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.
Copying errors, it turns out, aren't uncommon and fall into characteristic patterns, such as deletions and duplications-exactly the sorts of mistakes that geneticists have identified in DNA. Using approaches adapted from genetics, paleographers-scientists who study ancient writing-use these accumulated errors to trace the age and origins of a document, much in the same way biologists use the accumulation of genetic mutations to assess how similar two species are to each other. For example, by analyzing the oddities and duplicated errors in the 58 surviving versions of "The Wife of Bath's Prologue" from Chaucer's "Canterbury Tales," researchers deduced the content of the original version.
Mr. Arbesman's interest in the spread of knowledge also leads him to the story of Brontosaurus, the lovable, distinct herbivore we all grew up with—only it never existed. Originally described in 1879 by Othniel Marsh, the Brontosaurus was soon determined to be a type of dinosaur that Marsh had already discovered in 1877, the Apatosaurus. But since the original Apatosaurus was just "a tiny collection of bones," while the Brontosaurus that Marsh named "went on to be supplemented with a complete skeleton, beautiful to behold," the second discovery captured the public's imagination and the name "Brontosaurus" stuck for nearly a century. Only recently has the name "Apatosaurus" started to gain traction.
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.
To cover so much ground in a scant 200 pages, Mr. Arbesman inevitably sacrifices detail and resolution. And to persuade us that facts change in mathematically predictable ways, he seems to overstate the predictive power of mathematical extrapolation. Still, he does show us convincingly that knowledge changes and that scientific facts are rarely as solid as they appear.
In some cases, the facts themselves are variable. For example, the height of Mount Everest changes from year to year, as colliding continental plates push up and erosion wears the mountain down. The mountain even moves laterally at a rate of about six centimeters a year, thus making both its height and location a "mesofact"—a slowly changing piece of knowledge.
More commonly, however, changes in scientific facts reflect the way that science is done. Mr. Arbesman describes the "Decline Effect"—the tendency of an original scientific publication to present results that seem far more compelling than those of later studies. Such a tendency has been documented in the medical literature over the past decade by John Ioannidis, a researcher at Stanford, in areas as diverse as HIV therapy, angioplasty and stroke treatment. The cause of the decline may well be a potent combination of random chance (generating an excessively impressive result) and publication bias (leading positive results to get preferentially published).
If shaky claims enter the realm of science too quickly, firmer ones often meet resistance. As Mr. Arbesman notes, scientists struggle to let go of long-held beliefs, something that Daniel Kahneman has described as "theory-induced blindness." Had the Austrian medical community in the 1840s accepted the controversial conclusions of Dr. Ignaz Semmelweis that physicians were responsible for the spread of childbed fever—and heeded his hand-washing recommendations—a devastating outbreak of the disease might have been averted.
Science, Mr. Arbesman observes, is a "terribly human endeavor." Knowledge grows but carries with it uncertainty and error; today's scientific doctrine may become tomorrow's cautionary tale. What is to be done? The right response, according to Mr. Arbesman, is to embrace change rather than fight it. "Far better than learning facts is learning how to adapt to changing facts," he says. "Stop memorizing things . . . memories can be outsourced to the cloud." In other words: In a world of information flux, it isn't what you know that counts—it is how efficiently you can refresh.