WHAT MAKES HISTORY TICK?

We have no idea, and neither has anybody else, but Prof. Marchetti, well known to our readers for his simple and accurate formula for the growth, culmination and decline of energy sources in history [Apr. 78, Sept. 80], has found a neat way of describing the clockwork of the cycles of technical innovation. It seems that they click in synchronization with the culmination of certain energy sources.

Marchetti's Law says that energy sources develop along a learning curve; now he says that much of society does, too.

A learning curve (and readers who complain that this newsletter is 'too technical,' please just take it as some easily plotted curve and skip this paragraph) is one that describes the accumulation of knowledge in time as one learns a certain realm of facts. The speed of discovery is proportional to the facts already known, because they facilitate the search, but it also slows with the number of undiscovered facts, because they become harder to find as fewer of them are left. Where that statement is translated from English into mathematics, it results in a differential equation whose solution is log[F/(1 - F)] = at + b, where F is the fraction of the total learned, t is time, and a, b are constants. That is a straight line if plotted on logarithmic paper, and all that is needed is one point and the slope of the line to forecast the process.

For example, the number of chemical elements discovered through the 18^th and 19^th centuries follows the curve pretty well. But as is usual with simple formulas, a learning curve applies also to other processes. For example, epidemics spread that way. Just substitute healthy and infected for unknown and known fact in the reasoning above). In the 1950's it was found that a better product displaces its competitor's market that way, and Marchetti, slightly modifying the law for several competitors at a time, found that energy sources follow the curve quite well, haughtily ignoring such trifles as two world wars or the Arab oil embargo.

Marchetti defines an innovation as something that starts a brand-new industry; it is preceded by several discoveries. For example, the discovery of the steam engine (1769) and several others led to the innovation of the first factory for railroad engines (England, 1824). other examples of innovations in this sense are pedal bicycle, blast furnace, telegraph, food preservatives, dynamite, and the gasoline engine.