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. The same fractal magnified a hundred times. 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 This also leads to understanding a third feature, that fractals as mathematical equations are "nowhere differentiable". History Figure 2. Figure 3. Characteristics Emergence. In philosophy, systems theory, science, and art, emergence is a process whereby larger entities, patterns, and regularities arise through interactions among smaller or simpler entities that themselves do not exhibit such properties. Emergence is central in theories of integrative levels and of complex systems. For instance, the phenomenon life as studied in biology is commonly perceived as an emergent property of interacting molecules as studied in chemistry, whose phenomena reflect interactions among elementary particles, modeled in particle physics, that at such higher mass—via substantial conglomeration—exhibit motion as modeled in gravitational physics.
Neurobiological phenomena are often presumed to suffice as the underlying basis of psychological phenomena, whereby economic phenomena are in turn presumed to principally emerge. In philosophy, emergence typically refers to emergentism. In philosophy Main article: Emergentism Definitions Strong and weak emergence 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.
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. In their view, the descendant of the fertilised egg is merely one component of the system. The others are trillions of bacteria, each equally an individual, which are found in a person’s gut, his mouth, his scalp, his skin and all of the crevices and orifices that subtend from his body’s surface. 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. The Human Genome Is Far More Complex Than Scientists Thought. 100 Very Cool Facts About The Human Body. The Brain The human brain is the most complex and least understood part of the human anatomy. There may be a lot we don’t know, but here are a few interesting facts that we’ve got covered.
Nerve impulses to and from the brain travel as fast as 170 miles per hour. Ever wonder how you can react so fast to things around you or why that stubbed toe hurts right away? It’s due to the super-speedy movement of nerve impulses from your brain to the rest of your body and vice versa, bringing reactions at the speed of a high powered luxury sports car.The brain operates on the same amount of power as 10-watt light bulb. The cartoon image of a light bulb over your head when a great thought occurs isn’t too far off the mark. Hair and Nails While they’re not a living part of your body, most people spend a good amount of time caring for their hair and nails. Facial hair grows faster than any other hair on the body. Internal Organs The largest internal organ is the small intestine. Bodily Functions Senses.
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. Because most of what’s written about complexity theory is dense, academic and/or expensive, I thought I’d try to summarize the key points of complexity theory (focusing on the social/ecological aspects of it, not the mathematical/scientific ones) using lots of examples for clarity, and in a way that might be used practically by those grappling with complex issues and challenges.
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. Simplexity. Simplexity is an emerging theory that proposes a possible complementary relationship between complexity and simplicity. The term draws from General Systems Theory, Dialectics (philosophy) and Design.
Jeffrey Kluger wrote a book about this phenomenon that describes how house plants can be more complicated than industrial plants, how a truck driver's job can be as difficult as a CEO's and why 90% of the money donated to help cure diseases are given only to the research of 10% of them (and vice versa). The term has been adopted in advertising, marketing and the manufacture of left-handed screwdrivers. Design aspects Complexity tends to rise as system elements specialize and diversify to solve specific challenges.Simple interfaces tend to improve the usability of complex systems. History of the term Like most terms, it has been shaped through dialogues and discussions, in much the same way that a camel is a horse designed by committee. Education In science References 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. Why we hate Complexity. Natural and social systems are complex — that is, not entirely knowable, unpredictable, resistant to cause-and-effect analysis, in a word, mysterious.
For our first three million years on Earth we humans, like every other species on the planet, accepted that mystery. We adapted rather than trying to change our environment. We evolved by learning to accommodate ourselves to our environment. Those unable to accommodate perished. But with the invention of civilization, we stopped accommodating change and started imposing it on our environment so we wouldn’t have to change.
The problem is, our brains are severely limited in what they are capable of understanding. Once we invented civilization, and started to need to change our environment a lot, we needed to invent science. Even scientists loathe the imperfections in their models. One of the principles that stresses scientists, mathematicians, philosophers and theologists the most is the concept of infinity. Why? Morphological analysis (problem-solving) Morphological Analysis or General Morphological Analysis is a method developed by Fritz Zwicky (1967, 1969) for exploring all the possible solutions to a multi-dimensional, non-quantified complex problem. General Morphology was developed by Fritz Zwicky, the Bulgarian-born, Swiss-national astrophysicist based at the California Institute of Technology.
