When catastrophe strikes, analysts typically blame some combination of powerful mechanisms.

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.

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.

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.

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.

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.

1. The passage provides support for all of the following generalizations about large interactive systems EXCEPT:

(A) They can evolve to a critical state.
(B) They do not always yield to traditional analysis.
(C) They make it impossible for observers to make any predictions about them.
(D) They are subject to the effects of chain reactions.
(E) They are subject to more minor events than major events.

2. According to the passage, the criticality of a sandpile is determined by the

(A) size of the grains of sand added to the sandpile
(B) number of grains of sand the sandpile contains
(C) rate at which sand is added to the sandpile
(D) shape of the surface on which the sandpile rests
(E) balance between the amount of sand added to and the amount lost from the sandpile

3. It can be inferred from the passage that the theory employed by the investigators mentioned in the second paragraph would lead one to predict that which one of the following would result from the addition of a grain of sand to a sandpile?

(A) The grain of sand would never cause anything more than a minor disturbance.
(B) The grain of sand would usually cause a minor disturbance, but would occasionally cause a small avalanche.
(C) The grain of sand would usually cause either minor disturbance or a small avalanche, but would occasionally cause a catastrophic event.
(D) The grain of sand would usually cause a catastrophic event, but would occasionally cause only a small avalanche or an event more minor disturbance.
(E) The grain of sand would invariably cause a catastrophic event.

4. Which one of the following best describes the organization of the passage?

(A) A traditional procedure is described and its application to common situations is endorsed: its shortcomings in certain rare but critical circumstances are then revealed.
(B) A common misconception is elaborated and its consequences are described a detailed example of one of these consequences is then given.
(C) A general principle is stated and supported by several examples; an exception to the rule is then considered and its importance evaluated.
(D) A number of seemingly unrelated events are categorized: the underlying processes that connect them are then detailed.
(E) A traditional method of analysis is discussed and the reasons for its adoption are explained; an alternative is then described and clarified by means of an example.

5. Which one of the following is most analogous to the method of analysis employed by the investigators mentioned in the second paragraph?

(A) A pollster gathers a sample of voter preferences and on the basis of this information makes a prediction about the outcome of an election.
(B) A historian examines the surviving documents detailing the history of a movement and from these documents reconstructs a chronology of the events that initiated the movement.
(C) A meteorologist measures the rainfall over a certain period of the year and from this data calculates the total annual rainfall for the region.
(D) A biologist observes the behavior of one species of insect and from these observations generalizes about the behavior of insects as a class.
(E) An engineer analyzes the stability of each structural element of a bridge and from these analyses draws a conclusion about the structural soundness of the bridge.

6. In the passage, the author is primarily concerned with

(A) arguing against the abandonment of a traditional approach
(B) describing the evolution of a radical theory
(C) reconciling conflicting points of view
(D) illustrating the superiority of a new theoretical approach
(E) advocating the reconsideration of an unfashionable explanation.

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