This book presents introductions to the essential mathematical aspects of complexity science, suitable for advanced undergraduate/masters-level students and researchers.

Ecosystems, the human brain, ant colonies, and economic networks are all complex systems displaying collective behaviour, or emergence, beyond the sum of their parts. Complexity science is the systematic investigation of these emergent phenomena, and stretches across disciplines, from physics and mathematics, to biological and social sciences. This introductory textbook provides detailed coverage of this rapidly growing field, accommodating readers from a variety of backgrounds, and with varying levels of mathematical skill. Part I presents the underlying principles of (...) complexity science, to ensure students have a solid understanding of the conceptual framework. The second part introduces the key mathematical tools central to complexity science, gradually developing the mathematical formalism, with more advanced material provided in boxes. A broad range of end of chapter problems and extended projects offer opportunities for homework assignments and student research projects, with solutions available to instructors online. Key terms are highlighted in bold and listed in a glossary for easy reference, while annotated reading lists offer the option for extended reading and research. (shrink)

While complexity science is gaining interest among educational theorists, its constructs do not speak to educational responsibility or related core issues in education of power and ethics. Yet certain themes of complexity, as taken up in educational theory, can help unsettle the more controlling and problematic discourses of educational responsibility such as the potential to limit learning and subjectivity or to prescribe social justice. The purpose of this article is to critically examine complexity science against (...) notions of responsibility in terms of implications for education. First, themes of complexity science prominent in contemporary educational writing are explained. Then dilemmas of responsibility in complexity are explored, such as what forms and meanings responsibility can have in a ‘complexified’ perspective of education, how care for others is mobilised, and how desire can be understood. Analyses of ethical action grounded in complexity science are then examined, as well as theories of the ethical subject and participatory responsibility that are congruent with certain tenets of a complexity ontology. Finally, the possibility of an educational vision of responsibility animated by complexity theories is considered, drawing from related writings of Bai, Biesta, Derrida, Levinas and Varela. (shrink)

“Complexity sciences” are an interdisciplinary and transnational domain of study that aims at modeling natural and social “complex systems.” They appeared in the 1970s in Europe and the United States, but were boosted in the mid-1980s by the Santa Fe Institute (SFI) under the formula of “science of complexity.” This small but famous institution is the object of the present article. According to their promissory ambitions and to the enthusiastic claims of some scientific journalists, complexity sciences (...) were going to revolutionize all of knowledge and even private and public actors who had learned to master them. In the light of this, one would expect to observe a well-established and autonomous research and educational field, capable of reproducing itself through professional institutions. Yet this is not the case. To explain the paradox, I propose to combine different models of history and sociology of emergent and declining domains, in order to give account of the rise and failure of complexity sciences. (shrink)

This article addresses complexity by selecting some of its key aspects that share a common feature: the power to change. They seem to change not only the way the world is approached by scientists, but also the way this approach, the resulting perspectives and their multiple relationships, are interpreted. These main aspects are: (1) the challenge of measurability, with an unexpected result that escapes the gravitational field of the measurability problem; (2) the meaning of reproducibility and the redrawn boundaries (...) of scientific inquiry, with implications for the social sciences; (3) the altered expectations concerning prediction, which seem to break with a glorious tradition of unquestioned technological success; and (4) the discovery of all-embracing patterns of events that unavoidably include large events, possibly perceived as ‘crises’, which one may hope to understand and confront, rather than rule out. The resulting geography, with its new landmarks, new relationships among its elements and new means of orientation, is expected to reach the public sooner or later, even if the effect – according to complexity theory itself – cannot be foreseen in detail. All these fibres of change are considered in the context of a fresh meaning of time and of a topology dominated by network concepts. (shrink)

