Highlights
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René Descartes, one of reductionism’s earliest proponents, described his own scientific method thus: “to divide all the difficulties under examination into as many parts as possible, and as many as were required to solve them in the best way” and “to conduct my thoughts in a given order, beginning with the simplest and most easily understood objects, and gradually ascending, as it were step by step, to the knowledge of the most complex.”
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twentieth-century science was also marked by the demise of the reductionist dream. In spite of its great successes explaining the very large and very small, fundamental physics, and more generally, scientific reductionism, have been notably mute in explaining the complex phenomena closest to our human-scale concerns.
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By the mid-twentieth century, many scientists realized that such phenomena cannot be pigeonholed into any single discipline but require an interdisciplinary understanding based on scientific foundations that have not yet been invented. Several attempts at building those foundations include (among others) the fields of cybernetics, synergetics, systems science, and, more recently, the science of complex systems.
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neuroscience, which actually focused on those brain cells, had very little understanding of how thinking arises from brain activity. It was becoming clear that the reductionist approach to cognition was misguided—we just couldn’t understand it at the level of individual neurons, synapses, and the like.
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How is it that those systems in nature we call complex and adaptive—brains, insect colonies, the immune system, cells, the global economy, biological evolution—produce such complex and adaptive behavior from underlying, simple rules? How can interdependent yet self-interested organ
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sms come together to cooperate on solving problems that affect their survival as a whole? And are there any general principles or laws that apply to such phenomena? Can life, intelligence, and adaptation be seen as mechanistic and computational? If so, could we build truly intelligent and living machines? And if we could, would we want to?
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Each individual ant is nearly blind and minimally intelligent, but the marching ants together create a coherent fan-shaped mass of movement that swarms over, kills, and efficiently devours all prey in its path.
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“If 100 army ants are placed on a flat surface, they will walk around and around in never decreasing circles until they die of exhaustion.” Yet put half a million of them together, and the group as a whole becomes what some have called a “superorganism” with “collective intelligence.”
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First, neither a single science of complexity nor a single complexity theory exists yet
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DYNAMICAL SYSTEMS THEORY (or dynamics) concerns the description and prediction of systems that exhibit complex changing behavior at the macroscopic level, emerging from the collective actions of many interacting components
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The mathematician Pierre Simon Laplace saw the implication of this clockwork view for prediction: in 1814 he asserted that, given Newton’s laws and the current position and velocity of every particle in the universe, it was possible, in principle, to predict everything for all time. With the invention of electronic computers in the 1940s, the “in principle” might have seemed closer to “in practice.”
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The possibility of sensitive dependence on initial conditions was proposed by a number of people long before quantum mechanics was invented. For example, the physicist James Clerk Maxwell hypothesized in 1873 that there are classes of phenomena affected by “influences whose physical magnitude is too small to be taken account of by a finite being, [but which] may produce results of the highest importance.”
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The defining idea of chaos is that there are some systems—chaotic systems—in which even minuscule uncertainties in measurements of initial position and momentum can result in huge errors in long-term predictions of these quantities. This is known as “sensitive dependence on initial conditions.”
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the “many body” problem: predicting the future positions of arbitrarily many masses attracting one another under Newton’s laws. This problem was inspired by the question of whether or not the solar system is stable: will the planets remain in their current orbits, or will they wander from them? Poincaré started off by seeing whether he could solve it for merely three bodies.
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He did not completely succeed—the problem was too hard. But his attempt was so impressive that he was awarded the prize anyway. Like Newton with calculus, Poincaré had to invent a new branch of mathematics, algebraic topology, to even tackle the problem. Topology is an extended form of geometry, and it was in looking at the geometric consequences of the three-body problem that he discovered the possibility of sensitive dependence on initial conditions. He summed up his discovery as follows:
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If we knew exactly the laws of nature and the situation of the universe at the initial moment, we could predict exactly the situation of that same universe at a succeeding moment. But even if it were the case that the natural laws had no longer any secret for us, we could still only know the initial situation approximately. If that enabled us to predict the succeeding situation with the same approximation, that is all we require, and we should say that the phenomenon has been predicted, that it is governed by laws. But it is not always so; it may happen that small differences in the initial conditions produce very great ones in the final phenomenon. A small error in the former will produce an enormous error in the latter. Prediction becomes impossible…
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over the last decade or so, a growing group of applied mathematicians and physicists have become interested in developing a set of unifying principles governing networks of any sort in nature, society, and technology. The seeds of this upsurge of interest in general networks were planted by the publication of two important papers in the late 1990s: “Collective Dynamics of ‘Small World Networks’ ” by Duncan Watts and Steven Strogatz, and “Emergence of Scaling in Random Networks” by Albert-László Barabási and Réka Albert. These papers were published in the world’s two top scientific journals, Nature and Science, respectively, and almost immediately got a lot of people really excited about this “new” field. Discoveries about networks started coming fast and furiously.
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In science, network thinking is providing a novel language for expressing commonalities across complex systems in nature, thus allowing insights from one area to influence other, disparate areas. In a self-referential way, network science itself plays the role of a hub—the common connection among otherwise far-flung scientific disciplines.