Complex systems research is becoming ever more important in both the natural and social sciences. It is commonly implied that there is such a thing as a complex system, different examples of which are studied across many disciplines. However, there is no concise definition of a complex system, let alone a definition on which all scientists agree. We review various attempts to characterize a complex system, and consider a core set of features that are widely (...) associated with complex systems in the literature and by those in the field. We argue that some of these features are neither necessary nor sufficient for complexity, and that some of them are too vague or confused to be of any analytical use. In order to bring mathematical rigour to the issue we then review some standard measures of complexity from the scientific literature, and offer a taxonomy for them, before arguing that the one that best captures the qualitative notion of the order produced by complex systems is that of the Statistical Complexity. Finally, we offer our own list of necessary conditions as a characterization of complexity. These conditions are qualitative and may not be jointly sufficient for complexity. We close with some suggestions for future work. (shrink)

The complex systems approach (CSA) to characterizing cognitive function is purported to underlie a conceptual and methodological revolution by its proponents. I examine one central claim from each of the contributed papers and argue that the provided examples do not justify calls for radical change in how we do cognitive science. Instead, I note how currently available approaches in ‘‘standard’’ cognitive science are adequate (or even more appropriate) for understanding the CSA provided examples.

In the philosophy of science, increasing attention has been given to the methodological novelties associated with the study of complex systems. However, there is little agreement on exactly what complex systems are. Although many characterizations of complex systems are available, they tend to be either impressionistic or overly formal. Formal definitions rely primarily on ideas from the study of computational complexity, but the relation between these formal ideas and the messy world of empirical phenomena (...) is unclear. Here, I give a definition of complex systems that draws on algorithmic complexity theory, but also provides a way of interpreting the formal idea in an empirical setting. I then use the definition to show that two canonical forms of scientific idealization are empirically inade- quate when applied to complex systems. The inadequacy of these forms of idealization is shown to be the primary reason that complex systems require novel methods. Moreover, this demand for novel methods helps explain the rise of complex systems science as an autonomous discipline. (shrink)

The question of complex systems is relatively new for critics today. Analyzing complex systems in Renaissance texts shows that the Christian kabbalistical concept of harmonia mundi led to an aesthetical development, reflecting the worldview of harmonious parallel worlds. Failure to perceive the esoteric text uniting apparently contradicting themes has often led Renaissance scholars to elaborate a theory of the instability of atmospheres characterizing the English Baroque. This article gives an example of a complex system in (...) Shakespeare's Antony and Cleopatra revealing that the Christian kabbalistical Hercules unifies contradicting metaphors and intertexts of the play, and reintegrates this work in a form of semantic stability more in harmony with the aesthetics of its time.In the case of postmodern literature, contradictory intertexts appear as a device to deconstruct all values and logic previously established. With the study of a text structured by the optical questions around the refraction of light, this paper shows that in the case of Nabokov, the unifying system of apparently contradicting semantic systems is the underlying logic of scientific theory.In Nabokov's text, failing to perceive the fundamental intertext of scientific debate leads one to assimilate Nabokov's writing to a form of postmodern deconstruction. Both cases studied tend to show a continuity of a form of aesthetics through different epistemological eras. (shrink)

Consciousness has been the bone of contention for philosophers throughout centuries. Indian philosophy largely adopted lived experience as the starting point for its explorations of consciousness. For this reason, from the very beginning, experience was an integral way of grasping consciousness, whose validity as a tool was considered self-evident. Thus, in Indian philosophy, the question was not to move from the brain to mind but to understand experience of an individual and how such an experience is determined through mental structures (...) (and secondarily, the preoccupation with the brain and its relation to the mind). In contrast, cognitive science (the study of mind and cognition through 1 interdisciplinary methods, with emphasis on computational methods) found its debates soaked in discussion which primarily involved the brain and mind. Experience was not considered a primary source of information and its validity had to be established to consider it a source of information of mind. With the rise of physicalism and realization that mental states are correlative to brain states, the body was virtually neglected from involvement in understanding the mind and the attempts to reduce mind to the brain were rampant. The inability to explain subjective experience of an individual through neuroscientific findings alone has urged philosophers to explore other ways of understanding the ontology of mind. Over the last few years, embodied cognition and enactive approach have brought back the body as a central participant in this debate, providing fertile grounds to explain the relation of brain, body and mind. This paper proposes that we understand the brain as a complex system from which the mind emerges. This emergence is marked by the development of novel property of self-consciousness in human beings. The mind is a process which is embedded throughout the body and thus, the body acts as an actualizing medium for the individual. Thus, the brain is a necessary condition for the mind to be while the mind is embedded throughout the body. The brain and mind are in reciprocal causal relationship with one another, as is the body and environment with one another. In this paper, embodied cognition is understood through principles of Merleau Ponty's idea of embodiment, than through Andy Clark and Francis Varela's alone. (shrink)