Mechanistic frameworks of investigation and explanation dominate the cognitive, neural, and psychological sciences. In this dissertation, I argue that mechanistic frameworks cannot, in principle, explain some kinds of cognition. In its place, I argue that complexity science has methods and theories more appropriate for investigating and explaining some cognitive phenomena. -/- I begin with an examination of the term 'cognition.' I defend the idea that "cognition" has been a moving target of investigation in the relevant sciences. As such (...) it is not historically true that there has been a thoroughly entrenched and agreed upon conception of "cognition." Next, I take up mechanistic frameworks. Although 'mechanism' is an umbrella term for a set of loosely related characteristics, there are common features: linearity, localization, and component dominance. I then describe complexity science, with emphasis on its utilization of dynamical systems modeling. Next, I discuss two phenomena that typically fall under the purview of complexity science: nonlinearity and interaction dominance. -/- A complexity science framework guided by the theory of self-organized criticality and utilizing the methods of dynamical systems modeling can surmount a number of challenges that face mechanistic frameworks when investigating some kinds of cognition. The first challenge is epistemic and concerns the inadequacy of mechanistic frameworks to facilitate the comprehensibility of massive amounts of data across various scales and areas of inquiry. I argue that complexity science is more appropriate for making big data comprehensible when investigating cognition, particularly across disciplines. I demonstrate this via an approach called nested dynamical modeling (NDM). NDM can facilitate comprehensibility of large amounts of data obtained from various scales of investigation by eliminating irrelevant degrees of freedom of that system as relates to the target of investigation. -/- The second shortcoming concerns ontological blind spots within mechanistic frameworks. Cognitive phenomena like extended cognition often fail to meet most, if not all, of the criteria assumed by many mechanistic approaches, especially component dominance. I argue that research guided by the notion of interaction dominance allows for extended cognition to be a real, empirically supported phenomenon within complex systems frameworks. In this chapter I discuss some of my experimental work on extended cognitive systems. -/- The search for mechanisms can be a reasonable starting position when attempting to explain natural phenomena in the life sciences. However, too strict of an adherence to theoretical and methodological commitments such as linearity, localization, and component dominance can result in intractable epistemic challenges and ontological blind spots. Complexity science has theories and methods to overcome such challenges in the investigation of cognition. (shrink)

This text addresses the problems of complex systems in understanding natural phenomena and the behaviour of systems related to human activity, from a science and humanities perspective. It discusses molecular behaviour and structures, and offers examples of ecological and environmental modelling.

Complexity sciences have become famous worldwide thanks to several popular books that served as echo chambers of their promises. These consisted in departing from “classical science” defined as deterministic, reductionist, analytic and mono-disciplinary. Their founders and supporters declared that complexity sciences were going to give rise (or that they have given rise) to a post-Laplacian, antireductionist, holistic and interdisciplinary approach. By taking a closer look at their content and practices, I argue in this article that, because of (...) their physics-oriented, computationalist, and mathematical assumptions, complexity sciences have paradoxically produced knowledge at odds with these four tenets. (shrink)

While ethics in publishing has been increasingly debated, there seems to be a lack of a theoretical framework for making sense of existing rules of behavior as well as for designing, managing and enforcing such rules. This letter argues that systems-oriented disciplines, such as complexity science and human factors, offer insights into new ways of dealing with ethics in publishing. Some examples of insights are presented. Also, a call is made for empirical studies that unveil the context and (...) details of both retracted papers and the process of writing and publishing academic papers. This is expected to shed light on the complexity of the publication system as well as to support the development of a just culture, in which all participants are accountable. (shrink)

Complexity science is an investigative framework that stems from a number of tried and tested disciplines—including systems theory, nonlinear dynamical systems theory, and synergetics—and extends a common set of concepts, methods, and principles to understand how natural systems operate. By quantitatively employing concepts, such as emergence, nonlinearity, and self‐organization, complexity science offers a way to understand the structures and operations of natural cognitive systems in a manner that is conceptually compelling and mathematically rigorous. Thus, complexity (...) science both transforms understandings of cognition and reframes more traditional approaches. Consequently, if cognitive systems are indeed complex systems, then cognitive science ought to consider complexity science as a centerpiece of the discipline. (shrink)

