FAITH IS ALL THERE IS:

In 1870, German chemist Erich von Wolf analyzed the iron content of green vegetables and accidentally misplaced a decimal point when transcribing data from his notebook. As a result, spinach was reported to contain a tremendous amount of iron--35 milligrams per serving, not 3.5 milligrams (the true measured value). While the error was eventually corrected in 1937, the legend of spinach's nutritional power had already taken hold, one reason that studio executives chose it as the source of Popeye's vaunted strength.

The point, according to Samuel Arbesman, an applied mathematician and the author of the delightfully nerdy "The Half-Life of Facts," is that knowledge--the collection of "accepted facts"--is far less fixed than we assume. In every discipline, facts change in predictable, quantifiable ways, Mr. Arbesman contends, and understanding these changes isn't just interesting but also useful. For Mr. Arbesman, Wolf's copying mistake says less about spinach than about the way scientific knowledge propagates. [...]

Knowledge, then, is less a canon than a consensus in a state of constant disruption. Part of the disruption has to do with error and its correction, but another part with simple newness--outright discoveries or new modes of classification and analysis, often enabled by technology. A single chapter in "The Half-Life of Facts" looking at the velocity of knowledge growth starts with the author's first long computer download--a document containing Plato's "Republic"--journeys through the rapid rise of the "@" symbol, introduces Moore's Law describing the growth rate of computing power, and discusses the relevance of Clayton Christensen's theory of disruptive innovation. Mr. Arbesman illustrates the speed of technological advancement with examples ranging from the magnetic properties of iron--it has become twice as magnetic every five years as purification techniques have improved--to the average distance of daily travel in France, which has exponentially increased over the past two centuries.

Follow @brothersjudd