Part I [sections 2–4] draws out the conceptual links between modern conceptions of teleology and their Aristotelian predecessor, briefly outlines the mode of functional analysis employed to explicate teleology, and develops the notion of cybernetic organisation in order to distinguish teleonomic and teleomatic systems. Part II is concerned with arriving at a coherent notion of intentional control. Section 5 argues that intentionality is to be understood in terms of the representational properties of cybernetic systems. Following from this, section (...) 6 argues that intentional control needs to be seen as a particular type of relationship between the system and its environment. (shrink)

Using the concept of adjunction, for the comprehension of the structure of a complex system, developed in Part I, we introduce the notion of covering systems consisting of partially or locally defined adequately understood objects. This notion incorporates the necessary and sufficient conditions for a sheaf theoretical representation of the informational content included in the structure of a complex system in terms of localization systems. Furthermore, it accommodates a formulation of an invariance property of information communication (...) concerning the analysis of a complex system. (shrink)

Despite the close connection between the central limit theorem and renormalization group (RG) methods, the latter should be considered fundamentally distinct from the kind of probabilistic framework associated with statistical mechanics, especially the notion of averaging. The mathematics of RG is grounded in dynamical systems theory rather than probability, which raises important issues with respect to the way RG generates explanations of physical phenomena. I explore these differences and show why RG methods should be considered not just calculational tools (...) but the basis for a physical understanding of complex systems in terms of structural properties and relations. (shrink)

The arts are one of the most complex of human endeavours, and so it is fitting that a special issue on Complex Systems in Aesthetics and Arts is being published. As the editors of this special issue, we would like to thank the reviewers of the submitted papers for their hard work in making this issue possible, as well as the authors who submitted their work and were very responsive to the comments of the reviewers and editors.

Many of the diverse attempts to solve the Hard Problem of Consciousness rely on emergentism. Those who adopt a strong version of emergentism usually argue that consciousness is ontologically irreducible to its underlying physical processes. In contrast, those who adopt a weak version of emergentism usually argue that consciousness is explanatorily irreducible to its underlying physical processes — whether due to epistemic or pragmatic limitations. In this context, the central argument of this paper is that Daniel Dennett’s account of consciousness (...) can be understood as adopting a weak form of emergentism. His Multiple Drafts Model aligns neatly with a nuanced form of weak emergence, grounded both in circumstantial constraints and in the limits of our understanding. Although Dennett spoke rarely and cautiously about emergence, and despite his commitment to qualia-eliminativism (as a consequence of his Heterophenomenology), his account of consciousness nonetheless satisfies the central hallmark of weak emergentism: consciousness is, indeed, a phenomenon irreducible to its subphenomena — but only in practice, not in principle. (shrink)

Ecologist Richard Levins argues population biologists must trade‐off the generality, realism, and precision of their models since biological systems are complex and our limitations are severe. Steven Orzack and Elliott Sober argue that there are cases where these model properties cannot be varied independently of one another. If this is correct, then Levins's thesis that there is a necessary trade‐off between generality, precision, and realism in mathematical models in biology is false. I argue that Orzack and Sober's arguments (...) fail since Levins's thesis concerns the pragmatic features of model building not just the formal properties of models. (shrink)

Containing selected papers on the fundamentals and applications of Complexity Science, this multi-disciplinary book presents new approaches for resolving complex issues that cannot be resolved using conventional mathematical or software models. Complex Systems problems can occur in a variety of areas such as physical sciences and engineering, the economy, the environment, humanities and social and political sciences. Complexity Science problems, the science of open systems consisting of large numbers of diverse components engaged in rich interaction, can (...) occur in a variety of areas such as physical sciences and engineering, the economy, the environment, humanities and social and political sciences. The global behaviour of these systems emerges from the interaction of constituent components and is unpredictable but not random. The key attribute of Complex Systems is the ability to self-organise and adapt to unpredictable changes in their environment. (shrink)

This Special Issue of Journal of Critical Realism (JCR) is dedicated to the 2022 International Association for Critical Realism (IACR) Conference, which was hosted by the International Institute of...