This book is dedicated to the first ten years of Chaos and Complexity Letters - International Journal of Dynamical Systems Research. This journal was born to collect and disseminate complexity science related information to anybody interested in the topic; to speed up the evolutionary development of complexity science; to extend its interactions crossing over disciplines, levels of knowledge and geography; and to foster finding new pathways in research and new applications. The structure of CCL was (...) specifically designed to add value to the trans-disciplinary approach while, at the same time, differentiating the epistemology of different contributions. In this enterprise we were sustained and inspired by two great companions that in different ways shared our project during its prehistory: Ilya Prigogine and Francisco Varela. This book collects 16 papers appeared on the first ten volumes of Chaos and Complexity Letters. They range from the life sciences, to STEM and economy, in accordance with the interdisciplinary mission of the journal. A special highlight starts with Acceleration and entropy: a macroscopic analogue of the twin paradox, possibly the last paper written by the Nobel Prize Ilya Prigogine with Gonzalo Ordonez. Important academic specialists who wrote in our scientific journal passed away. For example, Walter Freeman, Tullio Minelli, Ilya Prigogine, and Joseph P. Zbilut. This special issue is also dedicated to them. We are in opinion that their trajectories in life and research designed some contours of the shape of a new science to come. (shrink)

Since their inception in the 1980s, complexity sciences have been described as a revolutionary new domain of research. By describing some of the practices and assumptions of its representatives, the present article shows that this field is an association of subdisciplines laying on existing disciplinary footholds. The general question guiding us here is: On what basis do complexity scientists consider their inquiry methods and results as valuable? To answer it, I describe five “epistemic argumentative regimes,” namely the ways (...) in which complexity scientists argue the credibility of their research, and five “ontological views,” that is the ways in which they interpret the material and formal causes of their study objects and models. Finally, the article proposes the term of “regime of evidence” to designate the specific combination of one ontological view with one or more epistemic argumentative regimes. (shrink)

A review of Sandra D. Mitchell's excellent book "Unsimple Truths" -/- I highly recommend this book to anyone interested in: -/- - Scientific metaphysics - Philosophy of science - Emergence - Science and epistemology - Philosophy of complexity and complex systems - Non-reductive physicalism - Philosophical analyses of simulations - Prediction .

This comprehensive Handbook is aimed at both academic researchers and practitioners in the field of complexity science. The book's 26 chapters, specially written by leading experts, provide in-depth coverage of research methods based on the sciences of complexity. The research methods presented are illustratively applied to practical cases and are readily accessible to researchers and decision makers alike.The Handbook's wide range of research methods are clearly illustrated with case studies that demonstrate their practical application. They range from (...) the regeneration of communities to musical performance; from complex governance networks to psychotherapy; from gender dynamics to agent-based modelling; and the appropriate response to pandemics. Some unusual research methods - based on art, psychology and multi-level networks - are also included. Furthermore, the book incorporates discussions on the philosophical aspect of research methods and explores important theoretical concepts, such as exaptation, emergence, self-organisation and co-evolution.This is an ideal resource for academics and researchers in the field seeking and exploring new research methods. For decision makers and researchers trying to address complex challenges it will be an essential source of inspiration that will arm them with effective state-of-the-art research methods for the future. (shrink)

Political scientists have conventionally assumed that achieving democracy is a one-way ratchet. Only very recently has the question of “democratic backsliding” attracted any research attention. We argue that democratic instability is best understood with tools from complexity science. The explanatory power of complexity science arises from several features of complex systems. Their relevance in the context of democracy is discussed. Several policy recommendations are offered to help stabilize current systems of representative democracy.

Complexity sciences are one of the most mediatized scientific fields of the last 40 years. While this domain has attracted the attention of many philosophers of science, its normative views have not yet been the object of any systematic study. This article is a contribution to the thin social science literature about complexity sciences and proposes a contribution focused on an analysis of the origins, models, and organization of the Santa Fe Institute (SFI), cradle of the (...) field. The paper defends the thesis that the notion of “complex adaptive systems” bears a project of naturalization of society through numerical and evolutionary lenses by promoting a Darwinian and capitalist view of the economy. At the same time, such a view has been embodied in the very way of functioning of the institute, which was conceived as an agile organization in a competitive environment and which relies on a fundraising philosophy that tends to commodify science. From a theoretical viewpoint, this text is anchored in the field of Science and Technology Studies and particularly in the coproductionist paradigm, which theorizes the dynamic entanglement of science and society. In terms of empirical sources, the article is based on interviews conducted by the author, and on the SFI's scientific publications as well as institutional archives. (shrink)

