Fractal Figure 1a. The Mandelbrot set illustrates self-similarity. As the image is enlarged, the same pattern re-appears so that it is virtually impossible to determine the scale being examined. Figure 1b. The same fractal magnified six times. Figure 1c. Figure 1d. Fractals are distinguished from regular geometric figures by their fractal dimensional scaling. As mathematical equations, fractals are usually nowhere differentiable. An infinite fractal curve can be conceived of as winding through space differently from an ordinary line, still being a 1-dimensional line yet having a fractal dimension indicating it also resembles a surface.:48:15 There is some disagreement amongst authorities about how the concept of a fractal should be formally defined. Introduction The word "fractal" often has different connotations for laypeople than mathematicians, where the layperson is more likely to be familiar with fractal art than a mathematical conception. History Figure 2.
ParadigmOfComplexity The last few decades have seen the emergence of a growing body of literature devoted to a critique of the so-called “old” or “Cartesian-Newtonian” paradigm which, in the wake of the prodigious successes of modern natural science, came to dominate the full range of authoritative intellectual discourse and its associated worldviews. Often coupled with a materialistic, and indeed atomistic, metaphysics, this paradigm has been guided by the methodological principle of reductionism. The critics of reductionism have tended to promote various forms of holism, a term which, perhaps more than any other, has served as the rallying cry for those who see themselves as creators of a “new paradigm.” At the forefront of such a challenge, and in many ways the herald of the new paradigm, is the relatively new movement of transpersonal psychology. In taking seriously such experiences, transpersonal theory has been compelled to transcend the disciplinary boundaries of mainstream psychology. C.
The human microbiome: Me, myself, us WHAT’S a man? Or, indeed, a woman? Biologically, the answer might seem obvious. A human being is an individual who has grown from a fertilised egg which contained genes from both father and mother. A growing band of biologists, however, think this definition incomplete. They see people not just as individuals, but also as ecosystems. A healthy adult human harbours some 100 trillion bacteria in his gut alone. And it really is a system, for evolution has aligned the interests of host and bugs. That bacteria can cause disease is no revelation. A bug’s life One way to think of the microbiome is as an additional human organ, albeit a rather peculiar one. The microbiome, too, is organised. Specialised; but not monotonous. That detail is significant. This early nutritional role, moreover, is magnified throughout life. The fat of the land This role in nutrition points to one way in which an off-kilter microbiome can affect its host: what feeds a body can also overfeed or underfeed it.
Complexity: It’s Not That Simple Complexity theory has been around for a generation now, but most people don’t understand it. I often read or listen to consultants, ‘experts’ and media people who proffer ludicrously simplistic ‘solutions’ to complex predicaments. Since it seems most people would prefer things to be simple, these ‘experts’ always seem to have an uncritical audience. Complexity theory argues that simple, complicated, complex and chaotic systems have fundamentally different properties, and therefore different approaches and processes are needed when dealing with issues and challenges in each of these types of systems. As the diagram above illustrates, natural systems (both social and ecological) are inherently complex. Human invention, for the most part, uses biomimicry, i.e. we attempt to manufacture, to replicate mechanically, things that appear to work in nature. Natural systems are highly effective but inefficient due to their massive redundancy (picture a tree dropping thousands of seeds).
Think Complexity by Allen B. Downey Buy this book from Amazon.com. Download this book in PDF. Read this book online. Description This book is about complexity science, data structures and algorithms, intermediate programming in Python, and the philosophy of science: Data structures and algorithms: A data structure is a collection that contains data elements organized in a way that supports particular operations. This book focuses on discrete models, which include graphs, cellular automata, and agent-based models. Complexity science is an interdisciplinary field---at the intersection of mathematics, computer science and physics---that focuses on these kinds of models. Free books! This book is under the Creative Commons Attribution-NonCommercial 3.0 Unported License, which means that you are free to copy, distribute, and modify it, as long as you attribute the work and don't use it for commercial purposes. Download the LaTeX source code (with figures and a Makefile) in a zip file.
Human Systems Dynamics Intelligent Complex Adaptive Systems I don’t believe in the existence of a complex systems theory as such and, so far, I’m still referring to complex systems science (CSS) in order to describe my research endeavours. In my view, the latter is constituted, up until now, by a bundle of loosely connected methods and theories aiming to observe— from contrasted standpoints—these fascinating objects of research called complex adaptive systems. Nearly 40 years after Von Bertalanffy’s General System Theory (1968) and Jacques Monod’s Chance and Necessity (1971), it is fair to look back and to try to assess how much remains to be said about these complex adaptive systems. After all, Prigogine’s Order out of Chaos (1984) already demonstrated that future wasn’t entirely predictable in a history- contingent world. The universe is a massive system of systems -- for example, ecological systems, social systems, commodity and stock markets.
- Glossary of Terms Category: Resources Posted by: Aaron and Ken The following definitions are brief, loose, and approximate. But despite these features, they should give readers a decent understanding of what we mean when we use these terms. Is there a term you would like to see here? Adaptive system engineering- the general enterprise of engineering a system to be adaptable. Applies, Fails to Apply, or Does not Apply- This is an important distinction in philosophy. Autocatalytic Set- An collection of entities (molecules, people, nations, institutions, whatever) that produces as outputs the same elements which are necessary inputs for expanding the collection. Autopoietic Set- Autopoiesis is the process of dynamics self-maintenance. Building Block- When parts of a collection organize themselves into patterns that we recognize as coherent phenomena then we say that it is an emergent phenomena. Complicated- Sometimes complication is considered a degenerate concept to complexity. Phylogenetic Tree-.
Complex systems made simple Albert-László Barabási and Yang-Yu Liu, together with their collaborator Jean-Jacques Slotine at M.I.T., have developed a method for observing large, complex systems. In the image above, red dots represent sensor nodes, which are required to reconstruct the entire internal state of one such system. Image by Mauro Martino. Just as the name implies, complex systems are difficult to tease apart. But that may not matter anymore. The approach takes advantage of the interdependent nature of complexity to devise a method for observing systems that are otherwise beyond quantitative scrutiny. “Connectedness is the essence of complex systems,” said Albert-László Barabási, one of the paper’s authors and a Distinguished Professor of Physics with joint appointments in biology and the College of Computer and Information Science. Using their novel approach, the researchers first identify all the mathematical equations that describe the system’s dynamics.
Activités - Chaire Edgar Morin de la Complexité Le programme des activités de la chaire Edgar Morin de la Complexité doit permettre : d’interroger le sens de la complexité du point de vue des disciplines de gestion et de quelques problématiques directrices des préoccupations de l’ESSEC (entrepreneuriat, business in society, etc).d’expliciter les enjeux de l’appréhension d’un environnement interne et externe complexe pour les praticiensexaminer les méthodes d’approche et de traitement de la complexité sur le terrainde considérer les qualités, compétences, savoir-faire requis pour gérer la complexité au sein des organisations sur les plans du management et du leadership individuel et collectif Quelques activités de la chaire dans ce contexte : les « Mises en boîtes » : présentation par des professeurs de l'ESSEC de leur vision et compréhension de la complexité au travers de certains de leurs résultats de recherche.
Observability of complex systems Author Affiliations Edited by Giorgio Parisi, University of Rome, Rome, Italy, and approved December 26, 2012 (received for review September 6, 2012) Abstract A quantitative description of a complex system is inherently limited by our ability to estimate the system’s internal state from experimentally accessible outputs. Footnotes Author contributions: Y.