the present study, instead of focusing on activity during perceptual switches, we highlighted brain activity during suppression periods to investigate a potential link between activity in human early visual areas and BR dynamics. We used a strong interocular suppression paradigm called continuous flash suppression to suppress and fluctuate the visibility of a probe stimulus and measured retinotopic responses to the onset of the invisible probe using functional MRI. There were ∼130-fold differences in the median suppression durations across 12 subjects. The individual differences in suppression durations could be predicted by the amplitudes of the retinotopic activity in extrastriate visual areas (V3 and V4v) evoked by the invisible probe. Weaker responses were associated with longer suppression durations. These results demonstrate that retinotopic representations in early visual areas play a role in the dynamics of perceptual alternations during BR. (shrink)

It is usual to identify initial conditions of classical dynamical systems with mathematical real numbers. However, almost all real numbers contain an infinite amount of information. I argue that a finite volume of space can’t contain more than a finite amount of information, hence that the mathematical real numbers are not physically relevant. Moreover, a better terminology for the so-called real numbers is “random numbers”, as their series of bits are truly random. I propose an alternative classical mechanics, which is (...) empirically equivalent to classical mechanics, but uses only finite-information numbers. This alternative classical mechanics is non-deterministic, despite the use of deterministic equations, in a way similar to quantum theory. Interestingly, both alternative classical mechanics and quantum theories can be supplemented by additional variables in such a way that the supplemented theory is deterministic. Most physicists straightforwardly supplement classical theory with real numbers to which they attribute physical existence, while most physicists reject Bohmian mechanics as supplemented quantum theory, arguing that Bohmian positions have no physical reality. (shrink)

Experts in Artificial Intelligence (AI) development predict that advances in the dvelopment of intelligent systems and agents will reshape vital areas in our society. Nevertheless, if such an advance isn't done with prudence, it can result in negative outcomes for humanity. For this reason, several researchers in the area are trying to develop a robust, beneficial, and safe concept of artificial intelligence. Currently, several of the open problems in the field of AI research arise from the difficulty of avoiding unwanted (...) behaviors of intelligent agents, and at the same time specifying what we want such systems to do. It is of utmost importance that artificial intelligent agents have their values aligned with human values, given the fact that we cannot expect an AI to develop our moral preferences simply because of its intelligence, as discussed in the Orthogonality Thesis. Perhaps this difficulty comes from the way we are addressing the problem of expressing objectives, values, and ends, using representational cognitive methods. A solution to this problem would be the dynamic cognitive approach proposed by Dreyfus, whose phenomenological philosophy defends that the human experience of being-in-the-world cannot be represented by the symbolic or connectionist cognitive methods. A possible approach to this problem would be to use theoretical models such as SED (situated embodied dynamics) to address the values learning problem in AI. (shrink)

In this paper, I consider how, given mutual knowledge of the information codified in a compositional semantic theory, an assertion of a sentence serves to update the shared information in a conversation. There is a standard account, due to Stalnaker, of how such conversational updating occurs. While this account has much to recommend it, in this paper I argue that it needs to be revised in light of certain patterns of updating that result from certain natural discourses. Having argued for (...) this, I present a new account of conversational updating that can be seen as a natural generalization of the standard account, and show how it can predict these patterns in a simple and principled manner. (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)

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.

A review of James Glieck's _Chaos: Making a New Science_, noting how nonmonotonic functions self-referentially take on their own values and lead to complexity without randomness.

The purpose of this paper is to open for investigation a range of phenomena familiar from dynamical systems or chaos theory which appear in a simple fuzzy logic with the introduction of self-reference. Within that logic, self-referential sentences exhibit properties of fixed point attractors, fixed point repellers, and full chaos on the [0, 1] interval. Strange attractors and fractals appear in two dimensions in the graphing of pairs of mutually referential sentences and appear in three dimensions in the graphing of (...) mutually referential triples. (shrink)