Readers of TopiCS are invited to join a debate about the utility of ideas and methods of complexity science. The topics of debate include empirical instances of qualitative change in cognitive activity and whether this empirical work demonstrates sufficiently the empirical flags of complexity. In addition, new phenomena discovered by complexity scientists, and motivated by complexity theory, call into question some basic assumptions of conventional cognitive science such as stable equilibria and homogeneous variance. The (...) articles and commentaries that appear in this issue also illustrate a new debate style format for topiCS. (shrink)

To understand how compliance develops both in everyday and corporate environments, it is crucial to understand how different mechanisms work together to shape individuals’ (non)compliant behavior. Existing compliance studies typically focus on a subset of theories (i.e., rational choice theories, social theories, legitimacy theories, capacity theories, and opportunity theories) to understand how key variables from one or several of these theories shape individual compliance. The present study provides a first integrated understanding of compliance, rooted in complexity science, in (...) which key elements from these theories are considered simultaneously, and their relations to compliance and each other are explored using network analysis. This approach is developed by analyzing online survey data (_N_ = 562) about compliance with COVID-19 mitigation measures. Traditional regression analysis shows that elements from nearly all major compliance theories (except for social theories) are associated with compliance. The network analysis revealed groupings and interconnections of variables that did not track the existing compliance theories and point to a complexity overlooked in existing compliance research. These findings demonstrate a fundamentally different perspective on compliance, which moves away from traditional narrow, non-network approaches. Instead, they showcase a complexity science understanding of compliance, in which compliance is understood as a network of interacting variables derived from different theories that interact with compliance. This points to a new research agenda that is oriented on mapping compliance networks, and testing and modelling how regulatory and management interventions interact with each other and compliance within such networks. (shrink)

Our socio-economic innovation ecosystem is riddled with ever-increasing complexity, as we are faced with more frequent and intense shocks, such as COVID-19. Unfortunately, addressing complexity requires a different kind of economic governance. There is increasing pressure on economics to not only going beyond its traditional mainstream boundaries but also to tackle real-world problems such as fostering structural change, enhancing sustained growth, promoting inclusive development in the era of the digital economy, and boosting green growth, while addressing the divide (...) between the financial sector and the real economy. This book demonstrates how to apply complexity science to economics, in an effective and instructive way, in the interest of life-enhancing policies. The book revolves around the non-negligible problem of why economics, to date, seems to be insufficient in guiding economic governance to navigate through real and ever-intensifying complex socio-economic and environmental challenges. With its interdisciplinary approach, the book scans the nuanced nexus between complexity and economics by incorporating, as well as transcending the state-of-the-art literature. It identifies ways to trigger opportunities for behaviour change in the economic profession with respect to how to teach and what, introducing and developing further complexity economics thinking with the configuration of its main principles and outlining the silhouette of next-generation economic governance. The book deciphers recommendations both for economic theory, practice, and education and economic governance. It will be of interest to students, scholars, academics, think tank researchers and economic policy practitioners at the national and/or supranational level. Olivér Kovács is a senior research fellow in the Department of Economics and International Economics at the University of Public Service, Budapest, Hungary. (shrink)

Political scientists have conventionally assumed that achieving democracy is a one-way ratchet. Only very recently has the question of ‘democratic backsliding’ attracted any research attention. We argue that democratic instability is best understood with tools from complexity science. The explanatory power of complexity science arises from several features of complex systems. Their relevance in the context of democracy is discussed. Several policy recommen- dations are offered to help stabilize current systems of representative democracy.