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

This paper introduces the Architecture of Complex Systems (ACS) as an ontological framework for understanding systems as coherent architectures rather than as collections of behaviors or dynamic processes. ACS addresses a foundational question: under what conditions does a system exist as a unified entity at all? The framework is grounded in the primacy of relations over observation and dynamics. Architectural truth is defined as relational and is shown to depend on coherence, closure, and invariants within a bounded (...) relational structure. On this basis, the paper establishes a fundamental boundary: no amount of observational data or knowledge of system dynamics suffices to reconstruct system ontology. Dynamics may describe state transitions and trajectories, but they do not uniquely determine architectural structure. A minimal relational algebra is introduced as a working language for architectural reasoning. This algebra is used to articulate admissibility, coherence, and architectural existence without reference to domain-specific implementations or empirical realizations. Architecture is treated as ontologically prior to both dynamics and observation. The contribution of this work is intentionally foundational. It fixes the ontological core of ACS and situates it within a broader research program concerned with discrete existence and the limits of observation. Domain-specific interpretations and applications are left as subsequent extensions built upon this explicitly defined foundation. (shrink)

So far, the sciences of complexity have received less attention from philosophers than from scientists. Responding to Salthe’s (Found Sci 15, 4(6):357–367, 2010a ) model of evolution, I focus on its metaphysical implications, asking whether the implications of his canonical developmental trajectory (CDT) must be materialistic as his reading proposes.

We develop a category theoretical scheme for the comprehension of the information structure associated with a complex system, in terms of families of partial or local information carriers. The scheme is based on the existence of a categorical adjunction, that provides a theoretical platform for the descriptive analysis of the complex system as a process of functorial information communication.

Regularities in natural language systems, despite their cognitive advantages in terms of storage and learnability, often coexist with exceptions, raising the question of whether and why irregularities survive. We offer a complex system perspective on this issue, focusing on the irregular past tense forms in English. Two separate processes affect the overall regularity: new verbs constantly entering the vocabulary in the regular form at low frequency, and transitions in both directions (from irregular to regular and vice-versa) occurring in (...) a narrow frequency range. The introduction of new verbs leads to an increase in regular types, that, entering at low frequencies, have a small impact on the perceived irregularity in terms of tokens. The frequency of usage acts as a control parameter, the majority of verbs types being fully-regular(irregular) at low(high) frequencies, with no evidence of irregularity facing extinction. Very few verbs types in an intermediate frequency region exhibit both regular and irregular forms at the same time, suggesting that the coexistence is unstable. The observed pattern of usage showing an abrupt change in response to small variations of the control parameter only appears in agent-based models provided that the word state is non-binary. By introducing this key ingredient, high-frequency irregular past-tense can survive the tendency to regularize over time, as observed in natural languages. (shrink)

Nowadays, the development of big data is getting faster and faster, and the related research on motion sensing recognition and complex systems under the background of big data is gradually being valued. At present, there are relatively few related researches on vertical Baduanjin in the academic circles; research in this direction can make further breakthroughs in motion sensor recognition. In order to carry out related action recognition research on the lifting action of vertical Baduanjin, this paper uses sensor (...) technology to collect the motion video image of vertical Baduanjin based on the background of big data and uses action recognition technology and related algorithms to obtain the action. Recognize the video image to obtain the data, get the acceleration, angular velocity, and EMG data, and count the end time and duration according to the change of the action. According to the data table and graph change trend compiled at the end of the experiment, we can see the following: after the data is preprocessed, the acceleration signal change range is limited to [−1, 1], and the acceleration change has a clear directionality; and, after 15 lifts of the detected object, its angular velocity in X-axis direction is basically negative. However, when the ninth lift is performed, the angular velocity of the movement in X-axis direction is 36.09, the largest of all angular velocities. When performing the 15th lifting action, the angular velocity of this action in Z-axis direction is −26.05, which is the smallest of all angular velocities. The longest duration of the left muscle discharge during the lifting action of the subject is 15.24 for the tibial anterior muscle and 8.91 for the external oblique muscle with the shortest duration. The longest discharge duration of the right muscle is also the tibial anterior muscle with 12.15, and the shortest duration is the erector spinae with 8.79. (shrink)

Can we understand important social issues by studying individual personalities and decisions? Or are societies somehow more than the people in them? Sociologists have long believed that psychology can't explain what happens when people work together in complex modern societies. In contrast, most psychologists and economists believe that if we have an accurate theory of how individuals make choices and act on them, we can explain pretty much everything about social life. Social Emergence takes a new approach to these (...) longstanding questions. Sawyer argues that societies are complex dynamical systems, and that the best way to resolve these debates is by developing the concept of emergence, focusing on multiple levels of analysis - individuals, interactions, and groups - and with a dynamic focus on how social group phenomena emerge from communication processes among individual members. This book makes a unique contribution not only to complex systems research but also to social theory. (shrink)