Among others, Zwicky applied Morphological Analysis (MA) to astronomical studies and the development of jet and rocket propulsion systems. As a problem-structuring and problem-solving technique, MA was designed for multi-dimensional, non-quantifiable problems where causal modeling and simulation do not function well, or at all. Consider a complex, real-world problem, like those of marketing or making policies for a nation, where there are many governing factors, and most of them cannot be expressed as numerical time series data, as one would like to have for building mathematical models. Ritchey, T. (1998). The Art of Complex Problem Solving.
Six degrees of separation. Six degrees of separation. Early conceptions Shrinking world Theories on optimal design of cities, city traffic flows, neighborhoods and demographics were in vogue after World War I. These conjectures were expanded in 1929 by Hungarian author Frigyes Karinthy, who published a volume of short stories titled Everything is Different. One of these pieces was titled "Chains," or "Chain-Links. " As a result of this hypothesis, Karinthy's characters believed that any two individuals could be connected through at most five acquaintances. A fascinating game grew out of this discussion. This idea both directly and indirectly influenced a great deal of early thought on social networks.
Small world Milgram continued Gurevich's experiments in acquaintanceship networks at Harvard University in Cambridge, Massachusetts, U.S. Milgram's article made famous his 1967 set of experiments to investigate de Sola Pool and Kochen's "small world problem. " Research John L. 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. An organism’s genome, a biochemical reaction, or even a social network all contain many interdependent components—and changing any one of them can have pervasive effects on all the others. 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. Using their novel approach, the researchers first identify all the mathematical equations that describe the system’s dynamics. 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.
Although the simultaneous measurement of all internal variables, like all metabolite concentrations in a cell, offers a complete description of a system’s state, in practice experimental access is limited to only a subset of variables, or sensors. Footnotes Author contributions: Y.
Complex Adaptive Systems. Chardin & The NooSphere. Unification of Science and Spirit: Chapter 6 - MIND AS A COMPLEX SYSETM. Chapter 6 Among my many memories of early childhood, a few stand out with particular vigor. First and foremost, there is Neil Armstrong walking on the moon -- this was around the time of my second birthday, but I remember it as well as anything I've watched on TV since. I understood where the moon was -- way up in the sky -- and that this man, dressed in a funny suit, was walking on it, having just flown there in something faster than an airplane.
I was puzzled by "One small step for a man, one great leap for mankind" -- I concluded, not unreasonably, that a "mankind" was some kind of miniature human being, perhaps a sort of midget-monkey hybrid. Another glowingly vivid memory, from a couple years later, is watching my mother roll out of the hospital in a wheelchair, holding my newborn baby sister in her arms.
Every day I would go over to her crib and watch the baby. I asked a lot of questions, but no one had any answers. I remember one moment in great detail, a sort of "Eureka! " Nonlinear Dynamics and Chaos - Steven Strogatz, Cornell University. This course of 25 lectures, filmed at Cornell University in Spring 2014, is intended for newcomers to nonlinear dynamics and chaos.
It closely follows Prof. Strogatz's book, "Nonlinear Dynamics and Chaos: With Applications to Physics, Biology, Chemistry, and Engineering. " The mathematical treatment is friendly and informal, but still careful. Analytical methods, concrete examples, and geometric intuition are stressed. This course of 25 lectures, filmed at Cornell University in Spring 2014, is intended for newcomers to nonlinear dynamics and chaos.
Network Science. Manuel Lima on the Power of Knowledge Networks in the Age of Infinite Connectivity. Wikipedia_as_a_complex_system.pdf. [1303.3891] Quantum Google in a Complex Network. CS edu & refs... Global Dynamics Processes: the Pattern which Connects from KaliYuga to Tao. Complexity and the philosophy of becoming.
Unification of Science and Spirit: Chapter 5 - THE COMPLEX, CHAOTIC WORLD. CS publications. Think Complexity. Think Complexity. Ecologyfj. Complexity. ComplexSystems. COMPLEXITY GRAPHICS. Links - ISC CNR. How the Downs-Thomson Paradox will ruin your commute. Eric Berlow: How complexity leads to simplicity. George Whitesides: Toward a science of simplicity.