Large interactive systems
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When catastrophe strikes, analysts typically blame some combination of powerful mechanisms. An earthquake is traced to an immense instability along a fault line; a stock market crash is blamed on the destabilizing effect of computer trading. These explanations may well be correct. But systems as large and complicated as the Earth's crust or the stock market can break down not only under the force of a mighty blow but also at the drop of a pin. In a large interactive system, a minor event can start a chain reaction that leads to a catastrophe
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Traditionally, investigators have analyzed large interactive systems in the same way they analyze small orderly systems, mainly because the methods developed for small systems have proved so successful. They believed they could predict the behavior of a large interactive system by studying its elements separately and by analyzing its component mechanisms individually. For lack of a better theory, they assumed that in large interactive systems the response to a disturbance is proportional to that disturbance.
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During the past few decades, however, it has become increasingly apparent that many large complicated systems do not yield to traditional analysis. Consequently, theorists have proposed a “theory of self-organized criticality”: many large interactive systems evolve naturally to a critical state in which a minor event starts a chain reaction that can affect any number of elements in the system. Although such systems produce more minor events than catastrophes, the mechanism that leads to minor events is the same one that leads to major events
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A deceptively simple system serves as a paradigm for self-organized criticality: a pile of sand. As sand is poured one grain at a time onto a flat disk, the grains at first stay close to the position where they land. Soon they rest on top of one another, creating a pile that has a gentle slope. Now and then, when the slope becomes too steep, the grains slide down, causing a small avalanche. The system reaches its critical state when the amount of sand added is balanced, on average, by the amount falling off the edge of the disk
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Now when a grain of sand is added, it can start an avalanche of any size, including a “catastrophic” event. Most of the time the grain will fall so that no avalanche occurs. By studying a specific area of the pile, one can even predict whether avalanches will occur there in the near future. To such a local observer, however, large avalanches would remain unpredictable because they are a consequence of the total history of the entire pile. No matter what the local dynamics are, catastrophic avalanches would persist at a relative frequency that cannot be altered. Criticality is a global property of the sandpile.