In this article we analyze in a new way the epistemological concept of mythical explanation. It is shown, within the framework of the theory of dynamic and complex systems, that this kind of explanation is grounded on the substitution of distributed causation by lineal and single causes. Considering four examples, we show which mechanism is operating in that substitution. The first one concerns a computational implementation of a racial segregation model. The second one will be the analysis of (...) an imaginary panic. The third one starts with the theory, developed by René Girard, concerning sacrifice rituals and the emergence of scapegoats. Finally, the fourth one is based on the introduction of the imitation mechanism as an explanation for the financial markets behavior. (shrink)

Complexity arises from interaction dynamics, but its forms are co-determined by the operative constraints within which the dynamics are expressed. The basic interaction dynamics underlying complex systems is mostly well understood. The formation and operation of constraints is often not, and oftener under appreciated. The attempt to reduce constraints to basic interaction fails in key cases. The overall aim of this paper is to highlight the key role played by constraints in shaping the field of complex (...) class='Hi'>systems. Following an introduction to constraints, the paper develops the roles of constraints in specifying forms of complexity and illustrates the roles of constraints in formulating the fundamental challenges to understanding posed by complex systems. (shrink)

Complex systems are dynamic and may show high levels of variability in both space and time. It is often difficult to decide on what constitutes a given complex system, i.e., where system boundaries should be set, and what amounts to substantial change within the system. We discuss two central themes: the nature of system definitions and their ability to cope with change, and the importance of system definitions for the mental metamodels that we use to describe and (...) order ideas about system change. Systems can only be considered as single study units if they retain their identity. Previous system definitions have largely ignored the need for both spatial and temporal continuity as essential attributes of identity. After considering the philosophical issues surrounding identity and system definitions, we examine their application to modeling studies. We outline a set of five alternative metamodels that capture a range of the basic dynamics of complex systems. Although Holling’s adaptive cycle is a compelling and widely applicable metamodel that fits many complex systems, there are systems that do not necessarily follow the adaptive cycle. We propose that more careful consideration of system definitions and alternative metamodels for complex systems will lead to greater conceptual clarity in the field and, ultimately, to more rigorous research. (shrink)

The reconstruction of a complex physical system, such as a human brain, from its destroyed state faces fundamental obstacles due to Heisenberg's uncertainty principle and the probabilistic nature of quantum mechanics. This paper presents a thought experiment that circumvents these limitations by replacing direct measurement with a statistical inference process based on antagonistic processing of probable and improbable scenarios, blind observation with syntactic shuffling, and resonance annihilation in feedback cycles. The proposed method suggests that by subjecting a system to (...) maximum noise and comparing results through successive cycles, one can isolate an informational invariant—a residual pattern that resists annihilation—which could, in principle, serve as a blueprint for physical reconstitution via entangled alignment principles. Philosophical implications for identity, consciousness, and the fundamental nature of information as primary reality are discussed. (shrink)

How might we usefully apply concepts and procedures derived from the study of other complex dynamical systems to analyzing systemic change in education? In this article we begin to define possible agendas for research toward developing systematic frameworks and shared terminology for such a project. We illustrate the plausibility of defining such frameworks and raise the question of the relation between such frameworks and the crucial task of aggregating data across ‘systemic experiments’, such as those conducted under the (...) Urban Systemic Initiative sponsored by the US National Science Foundation. Our discussion includes a review of key issues identified by groups of researchers regarding Defining the System, Structural Analysis, Relationships Among Subsystems and Levels, Drivers for Change, and Modeling Methods. (shrink)

Every essay in this book is original, often highly original, and they will be of interest to practising scientists as much as they will be to philosophers of science — not least because many of the essays are by leading scientists who are currently creating the emerging new complex systems paradigm. This is no accident. The impact of complex systems on science is a recent, ongoing and profound revolution. But with a few honourable exceptions, it has (...) largely been ignored by scientists and philosophers alike as an object of reflective study. (shrink)

Complex systems are pervasive in the world around us. Making sense of a complex system should require that a person construct a network of concepts and principles about some domain that represents key (often dynamic) phenomena and their interrelationships. This raises the question of how expert understanding of complex systems differs from novice understanding. In this study we examined individuals' representations of an aquatic system from the perspective of structural (elements of a system), behavioral (mechanisms), (...) and functional aspects of a system. Structure–Behavior–Function (SBF) theory was used as a framework for analysis. The study included participants from middle school children to preservice teachers to aquarium experts. Individual interviews were conducted to elicit participants' mental models of aquaria. Their verbal responses and pictorial representations were analyzed using an SBF‐based coding scheme. The results indicated that representations ranged from focusing on structures with minimal understanding of behaviors and functions to representations that included behaviors and functions. Novices' representations focused on perceptually available, static components of the system, whereas experts integrated structural, functional, and behavioral elements. This study suggests that the SBF framework can be one useful formalism for understanding complex systems. (shrink)

