Complexity: A Guided Tour. Melanie Mitchell

Encyclopedia of Ecology, 2nd Edition, 2018

This entry describes key concepts and features of complex systems, including emergence, self-organization, feedbacks, nonlinearity, sensitivity to initial conditions, critical or edge-of-chaos dynamics, symmetry breaking, resilience, as well as adaptation and evolution. It briefly introduces a few contemporary cross-disciplinary methodologies in the overlap of physics, computational and life sciences, such as agent-based models, dynamical systems, analysis of order/disorder phase transitions, information dynamics and information thermodynamics, guided self-organization and complex networks. A number of biological and ecological examples are used to illustrate the concepts and modelling techniques across a wide range of systems, from gene regulatory networks to ant colonies to food webs. The examples cover collective behaviors, information cascades, optimal path formation, stigmergy, predator-prey interactions, and tipping points in climate and ecosystems. Three information-processing components (memory, communications and modifications) are placed in the context of system ecology, drawing parallels with ecological memory, ecological interactions and ecological modifications. The entry concludes with a comparison between complex and complicated systems, drawing a distinction in the ways that adaptive and engineered systems achieve stability in the face of external perturbations.

Int. Journal of Applied Sciences and Engineering Research, 2016

This innovative essay covering frontier areas of science crystallizes research ideas with translational potentials. It begins with a motivation to simplify the complexity by identification of emerging patterns within it. Overarching the properties of self-organization, organization by life and organization of consciousness, the article unfolds what could be the future of science of information leading from signal to information, to knowledge and wisdom, and vice versa, and also delineates the principles of sensor development for robotics. An emerging new psychology has been identified where the psyche could be considered a five-piece structure and process, which has relevance in cell biology where the cellular cognition is dynamically supported by signal networks of downstream informational molecules. The overall map thus constructed is non-reductive, holistic and falls within the ambits of systems science. The model is testable at micro level of systems cell and at macro level of systems brain. It is applicable also at mega level of a self-conscious, mindful and live universe.

‘‘Complex’’ is a special attribute we can give to many kinds of systems. Although it is used often as a synonym of ‘‘difficult,’’ it has a specific epistemological meaning, which is going to be shared by the incoming science of complexity. ‘‘Difficult’’ is an object which, by means of an adequate computational power, can be deterministically or stochastically predictable. On the contrary ‘‘complex’’ is an object which can not be predictable because of logical impossibility or because its predictability would require a computational power far beyond any physical feasibility, now and forever. For complexity refers to some observing system, it is always subjective, and thus it is defined as observed irreducible complexity. Human systems are affected by several sources of complexity, belonging to three classes, in order of descending restrictivity. Systems belonging to the first class are not predictable at all, those belonging to the second class are predictable only through an infinite computational capacity, and those belonging to the third class are predictable only through a trans-computational capacity. The first class has two sources of complexity: logical complexity, directly deriving from self-reference and Goedel’s incompleteness theorems, and relational complexity, resulting in a sort of indeterminacy principle occurring in social systems. The second class has three sources of complexity: gnosiological complexity, which consists of the variety of possible perceptions; semiotic complexity, which represents the infinite possible interpretations of signs and facts; and chaotic complexity, which characterizes phenomena of nonlinear dynamic systems. The third class coincides with computational complexity, which basically coincides with the mathematical concept of intractability. Artificial, natural, biological and human systems are characterized by the influence of different sources of complexity, and the latter appear to be the most complex.

The distinction between complicated and complex systems is of immense importance, yet it is often overlooked. Decision-makers commonly mistake complex systems for simply complicated ones and look for solutions without realizing that 'learning to dance' with a complex system is definitely different from 'solving' the problems arising from it. The situation becomes even worse as far as modern social systems are concerned. This article analyzes the difference between complicated and complex systems to show that what is at stake is a difference of type, not of degree; (2) the difference is based on two different ways of understanding systems, namely through decomposition into smaller parts and through functional analysis; (3) complex systems are the generic, normal case, while complicated systems are highly distinctive, special, and therefore rare. * Here I use "complexity" with regard to both nonlinear phenomena (complexity proper) and infinite sensibility to initial and boundary conditions (what is usually called "chaos" or "deterministic chaos"). Both are based on an internal machinery of a predicative, algorithmic, i.e. mechanical, formal nature. † The following are some further aspects that a less cursory analysis will have to consider: (1) the "complicated" perspective point tends to work with closed systems, while the "complex" perspective point works with open systems; (2) the former naturally adopts a zerosum framework, while the latter can adopt a positivesum framework; (3) the former relies on firstorder systems, while the latter includes secondorder systems, that is systems that are able to observe themselves (which is one of the sources of their complexity).