We introduce the notion of complexity, first at an intuitive level and then in relatively more concrete terms, explaining the various characteristic features of complex systems with examples. There exists a vast literature on complexity, and our exposition is intended to be an elementary introduction, meant for a broad audience. -/- Briefly, a complex system is one whose description involves a hierarchy of levels, where each level is made of a large number of components interacting among themselves. The time evolution (...) of such a system is of a complex nature, depending on the interactions among subsystems in the next level below the one under consideration and, at the same time, conditioned by the level above, where the latter sets the context for the evolution. Generally speaking, the interactions among the constituents of the various levels lead to a dynamics characterized by numerous characteristic scales, each level having its own set of scales. What is more, a level commonly exhibits ‘emergent properties’ that cannot be derived from considerations relating to its component systems taken in isolation or to those in a different contextual setting. In the dynamic evolution of some particular level, there occurs a self-organized emergence of a higher level and the process is repeated at still higher levels. -/- The interaction and self-organization of the components of a complex system follow the principle commonly expressed by saying that the ‘whole is different from the sum of the parts’. In the case of systems whose behavior can be expressed mathematically in terms of differential equations this means that the interactions are nonlinear in nature. -/- While all of the above features are not universally exhibited by complex systems, these are nevertheless indicative of a broad commonness relative to which individual systems can be described and analyzed. There exist measures of complexity which, once again, are not of universal applicability, being more heuristic than exact. The present state of knowledge and understanding of complex systems is itself an emerging one. Still, a large number of results on various systems can be related to their complex character, making complexity an immensely fertile concept in the study of natural, biological, and social phenomena. -/- All this puts a very definite limitation on the complete description of a complex system as a whole since such a system can be precisely described only contextually, relative to some particular level, where emergent properties rule out an exact description of more than one levels within a common framework. -/- We discuss the implications of these observations in the context of our conception of the so-called noumenal reality that has a mind-independent existence and is perceived by us in the form of the phenomenal reality. The latter is derived from the former by means of our perceptions and interpretations, and our efforts at sorting out and making sense of the bewildering complexity of reality takes the form of incessant processes of inference that lead to theories. Strictly speaking, theories apply to models that are constructed as idealized versions of parts of reality, within which inferences and abstractions can be carried out meaningfully, enabling us to construct the theories. -/- There exists a correspondence between the phenomenal and the noumenal realities in terms of events and their correlations, where these are experienced as the complex behavior of systems or entities of various descriptions. The infinite diversity of behavior of systems in the phenomenal world are explained within specified contexts by theories. The latter are constructs generated in our ceaseless attempts at interpreting the world, and the question arises as to whether these are reflections of `laws of nature' residing in the noumenal world. This is a fundamental concern of scientific realism, within the fold of which there exists a trend towards the assumption that theories express truths about the noumenal reality. We examine this assumption (referred to as a ‘point of view’ in the present essay) closely and indicate that an alternative point of view is also consistent within the broad framework of scientific realism. This is the view that theories are domain-specific and contextual, and that these are arrived at by independent processes of inference and abstractions in the various domains of experience. Theories in contiguous domains of experience dovetail and interpenetrate with one another, and bear the responsibility of correctly explaining our observations within these domains. -/- With accumulating experience, theories get revised and the network of our theories of the world acquires a complex structure, exhibiting a complex evolution. There exists a tendency within the fold of scientific realism of interpreting this complex evolution in rather simple terms, where one assumes (this, again, is a point of view) that theories tend more and more closely to truths about Nature and, what is more, progress towards an all-embracing ‘ultimate theory’ -- a foundational one in respect of all our inquiries into nature. We examine this point of view closely and outline the alternative view -- one broadly consistent with scientific realism -- that there is no ‘ultimate’ law of nature, that theories do not correspond to truths inherent in reality, and that successive revisions in theory do not lead monotonically to some ultimate truth. Instead, the theories generated in succession are incommensurate with each other, testifying to the fact that a theory gives us a perspective view of some part of reality, arrived at contextually. Instead of resembling a monotonically converging series successive theories are analogous to asymptotic series. -/- Before we summarize all the above considerations, we briefly address the issue of the complexity of the {\it human mind} -- one as pervasive as the complexity of Nature at large. The complexity of the mind is related to the complexity of the underlying neuronal organization in the brain, which operates within a larger biological context, its activities being modulated by other physiological systems, notably the one involving a host of chemical messengers. The mind, with no materiality of its own, is nevertheless emergent from the activity of interacting neuronal assemblies in the brain. As in the case of reality at large, there can be no ultimate theory of the mind, from which one can explain and predict the entire spectrum of human behavior, which is an infinitely rich and diverse one. (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.