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

The deep crisis in modern fundamental science development is ever more evident and openly recognised now even by mainstream, official science professionals and leaders. By no coincidence, it occurs in parallel to the world civilisation crisis and related global change processes, where the true power of unreduced scientific knowledge is just badly missing as the indispensable and unique tool for the emerging greater problem solution and further progress at a superior level of complex world dynamics. Here we reveal (...) the mathematically exact reason for the crisis in conventional science, containing also the natural and unified problem solution in the form of well-specified extension of usual, artificially restricted paradigm. We show how that extended, now causally complete science content provides various "unsolvable" problem solutions and opens new development possibilities for both science and society, where the former plays the role of the main, direct driver for the latter. We outline the related qualitative changes in science organisation, practice and purposes, giving rise to the sustainability transition in the entire civilisation dynamics towards the well-specified superior level of its unreduced, now well understood and universally defined complexity. (shrink)

This book explores solving the problem of complexity for science in the 21st century.

This chapter contains sections titled: References.

An extended approach to the comprehension of virtual reality is developed in the article. Virtual reality is understood not only as a logically possible or cybernetically constructed reality but also as continuous turbulence of potencies of the complex natural and social world we live in, the wandering of complex systems and organizations over a field of possibilities, such a realization of forms and structures in which many formations remain in latent, potential forms, and are in the permanent process of making (...) and multiplying a spectrum of possibilities, lead to the growth of the evolutionary tree of paths of development. It is shown that such an understanding of virtual reality corresponds to concepts and notions developed in the modern science of complexity. The most significant concepts are considered, such as the nonlinearity of time, the relationship of space and time, the uncertainty of the past and the openness of the future, the choice and construction of the future at the moments of passing the bifurcation points. Some cultural and historical prototypes of these modern ideas of virtual reality are given. It is substantiated that the vision of virtual reality being developed today can play the role of a heuristic tool for understanding the functioning and stimulation of human creativity. (shrink)

Science has lost its ethical imperatives as it moved away from a science of ought to a science of is. Subsequently, it might have answers for how we can address global challenges, such as climate change and poverty, but not why we should. This supposedly neutral stance leaves it to politics and religions (in the sense of non-scientific fields of social engagement) to fill in the values. The problem is that through this concession, science implicitly acknowledges (...) that it is not of universal relevance. Objective knowledge, as Karl Popper calls for, might be less easily attainable in the world of ideas and within the confines of scientific idealism. However, if ideas, values and meaning have equal claim to be drivers of change in the sense of causation, aspiring to identify objective knowledge about the world of ideas and of meaning is necessary. If the sciences and disciplines aim to give objectively valid reasons for our actions (and for how to address global challenges), we need to elevate the study of meaning beyond the cultural, disciplinary and ideational delineations. We need to come to a meta understanding of values and meaning equal to objective knowledge about the material world. But differently than in the material world this meta understanding needs to incorporate individual and subjective experiences as cornerstones of objectivity on a meta-level. We need a science of meaning; one that can scientifically answer Kant's third question of 'what may we hope for'."--Page 4 of cover. (shrink)

The world is complex, but acknowledging its complexity requires an appreciation for the many roles context plays in shaping natural phenomena. In _Unsimple Truths, _Sandra Mitchell argues that the long-standing scientific and philosophical deference to reductive explanations founded on simple universal laws, linear causal models, and predict-and-act strategies fails to accommodate the kinds of knowledge that many contemporary sciences are providing about the world. She advocates, instead, for a new understanding that represents the rich, variegated, interdependent fabric of many (...) levels and kinds of explanation that are integrated with one another to ground effective prediction and action. Mitchell draws from diverse fields including psychiatry, social insect biology, and studies of climate change to defend “integrative pluralism”—a theory of scientific practices that makes sense of how many natural and social sciences represent the multi-level, multi-component, dynamic structures they study. She explains how we must, in light of the now-acknowledged complexity and contingency of biological and social systems, revise how we conceptualize the world, how we investigate the world, and how we act in the world. Ultimately _Unsimple Truths _argues that the very idea of what should count as legitimate science itself should change. (shrink)

The 21st century is the time of complexity. We delineate it and its importance as necessary to solve ‘wicked problems.’ Inherently transdisciplinary, trans-scale, and interconnected to living systems, the solution to Heliophysics’ identity crisis and to unlock the next generation of scientific discovery may be to embrace complexity. With the right foresight, direction, and incentive over the next ten years, Heliophysics can become a beacon for how all of society thinks about and does complexity science.