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)

This monograph focuses on two major themes of current interest---those of complexity and emergence. Neither of the two concepts is, in the very nature of things, precisely defined or easily comprehended. Complexity is all around us while the sciences often analyze entities and events by making simplifications. But the fault lines in the latter get exposed over larger spans of space and time. Complexity entails emergence that involves discontinuity and novelty in the evolution of complex systems, based on the appearance (...) of distinctive spatial and temporal structures. Underlying an occurrence of emergence is an instability involving the transition from one stable regime to another, where distinct space-time scales acquire relevance across the transition. The structures on the two sides of the transition are characterized by distinct sets of state variables where, on one side of the transition, collective variables make their appearance. -/- Complexity and emergence are viewed in this book in the context of the Kantian noumenal-phenomenal divide. The noumenal reality is the repository of all the complexity that there is, while the phenomenal reality emerges from the noumenal in the process of our perception, interpretation, and inference. The noumenal exists in itself as a self-determined whole, and reveals itself to us in fragmentary patches as skewed projections that we assemble to form our phenomenal world that keeps on emerging ceaselessly. Our own biological evolution and the evolution of our phenomenal world occurs in a mutually consistent process, that can be referred to as co-evolution. -/- We seek regularities in the phenomenal world by means of our scientific theories which are often successful, but that success is fragile as, over larger spans of space and time, anomalies make their appearance, giving a lie to the simplicity and regularity previously presumed to have been unearthed. Simplicity, regularity, and harmony are only fleetingly located in the phenomenal world by means of our theories as these keep on being revised endlessly and often radically, thereby generating a mosaic of theories that becomes ever more complex, indicating a pervasive complexity of the noumenal world from which the phenomenal emerges by way of strictly limited projections. The foundational metaphysics on which this book is based tells us that reality is fundamentally complex, while tiny islands of simplicity, regularity, and harmony are embedded in it in isolated space-time domains. (shrink)

This monograph is an in-depth and engaging discourse on the deeply cognitive roots of human scientific quest. The process of making scientific inferences is continuous with the day-to-day inferential activity of individuals, and is predominantly inductive in nature. Inductive inference, which is fallible, exploratory, and open-ended, is of essential relevance in our incessant efforts at making sense of a complex and uncertain world around us, and covers a vast range of cognitive activities, among which scientific exploration constitutes the pinnacle. Inductive (...) inference has a personal aspect to it, being rooted in the cognitive unconscious of individuals, which has recently been found to be of paramount importance in a wide range of complex cognitive processes. One other major aspect of the process of inference making, including the making of scientific inferences, is the role of a vast web of beliefs lodged in the human mind, as also of a huge repertoire of heuristics, that constitute an important component of ‘unconscious intelligence’. Finally, human cognitive activity is dependent in a large measure on emotions and affects, that operate mostly at an unconscious level. Of special importance in scientific inferential activity is the process of hypothesis making, which is examined in this book, along with the above aspects of inductive inference, at considerable depth. The book focuses on the inadequacy of the viewpoint of naive realism in understanding the contextual nature of scientific theories, where a cumulative progress towards an ultimate truth about Nature appears to be too simplistic a generalization. It poses a critique to the commonly perceived image of science which is seen as the last word in logic and objectivity, the latter in the double sense of being independent of individual psychological propensities and, at the same time, approaching a correct understanding of the workings of a mind-independent nature. Adopting the naturalist point of view, it examines the essential tension between the cognitive endeavours of individuals and scientific communities, immersed in belief systems and cultures, on the one hand, and the engagement with a mind-independent reality on the other. In the end, science emerges as an interpretation of nature, which is perceived by us only contextually, as successively emerging cross-sections of limited scope and extent. Successive waves of theory building in science appear as episodic and kaleidoscopic changes in perspective as certain in-built borders are crossed, rather than as a cumulative progress towards some ultimate truth. While written in an informal and conversational style, the book raises a number of deep and intriguing questions located at the interface of cognitive psychology and philosophy of science, meant for both the general lay reader and the specialist. Of particular interest is the way it explores the role of belief (aided by emotions and affects) in making the process of inductive inference possible since belief is a subtle though all-pervasive cognitive factor not adequately investigated in the current literature. (shrink)

What beliefs are, what they do for us, how we come to hold them, and how to evaluate them. Our beliefs constitute a large part of our knowledge of the world. We have beliefs about objects, about culture, about the past, and about the future. We have beliefs about other people, and we believe that they have beliefs as well. We use beliefs to predict, to explain, to create, to console, to entertain. Some of our beliefs we call theories, and (...) we are extraordinarily creative at constructing them. Theories of quantum mechanics, evolution, and relativity are examples. But so are theories about astrology, alien abduction, guardian angels, and reincarnation. All are products (with varying degrees of credibility) of fertile minds trying to find explanations for observed phenomena. In this book, Nils Nilsson examines beliefs: what they do for us, how we come to hold them, and how to evaluate them. We should evaluate our beliefs carefully, Nilsson points out, because they influence so many of our actions and decisions. Some of our beliefs are more strongly held than others, but all should be considered tentative and changeable. Nilsson shows that beliefs can be quantified by probability, and he describes networks of beliefs in which the probabilities of some beliefs affect the probabilities of others. He argues that we can evaluate our beliefs by adapting some of the practices of the scientific method and by consulting expert opinion. And he warns us about “belief traps”—holding onto beliefs that wouldn't survive critical evaluation. The best way to escape belief traps, he writes, is to expose our beliefs to the reasoned criticism of others. (shrink)