Recently, Kirchhoff and Kiverstein have argued that the extended consciousness thesis, namely the claim that the material vehicles of consciousness extend beyond our heads, is entirely compatible with, and actually mandated by, a correct interpretation of the predictive processing framework. To do so, they rely on a potent argument in favor of the extended consciousness thesis, namely the Dynamical Entanglement and Unique Temporal Signature (DEUTS) argument. Here, we will critically examine Kirchhoff and Kiverstein’s endeavor, arguing for the following three claims. (...) First, we will claim that Kirchhoff and Kiverstein’s emphasis on culture and cultural practices does not help them substantiate the extended consciousness thesis. Secondly, we will argue that the way in which Kirchhoff and Kiverstein formalize the boundaries of a subject’s conscious mind is inadequate, as it yields conclusions running counter some of their assumptions. Lastly, we will argue that the DEUTS argument does not establish the extended consciousness thesis, as it licenses a phenomenal bloat objection which is exactly analogous to the “cognitive bloat” objection to the extended mind thesis. We will thus conclude that Kirchhoff and Kiverstein’s proposed marriage between the extended consciousness thesis and predictive processing fails, and that, contrary to a popular opinion, DEUTS is not a strong argument in favor of the extended consciousness thesis. (shrink)

Abstract: This research delves into the utilization of Artificial Neural Networks (ANNs) as a powerful tool for predicting the overall ratings of books by leveraging a diverse set of attributes. To achieve this, we employ a comprehensive dataset sourced from Goodreads, enabling us to thoroughly examine the intricate connections between the different attributes of books and the ratings they receive from readers. In our investigation, we meticulously scrutinize how attributes such as genre, author, page count, publication year, and reader reviews (...) influence a book's overall rating. Through rigorous analysis and experimentation, we construct an advanced ANN model tailored for predictive analysis in the realm of book ratings. The outcomes of our study reveal the remarkable potential of ANNs in this domain. The ANN model exhibits an impressive level of accuracy when it comes to forecasting book ratings, underlining the efficacy and promise of artificial neural networks in enhancing our understanding and prediction of book evaluations. This research opens up new avenues for leveraging machine learning techniques to gain deeper insights into the dynamics of book ratings and reader preferences. (shrink)

The standing tradition in theorizing about meaning, since at least Frege, identifies meaning with propositions, which are, or determine, the truth-conditions of a sentence in a context. But a recent trend has advocated a departure from this tradition: in particular, it has been argued that modal claims do not express standard propositional contents. This non-propositionalism has received different implementations in expressivist semantics and certain kinds of dynamic semantics. They maintain that the key aspect of interpretation of modal claims is the (...) characteristic dynamic effect they have on the context. I argue that pessimism about truth-conditions arises from an overly simplistic picture of content, context and their interaction. While I agree with the critics that an important aspect of modal meaning is the dynamic effect modals have on the context, I argue that they have mischaracterized the nature and the complexity of this effect. A more nuanced account of the interaction between modals and context shows that far from being incompatible with propositional meaning, the dynamic aspect of meaning is precisely what allows us to predict the correct propositional content of an utterance. (shrink)

A recent surge of work on prediction-driven processing models--based on Bayesian inference and representation-heavy models--suggests that the material basis of conscious experience is inferentially secluded and neurocentrically brain bound. This paper develops an alternative account based on the free energy principle. It is argued that the free energy principle provides the right basic tools for understanding the anticipatory dynamics of the brain within a larger brain-body-environment dynamic, viewing the material basis of some conscious experiences as extensive--relational and thoroughly world-involving.

When does opinion formation within an interacting group lead to consensus, polarization or fragmentation? The article investigates various models for the dynamics of continuous opinions by analytical methods as well as by computer simulations. Section 2 develops within a unified framework the classical model of consensus formation, the variant of this model due to Friedkin and Johnsen, a time-dependent version and a nonlinear version with bounded confidence of the agents. Section 3 presents for all these models major analytical results. (...) Section 4 gives an extensive exploration of the nonlinear model with bounded confidence by a series of computer simulations. An appendix supplies needed mathematical definitions, tools, and theorems. (shrink)

Determinism and unpredictability are compatible since deterministic flows can produce, if sensitive to initial conditions, unpredictable behaviors. Within this perspective, the notion of scenario to chaos transition offers a new form of predictability for the behavior of sensitive to initial condition systems under the variation of a control parameter. In this paper I first shed light on the genesis of this notion, based on a dynamical systems approach and on considerations of structural stability. I then suggest a link to (...) the figure of epigenetic landscape, partially inspired by a dynamical systems perspective, and offering a theoretical framework to apprehend developmental noise. (shrink)