The study of complex systems, although an interdisciplinary endeavor, is considered as an integrating part of physical sciences. Contrary to the historical fact that the field is already mature, it still lacks a clear and unambiguous definition of its main object of study. Here, I propose a definition of complex systems based on the conceptual clarifications made by Edgar Morin about the bidirectional non-separability of parts and whole produced by the nature of interactions. Then, a (...) class='Hi'>complex system is defined as the system where there is a bidirectional non-separability between the identities of the parts and the identity of the whole. Thus, not only the identity of the whole is determined by the constituent parts, but also the identity of the parts are determined by the whole due to the nature of their interactions. This concept allows, as shown in the paper, to derive some of the main properties that such systems must have as well as to propose its mathematical formalization. (shrink)

Complex adaptive systems and nursingThere have been numerous references to complexity theory and complex systems in the recent healthcare literature, including nursing. However, exaggerated claims have (in my view) been made about how they can be applied to health service delivery, and there is a widespread tendency to misunderstand some of the concepts associated with complexity thinking (usually justified by describing the misconception as a metaphor). These conceptscanbe extended to systems and structures in healthcare organisations (...) but, at this stage in the development of complexity science, only in a modest and very cautious way. In this paper I first outline some of the key ideas in the theory of complex adaptive systems, and then suggest that they have been distorted by a series of influential articles in the medical literature. I go on to present a simple case study of my own and undertake a complexity analysis of it. In the conclusion I suggest that we should beware of some outdated ideas being trotted out in the guise of complexity — an exciting and diverse area of enquiry that those old ideas do not, in fact, resemble. (shrink)

The relationship between brain and mind has been extensively explored through the developments within neuroscience over the last decade. However, the ontological status of mind has remained fairly problematic due to the inability to explain all features of the mind through the brain. This inability has been considered largely due to partial knowledge of the brain. It is claimed that once we gain complete knowledge of the brain, all features of the mind would be explained adequately. However, a challenge to (...) such a position is downward causation: How do we explain the causal power that mental states exert over brain activities? If we agree that downward causation occurs, then to what extent could a sole explanation of brain activities account for our behaviour? (For they would in themselves be conditioned by the mental states which are left unexplained). This dissertation is an attempt to understand relation between brain and mind through the concept of emergence, placed in the context of complex systems approach. This will create a space to account for the causal power of mental states. The complex systems approach says that as the complexity of a system increases, we witness the emergence of novel qualities and after a certain threshold (of complexity), the emergence of a novel structure. When the body (and correspondingly, brain) reaches a certain level of complexity, the mind emerges. The brain is a complex system from which the mind emerges. The brain, consisting of billions of neurons interacting with each other, regulates the body placed in the environment. The interaction of neurons (local interactions involving self-organization) result in dynamical brain signatures (global synergy). Such signatures are correlative to mental states. Mind is the process of a living organism embodying an intentional stance. This object could be the subject itself or another distinct from the subject. With the emergence of mind, the causal powers of brain are conditioned by the mind. Such a conditioning is evident through the causal efficacy of mental states. While the brain is minimal condition for the mind to emerge, the mind in itself is embedded (showcased/explicated/manifested) throughout the body. The mind is a process that belongs to body-as-a-whole with the novel quality of intentionality. A preliminary to understanding this relation is its metaphysical inclination. A large portion of the history of philosophy of mind has advocated a metaphysics of entities where the mind and body have been seen as two entities with distinct essences. However, such attribution of entity-ship does not take into account the processual nature of these existents (that they are essentially dependent on their environment for their existence and sustenance). Thus, the category of processual unity has been introduced which sought to account for existent as emergent wholes that move towards a stable equilibrium through self-organization. By considering existents to be processual unities, we can account for their identity as a whole-in-itself (what has been called organizational closure) and also for their processual nature. The brain is a component of the body which is a complex system and is representative of the body’s stance in the world. The brain, consisting of billions of neurons interacting with each other, regulates the body placed in the environment. The interaction of neurons (local interactions involving self-organization) result in dynamical brain signatures (global synergy). Such signatures are correlative to mental states. These mental states in turn condition the brain patterns, that allows the embodying of mental states. Thus, the three-way process of the representation of body in the world by the brain, the emergence of mental state through dynamic brain patterns and the reciprocal causal power on the brain patterns by the mental states marks embodiment. The relation between brain, body and mind can be outlined as follows: A. There are complex interactions in the brain. These interactions are representative of the body’s stance in the world and are present in form of dynamical brain signatures. B. The dynamical brain signatures lead to emergence of mind as a process. The mental state has causal power which conditions the brain. C. The brain conditioned by causal power of the mind carries out embodiment of the mind throughout the body. In the dissertation, an exposition on relation between brain and mind through complex system approach is followed by a brief on relation between body and mind. The radical embodiment approach adopts the nonlinear dynamic systems theory to understand relation of brain, body and mind. It states a shift from mapping of cognitive states onto Neural Correlates of Consciousness to their mapping through dynamic brain signatures. Every mental state is embedded throughout the body. The dissertation explores the three features of consciousness, intentionality and qualia. These have previously formed a challenge within a dualistic framework and the dissertation intends to show a direction in which they can be accounted for, within the complex systems approach and radical embodiment viewpoint. After a certain threshold of the rate of production of cell assemblies is bypassed, we become conscious of the representation itself. This leads to emergence of phenomenal states. Qualia is the qualitative character of such states, which belong to the body-as-a-whole and for this reason, cannot be reduced to properties of any of the components from which it emerges (the dynamic brain signatures) or in which it is embodied (the body and its individual parts) alone. Intentionality is the novel property of mind of moving towards a certain set of attractors where attractors refer to the states that the system prefers (which would positively contribute to its fitness). The scope of this dissertation is to delineate the relation of brain to the mind and unravel some persistent troubles of philosophy of mind within such delineation. The types of components and their relation within the mind preceded by a thorough study of how the mind is embodied is an area yet to be extensively explored in the coming works. (shrink)