WSEAS TRANSACTIONS ON ADVANCES in ENGINEERING EDUCATION

This contribution examines, for didactic purposes, the peculiarities of systems that have the ability to acquire, maintain and deactivate properties that cannot be deduced from those of their components. We evaluate complex systems that can acquire, lose, recover, vary the predominance of property sequences, characterized by their predominant coherence and variability, through the processes of self-organization and emergence, when coherence replaces organization. We consider correspondingly systemic epistemology as opposed to the classical analytic approach and to forms of reductionism. We outline aspects of the science of complexity such as coherence, incompleteness, quasiness and issues related to its modeling. We list and consider properties and types of complex systems. Then we are dealing with forms of correspondence that concern the original conception of intelligence of primitive artificial intelligence, which was substantially based on the high ability to manipulate symbols,...

Futures, 1994

Complex systems are becoming the focus of important innovative research and application in many areas, reflecting the progressive displacement of classical physics and the emergence of a new and creative role for mathematics. This article makes a distinction between ordinary and emergent complexity and argues that a full analysis requires dialectical thinking. In so doing the authors aim to provide a philosophical foundation for post-normal science. The exploratory analysis developed here is complementary to those conducted with a more formal, mathematical approach, and begins to articulate what lies on the other side of that somewhat indistinct divide, the conceptual space called emergent complexity.

Electrical networks, flocking birds, transportation hubs, weather patterns, commercial organisations, swarming robots... Increasingly, many of the systems that we want to engineer or understand are said to be ‘complex’. These systems are often considered to be intractable because of their unpredictability, non-linearity, interconnectivity, heterarchy and ‘emergence’. Such attributes are often framed as a problem, but can also be exploited to encourage systems to efficiently exhibit intelligent, robust, self-organising behaviours. But what does it mean to describe systems as complex? How do these complex systems differ from the more easily understood ‘modular’ systems that we are familiar with? What are the underlying similarities between different systems, whether modular or complex? Answering these questions is a first step in approaching the design and science of complexity. However, to do so, it is necessary to look beyond the specifics of any particular system or field of study. We need to consider the fundamental nature of systems, looking for a common way to view ostensibly different phenomena. This primer introduces a domain-neutral framework and diagrammatic scheme for characterising the ways in which systems are modular or complex. Rather than seeing modularity and complexity as inherent attributes of systems, we instead see them as ways in which those systems are characterised by those who are interested in them. The framework is not tied to any established mode of representation (e.g. networks, equations, formal modelling languages) nor to any domain-specific terminology (e.g. ‘vertex’, ‘eigenvector’, ‘entropy’). Instead, it consists of basic system constructs and three fundamental attributes of modular system architecture, namely structural encapsulation, function-structure mapping and interfacing. These constructs and attributes encourage more precise descriptions of different aspects of complexity (e.g. emergence, self-organisation, heterarchy). This allows researchers and practitioners from different disciplines to share methods, theories and findings related to the design and study of different systems, even when those systems appear superficially dissimilar.

Complex Systems Science aims to understand concepts like complexity, self-organization, emergence and adaptation, among others. The inherent fuzziness in complex systems definitions is complicated by the unclear relation among these central processes: does self-organisation emerge or does it set the preconditions for emergence? Does complexity arise by adaptation or is complexity necessary for adaptation to arise? The inevitable consequence of the current impasse is miscommunication among scientists within and across disciplines. We propose a set of concepts, together with their informationtheoretic interpretations, which can be used as a dictionary of Complex Systems Science discourse.

Complexity is an interdisciplinary program publishing the best research and academic-level teaching on both fundamental and applied aspects of complex systemscutting across all traditional disciplines of the natural and life sciences, engineering, economics, medicine, neuroscience, social and computer science.

Complexly organized systems include biological and cognitive systems, as well as many of the everyday systems that form our environment. They are both common and important, but are not well understood. A complex system is, roughly, one that cannot be fully understood via analytic methods alone. An organized system is one that shows spatio-temporal correlations that are not determined by purely local conditions, though organization can be more or less localizable within a system. Organization and complexity can vary independently to some extent, but they are interconnected: organisation requires some complexity, but complexity cannot be maximum in an organized system. I will define complexity and organization more precisely, and show how these definitions imply the above properties. Next I will discuss how organized complexity can be modelled, with an eye to limitations on the tractability of both the models and the modelling process.