(This is Part 3 of a series. Go back to Part 2.)
The San Andrea Fault runs north-south through the western edge of California. This long line, visible from the air, marks the boundary between two tectonic plates—the North American Plate, underlying North America, and the Pacific Plate, underlying the Pacific Ocean.
These two plates are sliding against each other. The Pacific Plate is moving northward two to three centimeters per year relative to the North American Plate, which is simultaneously moving southward.
This motion against each other isn't usually apparent, because the two plates tend to stick together by friction. However, as the one plate moves north and the other south, tension and stress build up along the boundary line. When this stress is great enough the two plates slip against each other: an event we call an "earthquake."
Note the similarity to the slow build-up of financial stress in an empire, followed by the relatively rapid collapse. Notice too the similarity to the slow build-up of stresses of discrepancy in a successful paradigm, followed by the rapid resolution of the stress in a scientific revolution.
In the 1950s, seismologists Beno Gutenberg and Charles Richter were attempting to establish the average size of an earthquake. After all, there was an average size for apples, test scores, the heights of human beings and so on. And so they measured how many earthquakes there were of magnitude 2, magnitude 3, magnitude 4 and so on.
And what they found astonished them. There was no average size for earthquakes! There were thousands of small ones, a lesser number of middle-size ones and a few large ones.
In fact, they found that the size of earthquakes followed a law known to mathematicians as a power law. This law, now known as the Gutenberg-Richter Law, states that when you double the energy of an earthquake it happens four times less frequently.
What's remarkable about the Gutenberg-Richter Law is that it holds for quakes over a range of sizes exceeding a million to one. That is, the law is scale invariant—it holds for small earthquakes just as much as for middle-range or gigantic ones.
Since earthquakes and the sudden falling of empires have a certain similiarity, the British physicist Leslie Richardson decided to see if a power law might apply to the various wars attendent upon nations and empires jockeying for power.
To measure the size of a war, Richardson used a grim statistic: the number of war deaths. And he found another amazing power law: If you double the size of the war, it becomes four times less common. And this applied to all sizes of wars!
What makes this remarkable is that phenomena which exist on a power law are "expected" to have large events. Large events are no more unusual than small ones; it's just that the large ones occur less frequently. As the size goes up the frequency goes down, and vice-versa, all on a smooth mathematical curve.
This in spite of the fact that wars are undertaken for all sorts of different historical reasons. Behind this apparent chaos of varying incidents and differing motivations is apparently a deep natural order.
Meanwhile, the physicist Sidney Redner wondered if there was some way to measure the size of scientific revolutions. And he came up with an ingenious way:
All scientists publish research papers detailing their findings or insights in a particular area. And at the end each paper has a number of citations, references to earlier papers. Redner realized that the number of times a particular paper was cited was reflective of its importance.
The Science Citation Index is a resource listing all the citations that any scientific research paper ever received. Using this data, Redner measured how often a given paper was cited. And what he found was, again, amazing: He found that the number of citations followed a power law!
Redner's Law is as follows: It states that as we double the number of citations (that a given paper receives) the number of papers receiving that many citations is reduced by a factor of eight.
The implications of this are that scientific revolutions themselves follow a smooth mathematical power law, meaning that large scientific revolutions do not need exceptional reasons to occur. They are to be expected from time to time.
Like wars and earthquakes then, scientific revolutions partake of a natural process where, following a smooth mathematical curve, events of all different magnitudes—including gigantic ones from time to time—are normal.
Good. But what does that have to do with you and me?
(This is the end of Part 3. Go to Part 4.)
—jim sloman, 2.16.04 for Oct 2
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