We develop a general covariant categorical modeling theory of natural systems’ behavior based on the fundamental functorial processes of representation and localization-globalization. In the first part of this study we analyze the process of representation. Representation constitutes a categorical modeling relation that signifies the semantic bidirectional process of correspondence between natural systems and formal symbolic systems. The notion of formal systems is substantiated by algebraic rings of observable attributes of natural systems. In this perspective, the (...) distinction between simple and complex systems is reflected in the appropriate qualification of their corresponding rings of observables. The crucial distinguishing requirement with respect to the coordinatizing rings of observables has to do with the property of global commutativity. The global information structure representing the behavior of a complex system is modeled functorially in terms of its Spectrum functor. Due to the fact that, the fundamental process of representation is bidirectional by construction, it admits a precise categorical formulation in terms of the syntactic language of adjoint functors, constituting thus, a categorical adjunction. The left adjoint functor of this adjunction signifies the process of encoding the information related with phenomena of natural systems in terms of coordinatizing rings of observables, whereas, the right adjoint functor signifies the inverse process of information decoding, which, can be used for making predictions about the behavior of natural systems. (shrink)

This work presents a formal architectural model for complex systems based on a directed object–relation graph. In contrast to diagram-centric approaches, architecture is defined independently of representation, notation, or tooling. Objects and directed relations constitute the complete ontological core, while diagrams and viewpoints are treated as computable projections derived through canonical graph operators. -/- The paper introduces formal definitions of reachability, path analysis, and structural vulnerability as intrinsic architectural properties. Minimality and irreducibility of the object–relation model are established (...) with respect to canonical architectural views, demonstrating that storing diagrams as primary architectural artifacts introduces no additional structural information. -/- Grounded in the principles of the Architecture of Complex Systems (ACS), the proposed model enables invariant architectural reasoning across representations and supports rigorous analysis of architectural structure prior to implementation. A reference implementation illustrates the feasibility of executing architectural operators directly at the data layer, independent of visualization mechanisms. (shrink)

Complex systems are used, studied and instantiated in science, with what con-sequences? To be clear and systematic in response it is necessary to distin-guish the consequences, for science, of science using and studying complex systems, for philosophy of science, of science using and studying complex systems, for philosophy of science, of philosophy of science modelling sci-ence as a complex system. Each of these is explored in turn, especially. While has been least studied, it (...) will be shown how modelling science as a complex process may change our conception of science and thereby query what a philosophy of science adequate to this complexity might look like. (shrink)

In this article, network science is discussed from a methodological perspective, and two central theses are defended. The first is that network science exploits the very properties that make a system complex. Rather than using idealization techniques to strip those properties away, as is standard practice in other areas of science, network science brings them to the fore, and uses them to furnish new forms of explanation. The second thesis is that network representations are particularly helpful in explaining the (...) properties of non-decomposable systems. Where part-whole decomposition is not possible, network science provides a much-needed alternative method of compressing information about the behavior of complex systems, and does so without succumbing to problems associated with combinatorial explosion. The article concludes with a comparison between the uses of network representation analyzed in the main discussion, and an entirely distinct use of network representation that has recently been discussed in connection with mechanistic modeling. (shrink)

