It is summer and many of us are drawn to wander down to the beach. Children happily unpack their buckets and spades, settle close to the water, and build little piles of sand. Gradually the mounds get bigger until—swoosh—avalanches shrink them to near nothing. Undiscouraged, the kids start over again, building more piles until they too are destroyed by avalanches. What a great opportunity for Dad to get his hands dirty and give one of his educational lectures. If only they would pay attention, he groans, surely the kids could succeed in building a higher sandcastle. But what does he know? No matter how careful, sand avalanches always make the piles fall apart. It does not help to allow the sand to run ever so slowly through one’s fingers. Amazingly, avalanches always occur when the piles have reached a certain height.

What hides behind these jolly summer activities is, of course, nothing but a law of physics. Every sand particle has inertia, and the forces at work are gravity and friction. But this alone does not yet explain why avalanches occur. The behavior of sand piles can only be understood by looking at them in their entirety.

Let us first focus on sand at the micro level. Sprinkle grains of sand, one by one, on a table. The grains attempt to reach the lowest level of energy by seeking out the lowest-possible surface. If one carried out the experiment with a fluid, it would spread across the entire tabletop and, eventually, spill over the edge. Grains of sand, however, cling to each other because of friction. So as along as the pile is relatively low, every additional grain will remain on the very spot on which it was dropped. The landing place may happen to be the top of a grain, which in turn may lie on another grain. Once several layers of

grain lie on top of each other, additional grains may slip over the side and, possibly, trigger an avalanche.

Small avalanches, but also big ones, ensure that the steepness of the sand pile does not exceed a certain limit. During experiments scientists observed that the strength of the sand avalanches was governed by a law that Beno Gutenberg and Charles Richter had proposed in the 1950s to describe the occurrence of earthquakes: Quakes of a magnitude of 6 occur 10 times more rarely than those that show a magnitude of 5 on the Richter scale.

The phenomenon of sand avalanches is an example of a so-called self-organized criticality. This phrase was coined by Per Bak, a Danish physicist, in 1988.* Together with Chao Tank and Kurt Wiesenfeld, Bak found that systems which consist of very many nearly identical components spontaneously find a certain state around which they will vary. In the case of sand piles it is the steepness of the flanks that determines the critical state.

Bak and his colleagues formulated their ideas on the subject wholly on a general basis. Hence, their conclusions are not limited to sand piles. Different systems or events such as forest fires, traffic jams, stock market crashes, and evolutionary processes are governed by the same laws.

Take the stock market. An investor, let’s call her Mrs. Wall, could decide to sell her stock once its price reached a certain level. Mr. Street, a colleague who always follows what Mrs. Wall does, decides to follow suit and sell his shares. Others may follow the lead of Wall Street, and this may trigger selling orders of yet more investors. It is quite conceivable that the behavior of only a few investors will cause a selling wave and trigger a collapse of the market. Indeed, statisticians have observed that stock market crashes, some smaller, some bigger, occur at similar frequencies as do the avalanches that destroy the sand piles.

Yet another example of self-organized criticalities is traffic jams. Even before the relaxing vacation on the seaside, one has to brave the journey to the beach. Traffic is

slow but steady. All of a sudden a driver in front of you hits the brakes. If the individual cars do not follow each other at too close a distance, nothing untoward will happen. But just as a single grain of sand may cause an avalanche, so a small braking maneuver by one driver can, if traffic is heavy and cars are dense, cause the dreaded traffic jam. Statistically speaking, the number of cars backed up in a traffic jam is comparable to the size of sand avalanches.