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)

The mainstream view of meaning is that it is emergent, not fundamental, but some have disputed this, asserting that there is a more fundamental level of reality than that addressed by current physical theories, and that matter and meaning are in some way entangled. In this regard there are intriguing parallels between the quantum and biological domains, suggesting that there may be a more fundamental level underlying both. I argue that the organisation of this fundamental level is already to a (...) considerable extent understood by biosemioticians, who have fruitfully integrated Peirce’s sign theory into biology; things will happen there resembling what happens with familiar life, but the agencies involved will differ in ways reflecting their fundamentality, in other words they will be less complex, but still have structures complex enough for what they have to do. According to one approach involving a collaboration with which I have been involved, a part of what they have to do, along with the need to survive and reproduce, is to stop situations becoming too chaotic, a concept that accords with familiar ‘edge of chaos’ ideas. Such an extension of sign theory (semiophysics?) needs to be explored by physicists, possible tools being computational models, existing insights into complexity, and dynamical systems theory. Such a theory will not be mathematical in the same way that conventional physics theories are mathematical: rather than being foundational, mathematics will be ‘something that life does’, something that sufficiently evolved life does because in the appropriate context so doing is of value to life. (shrink)

A standard way to challenge convergence-based accounts of inductive success is to claim that they are too weak to constrain inductive inferences in the short run. We respond to such a challenge by answering some questions raised by Juhl (1994). When it comes to predicting limiting relative frequencies in the framework of Reichenbach, we show that speed-optimal convergence—a long-run success condition—induces dynamic coherence in the short run.

Protein α-helices provide an ordered biological environment that is conducive to soliton-assisted energy transport. The nonlinear interaction between amide I excitons and phonon deformations induced in the hydrogen-bonded lattice of peptide groups leads to self-trapping of the amide I energy, thereby creating a localized quasiparticle (soliton) that persists at zero temperature. The presence of thermal noise, however, could destabilize the protein soliton and dissipate its energy within a finite lifetime. In this work, we have computationally solved the system of (...) stochastic differential equations that govern the quantum dynamics of protein solitons at physiological temperature, T=310 K, for either a single isolated α-helix spine of hydrogen bonded peptide groups or the full protein α-helix comprised of three parallel α-helix spines. The simulated stochastic dynamics revealed that although the thermal noise is detrimental for the single isolated α-helix spine, the cooperative action of three amide I exciton quanta in the full protein α-helix ensures soliton lifetime of over 30 ps, during which the amide I energy could be transported along the entire extent of an 18-nm-long α-helix. Thus, macromolecular protein complexes, which are built up of protein α-helices could harness soliton-assisted energy transport at physiological temperature. Because the hydrolysis of a single adenosine triphosphate molecule is able to initiate three amide I exciton quanta, it is feasible that multiquantal protein solitons subserve a variety of specialized physiological functions in living systems. (shrink)

Philosophy of science has witnessed substantial recent debate over the existence of a structural analogue of chaos, which is alleged to spell trouble for certain uses of climate models. The debate over the analogy can and should be separated from its alleged epistemic implications: chaos-like behavior is neither necessary nor sufficient for small dynamical misrepresentations to generate erroneous results. The kind of sensitivity that matters in epistemology is one that induces unsafe beliefs, and the existence of a structural analogue to (...) chaos is better seen as an explanation for known safety failures than as providing evidence for unknown ones. (shrink)