Introduction to complexity and complex systems -- Introduction to large linear systems -- Introduction to biochemical oscillators and nonlinear biochemical systems -- Modularity, redundancy, degeneracy, pleiotropy and robustness in complex biological systems -- The evolution of biological complexity; invertebrate immune systems -- Irreducible and specified complexity in living systems -- The complex adaptive and innate human immune systems -- Complexity in quasispecies : microRNAs -- Introduction to complexity in economic (...) class='Hi'>systems -- Complexity in quasispecies : micrornas -- Dealing with complexity. (shrink)

The development of new theory is often spurred by novel techniques that provide better answers to existing questions, or that allow asking new ones. In the field of strategy and organization science, models of complex adaptive systems have renewed theoretical work on a fundamental question: how organizations can adapt effectively to their environments. This article has three objectives: to highlight some areas where models of organizations as complex adaptive systems have made substantial contributions: the search for (...) solutions to sets of interdependent choices, the challenge of balancing processes of exploration and exploitation, and the organization of imperfect decision makers; to point to several challenges and tradeoffs which can limit the explanatory power and eventual impact of the modeling enterprise; and to sketch out possible future directions of research that would do further justice to the notion of organizations as complex adaptive systems. (shrink)

The standard assumptions that underlie many conceptual and quantitative frameworks do not hold for many complex physical, biological, and social systems. Complex systems science clarifies when and why such assumptions fail and provides alternative frameworks for understanding the properties of complex systems. This review introduces some of the basic principles of complex systems science, including complexity profiles, the tradeoff between efficiency and adaptability, the necessity of matching the complexity of systems to (...) that of their environments, multiscale analysis, and evolutionary processes. Our focus is on the general properties of systems as opposed to the modeling of specific dynamics; rather than provide a comprehensive review, we pedagogically describe a conceptual and analytic approach for understanding and interacting with the complex systems of our world. This paper assumes only a high school mathematical and scientific background so that it may be accessible to academics in all fields, decision-makers in industry, government, and philanthropy, and anyone who is interested in systems and society. (shrink)

We develop a general covariant categorical modeling theory of natural systems' behavior based on the fundamental functorial processes of representation and localization-globalization. In the second part of this study we analyze the semantic bidirectional process of localization-globalization. The notion of a localization system of a complex information structure bears a dual role: Firstly, it determines the appropriate categorical environment of base reference contexts for considering the operational modeling of a complex system's behavior, and secondly, it specifies the (...) global compatibility conditions of local contextual information. A localization system acts on the global information structure of a complex system, partitions it into sorts, and eventually, forces the consistent sheaf-theoretic fibering of the latter over the base category of commutative reference contexts. In this manner, the sheafification of the Spectrum functor of a complex information structure takes place by imposing on the uniform and homologous fibered structure of elements of the Spectrum presheaf the following two requirements of coherence in relation to the localization-globalization process: [i]. Compatibility of information under restriction from the global to the local level, and [ii]. Compatibility of information under extension from the local to the global level. Correspondingly, the options of local and global receive a concrete mathematical meaning with respect to a suitable notion of topology (categorical Grothendieck topology) defined on the base category of commutative reference contexts. Finally, the accurate functorial process modeling of a complex system's behavior, respecting the processes of representation and localization-globalization, is being effectuated by means of establishing a categorical dual equivalence between the category of complex information structures, and the topes of sheaves over the base category of partial or local information carriers, equipped with the categorical topology of epimorphosis families. (shrink)

Systems architecture and its associated parallel biology generate architectural forms that are both green and surreal by nature. The connection between systems architecture and Leo Lionni's fantastic book Parallel Botany are considered as architects are now starting to have the ability to create great works of biological parallelism using technologies that are highly sur real, they are on top of the real.

