(This is Part 4 of a series. Go back to Part 3.)
To delve into this matter a little further, let's study the work of three nonequilibrium physicists: Per Bak, Chao Tang and Kurt Weisenfeld.
They were thinking about avalanches, the kind that occur on mountains, the kind that occur in scientific revolutions, the kind that occur in earthquakes. A useful analogue, they thought, was the humble sandpile...
Imagine a flat table where we're dropping grains of sand, one at a time. Slowly a sandpile builds up, and slowly, slowly the sides of the sandpile get more steep. In scientific terms, the slope of the sandpile increases.
As the steepness of the sandpile increases the sandpile gets more and more unstable, until finally an "avalanche" occurs—and the sandpile lowers a bit. Then, as grains of sand keep falling onto the pile, it builds up to a higher slope again, only to have another "avalanche," in a rhythm of slowly building and suddenly falling.
Then they got the bright idea of modeling the sandpile on a computer, simulating the sandpile in effect. Now, in the same time that they could do one experiment before, they could do millions and millions of simulations.
And what they found is fascinating. They found that the sandpile slowly built up to a self-organized critical state. That is, the sandpile would eventually reach a point where—because its sides were so steep—it was prone to have an avalanche.
Then they had the computer assign the color green to those grains of sand that were in a stable configuration and the color red to those grains that were in a steep and unstable position.
Now imagine looking down at the sandpile from above. It's mostly green. But as the sandpile grows, red "fingers of instability" form here and there and gradually weave a skeleton of red amongst the green.
They found that if one of these red "fingers of instability" is hit by a falling grain of sand, an avalanche is triggered. But here's the interesting part: The avalanche could be small, medium or large, depending only on the size of the region of instability and whether or not it was connected to other such regions in the sandpile.
To put this another way, the sandpile slowly grows and becomes steeper until it reaches the critical state. Once it is in the critical state, it 1) tends to stay there, and 2) is prone to avalanches of all sizes. These avalanches serve to relieve some of the strain and tension that have built up in the sandpile.
What this means, further, is that large avalanches do not need a large cause. They are part of the normal course of events—something to be expected—and do not need to have some "significant cause." A cataclismic avalanche can be initiated by a single grain of sand.
Finally, the researchers discovered that avalanches in sandpiles follow the same power law that wars and scientific revolutions do, with slightly different numbers. That is, if we double the size of a sandpile avalanche, it occurs 2.14 times less frequently.
Oh, the researchers found one more thing: When they added up the small avalanches which occurred so much more frequently, they didn't amount to much. They were outweighed by the large avalanches. In other words, It was the large avalanches, the large "revolutions" that enabled the sandpile to evolve.
What this means is that it is the large "catastrophes" in a system that, by allowing it to relieve the stresses and strains that have bult up, enable the system to begin another long period of success. It is the "cataclisms" that enable the system to continue its journey up the mountain.
(This is the end of Part 4. Go to Part 5.)
—jim sloman, 2.17.04 for Oct 26
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