The file on this site provides the slides for a lecture given in Hangzhou in May 2018, and the lecture itself is available at the URL beginning 'sms' in the set of links provided in connection with this item. -/- It is commonly assumed that regular physics underpins biology. Here it is proposed, in a synthesis of ideas by various authors, that in reality structures and mechanisms of a biological character underpin the world studied by physicists, in principle supplying detail (...) in the domain that according to regular physics is of an indeterminate character. In regular physics mathematical equations are primary, but this constraint leads to problems with reconciling theory and reality. Biology on the other hand typically does not characterise nature in quantitative terms, instead investigating in detail important complex interrelationships between parts, leading to an understanding of the systems concerned that is in some respects beyond that which prevails in regular physics. It makes contact with quantum physics in various ways, for example in that both involve interactions between observer and observed, an insight that explains what is special about processes involving observation, justifying in the quantum physics context the replacement of the unphysical many-worlds picture by one involving collapse. The link with biology furthermore clarifies Wheeler’s suggestion that a multiplicity of observations can lead to the ‘fabrication of form’, including the insight that this process depends on very specific ‘structures with power’ related to the 'semiotic scaffolding' of the application of sign theory to biology known as biosemiotics. -/- The observer-observed 'circle' of Wheeler and Yardley is a special case of a more general phenomenon, oppositional dynamics, related to the 'intra-action' of Barad's Agential Realism, involving cooperating systems such as mind and matter, abstract and concrete, observer and observed, that preserve their identities while interacting with one another in such a way as to act as a unit. A third system may also be involved, the mediating system of Peirce linking the two together. Such a situation of changing connections and separations may plausibly lead in the future to an understanding of how complex systems are able to evolve to produce 'life, the universe and everything'. -/- (Added 1 July 2018) The general structure proposed here as an alternative to a mathematics-based physics can be usefully characterised by relating it to different disciplines and the specialised concepts utilised therein. In theoretical physics, the test for the correctness of a theory typically involves numerical predictions, corresponding to which theories are expressed in terms of equations, that is to say assertions that two quantities have identical values. Equations have a lesser significance in biology which typically talks in terms of functional mechanisms, dependent for example on details of chemistry and concepts such as genes, natural selection, signals and geometrical or topologically motivated concepts such as the interconnections between systems and the unfolding of DNA. Biosemiotics adds to this the concept of signs and their interpretation, implying novel concepts such as semiotic scaffolding and the semiosphere, code duality, and appreciation of the different types of signs, including symbols and their capacity for abstraction and use in language systems. Circular Theory adds to this picture, as do the ideas of Barad, considerations such as the idea of oppositional dynamics. The proposals in this lecture can be regarded as the idea that concepts such as those deriving from biosemiotics have more general applicability than just conventional biology and may apply, in some circumstances, to nonlinear systems generally, including the domain new to science hypothesised to underlie the phenomena of present-day physics. -/- The task then has to be to restore the mathematical aspect presumed, in this picture, not to be fundamental as it is in conventional theory. Deacon has invoked a complex sequence of evolutionary steps to account for the emergence over time of human language systems, and correspondingly mathematical behaviour can be subsumed under the general evolutionary mechanisms of biosemiotics (cf. also the proposals of Davis and Hersh regarding the nature of mathematics), so that the mathematical behaviour of physical systems is consistent with the proposed scheme. In conclusion, it is suggested that theoretical physicists should cease expecting to find some universal mathematical ‘theory of everything’, and focus instead on understanding in more detail complex systems exhibiting behaviour of a biological character, extending existing understanding. This may in time provide a more fruitful understanding of the natural world than does the regular approach. The essential concepts have an observational basis from both biology and the little-known discipline of cymatics (a discipline concerned with the remarkable patterns that specific waveforms can give rise to), while again computer simulations also offer promise in providing insight into the complex behaviours involved in the above proposals. -/- References -/- Jesper Hoffmeyer, Semiotic Scaffolding of Living Systems. Commens, a Digital Companion to C. S. Peirce (on Commens web site). Terrence Deacon, The Symbolic Species, W.W. Norton & Co. Karen Barad, Meeting the Universe Halfway: Quantum Physics and the Entanglement of Matter and Meaning, Duke University Press. Philip Davis and Reuben Hersh, The Mathematical Experience, Penguin. Ilexa Yardley, Circular Theory. (shrink)

Recent theory suggests that action prediction relies of a motor emulation mechanism that works by mapping observed actions onto the observer action system so that predictions can be generated using that same predictive mechanisms that underlie action control. This suggests that action prediction may be more accurate when there is a more direct mapping between the stimulus and the observer. We tested this hypothesis by comparing prediction accuracy for two stimulus types. A mannequin stimulus which contained information about the effectors (...) used to produce the action and a point stimulus, which contained identical dynamic information but no effector information. Prediction was more accurate for the mannequin stimulus. However, this effect was dependent on the observer having previous experience performing the observed action. This suggests that experienced and na¨ıve observers might generate predictions in qualitatively difference ways, which may relate to the presence of an internal representation of the action laid down through action performance. (shrink)