In lieu of an abstract, here is a brief excerpt of the content:Complex Mimetic SystemsHans Weigand (bio)The goal of science is to make the wonderful and complex understandable and simple—but not less wonderful.—Herb Simon, The Sciences of the Artificial11. IntroductionComplex systems theory stands for an approach in the social as well as natural and computational sciences that studies how interactions between parts give rise to collective behaviors of a system, and how the system interacts and forms relationships (...) with its environment. A typical example is the market economy, in which the order is emergent: it is the result of human action, but not the execution of any human design.2 Complex systems theory is currently a popular vehicle for understanding the complexities of the Internet; other examples of its application are as diverse as the stock market, ant colonies, epidemics, and the spread of business innovations. The focus in this article is on modeling social systems rather than physical or biological phenomena. [End Page 63]The mimetic theory developed by René Girard fits well with a systems perspective, as it has specific ideas about the drivers of human action (at the micro level) and cultural processes (at the macro level). The relationship has been explored earlier in several books and articles;3 in particular, in the work of the Centre de Recherche en Epistémologie Appliquée (CREA) in Paris. The systems perspective received a new stimulus in the 1990s in the form of complex adaptive systems (CAS),4 not least because of the agent-based computer simulations adopted at that time. The objective of this article is to introduce a special version of CAS, called complex mimetic systems (CMS), which builds on mimetic theory. The purpose of this article is twofold. On the one hand, the phrasing of mimetic theory in terms of CMS poses an interesting challenge to the theory to formalize its concepts and explicate possible limitations. On the other hand, CMS might be a useful contribution to the CAS field, as it incorporates concepts such as “social influence” that are very basic to but typically not spelled out in current CAS work.The structure of this article is as follows. In section 2, I briefly review the CAS literature and introduce the idea of complex mimetic systems. Section 3 describes a straw-man agent architecture for CMS, whereas in section 4, I move to the macro level and formalize the culture reproduction cycle. To illustrate the applicability of the CMS framework, I discuss in section 5 Ingo Piepers’s recent CAS analysis of the European international system in the period 1490–1945, and comment on it from a CMS perspective.2. Complex Mimetic SystemsThe characteristic features of complex systems are as follows:• Nonlinear effects: a small perturbation may have a large effect.• Feedback loops: the effects of an element’s behavior are fed back to it in some way. The feedback can be positive (amplification, runaway) or negative (damping).• Openness: a typical complex system interacts with its environment.• Memory: the history of a complex system may be important. Prior states may have an influence on present states.• Nesting, hierarchy: a complex system may itself be an element of a larger complex system. For example, clans in a tribal society, nation-states in an international system, or divisions in a company. [End Page 64]• Topology: the interactions of the elements are enabled and constrained by the network, or grid, of relationships between them.Complex Adaptive SystemsComplex adaptive systems (CAS) are a modern variant of complex systems theory. The elements of a complex adaptive system are called agents, as CAS builds on computational research in the field of multiagent systems.5 Although there is not much difference in the overall objectives, the use of agent simulation opens up interesting research opportunities. Let me clarify this by means of an introductory example given by Miller and Page, the standing ovation problem.6Standing ovations, in which waves of audience members stand up to express their particular appreciation of a performance, usually arise and evolve spontaneously. Suppose that we want to model this phenomenon. A starting point could be a simple mathematical model in which we distinguish N people, each receiving a signal... (shrink)

Crossing the road within the traffic system is an example of an action human agents perform successfully day-to-day in complex systems. How do they perform such successful actions given that the behaviour of complex systems is often difficult to predict? The contemporary literature contains two contrasting approaches to the epistemology of complex systems: an analytic and a post-modern approach. We argue that neither approach adequately accounts for how successful action is possible in complex (...) systems. Agents regularly perform successful actions without obeying (explicit or implicit) algorithmic rules (as the analytic approach suggests) and without an existential leap to action (as the post-modern approach suggests). We offer an alternative: A common-sense pragmatist epistemology, one that focuses on the kind of actions making up most agents’ successful moment-to-moment actions in complex systems. Successful actions obtain when agents apply ceteris paribus rules-of-thumb during predictive and decisional practices while achieving some desired goal. (shrink)

This thesis presents the first comprehensive empirical investigation of ontological instability in complex systems, introducing a novel theoretical framework called Quantitative Ontological Dynamics (QOD) that bridges philosophical ontology with empirical measurement. Through systematic analysis of quantum mechanical systems, biological phase transitions, economic market dynamics, and other complex phenomena, we demonstrate that ontological categories are not fixed but exhibit measurable fluctuations that can be quantified, predicted, and analyzed using rigorous mathematical methods. -/- Our research reveals that traditional (...) fixed ontological positions fail to account for the dynamic nature of reality as observed in complex systems. We introduce five fundamental metrics for measuring ontological instability: fluctuation intensity, correlation dynamics, phase transition indicators, ontological uncertainty, and giant component dynamics. These metrics, combined into a composite Ontological Instability Index (OII), provide unprecedented insight into how the fundamental nature of systems changes over time. -/- The empirical evidence presented demonstrates that ontological instability is not merely a philosophical curiosity but a measurable phenomenon with practical implications for understanding and predicting system behavior. Our analysis of financial market crises, biological phase transitions, and quantum measurement processes reveals consistent patterns of ontological fluctuation that challenge conventional approaches to system analysis and prediction. -/- This work establishes ontological instability as a legitimate subject of scientific inquiry and provides the theoretical and methodological foundation for a new field of quantitative ontology. The implications extend beyond academic philosophy to practical applications in risk assessment, system design, and crisis prediction across multiple domains. (shrink)

Scientists depend on complex computational systems that are often ineliminably opaque, to the detriment of our ability to give scientific explanations and detect artifacts. Some philosophers have s...

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