It’s an irony of modern life that the exponential spread of information has given rise to another exponential spread, of books about the exponential spread of information. We’ve got more facts than we ever had before, and so we’ve got more ruminations on how those facts affect us. Does Google make us stupid, or has it given us a deeper knowledge? Is there now so much to read and learn that we’ll never master anything (a concern that dates back at least 800 years)? Are all these facts disposable, such that what we learn today will be obsolete tomorrow?
The Harvard network scientist and pop theorist Samuel Arbesman stokes our fears of information on the cover of his recent book, The Half-Life of Facts: Why Everything We Know Has an Expiration Date. Watch out, that title says: The truth is melting! But the argument that Arbesman lays out (in a set of loosely connected anecdotes and essays) works to do the opposite. He uses math as a medication for this anxiety, to keep us calm in the face of shifting knowledge. His book works like a data-beta-blocker: By fitting fickle truths to models and equations, it promises a way to handle life’s uncertainty and keep abreast of “the vibrations in the facts around us.” In the end, though, the prescription runs afoul of a more fundamental ambiguity: What does it mean to call a fact a fact to start with?
Arbesman’s book expands on a piece he wrote in 2010 for the Ideas section of the Boston Globe. That short essay, called “Warning: Your reality is out of date,” laid out a theory of what Arbesman named the mesofact. “When people think of knowledge,” he wrote, “they generally think of two sorts of facts.” One includes the data that should never change, like the atomic weight of hydrogen, while the other comprises all the tidbits that shift from day to day, like the closing price of the Dow Jones Industrial Average. Even in the stable camp, facts can mutate: An atom’s weight, for example, varies depending on the isotope. But Arbesman is more interested in a third category of knowledge, one that’s nestled between the other two in terms of how amenable it is to change. These are the facts that shift too slowly for us to notice, but not so slowly that they’ll only matter to our children. “Mesofacts,” he says, evolve within our lifetimes but often out of view.
Mesofacts are the hardest to keep track of, as we have a natural inclination to assume that much of what we learned in school would hold forever true. That means they’re just the things we ignore and overlook, leaving us misinformed about the world. Add in the changing fact(!) that there are now more new facts than there were before, and that many of these facts are different, and the problem of the mesofact seems bigger still. But Arbesman hopes to teach us to navigate this blind spot by acknowledging that it’s there. If we learn to think about these things that transform behind our backs—if Arbesman can succeed in “raising awareness of the middle category of facts,” as he promises on a website he’s set up called Mesofacts.org—then we’ll be able to expand our minds and fix the world and …
Well, I’m not sure what else. It’s still a little vague, and even after reading The Half-Life of Facts, I haven’t fully grasped the real-world stakes involved. What’s clear enough is that the science of mesofacts offers a certain kind of comfort. Instead of showing all this information as a creepy, growing thing, fanning out down paths we’ll never follow, Arbesman turns data-spread into something clean and geological—a hard science with hard laws. Facts, he says, crumble according to the rules of mathematics, and though these changes may be susceptible to landslides or tectonic shifts (the invention of the printing press, the theory of evolution, etc.), their changing composition can be understood and explicated.
For example, studies show that the “half-life” of a scientific paper—that is to say, the time it takes to lose half its influence in the field, in terms of how often it gets cited—can be described with some precision. A study in a physics journal loses half its value at a period of 10 years, he says, while the similar decay in urology goes a little faster, at 7.1 years. Or here’s another stat: About half the facts we know about the treatment of cirrhosis or hepatitis are rendered obsolete every 45 years.
These rules don’t just apply to specialists. One of the most book’s most charming observations concerns the rate at which the rest of us, the nonscientists, figure out that what we thought we knew was wrong. Certain schoolroom facts, says Arbesman, like the fleshy forms of dinosaurs, tend to shift just once per generation. That’s because what we learn about these animals gets baked in by our grade-school teachers. If paleontologists make a new discovery—let’s say, that dinosaurs had feathers—we may not hear about it until our own kids bring the news home from school. I’m guessing something similar might apply to culture, too: How many people raised on George Romero would have to learn about the changing speed of zombies from their children, too?
But what solace the math provides can seem a little slippery. The half-lives and other laws that Arbesman gives have their own propensity to shift and slide. For example, many of the relationships are of a certain shape: The importance (or truth-value) of a given scientific finding will tend to fall along a curvy slope that can be described by a decaying exponential function. Likewise, citing the work of Derek J. de Solla Price, Arbesman points out that the body of scientific work—the number of new findings, or papers published—increases in a similar way, by rising up an exponential. (These two findings, about the decay of science facts and the growth of scientific output, are closely related: With each new discovery, an older understanding is often overturned or made irrelevant, so an increase in discoveries corresponds to an increase in fact-obsolescence.)
Yet not every evolution of a fact can be described with an exponential function. Arbesman explains that some specimens of truth (or technology, or trivia) develop according to what’s called a logistic function, an S-shaped curve that starts off looking exponential but flattens on both ends. A population of bacteria cultured in a dish will grow along these lines, dividing freely until the organisms approach a natural limit—a point at which their numbers are restricted by space or nutrients. Arbesman gives an example in his book of the rate at which documents from the Early Middle Ages were duplicated or destroyed. The researcher he cites chose to model this relationship as a logistic function, because, says Arbesman, “books cannot grow without a bound” and there is a “maximum number of copies of a book that can be made.” But it’s not clear why this would be the case. Does he mean that the medieval scribes would run out of ink or paper? Or that they’d just decide, one day, that they’ve made enough transcriptions?
There may be a good reason to assume a logistic function in this case, but the example makes it clear that the predictability of changing facts can itself be unpredictable. In 1963, Derek J. de Solla Price wrote up his research on the growth of science and concluded that his exponential function could not describe the future. Since the number of scientists was growing more quickly than the population, at some point we’d reach a saturation point where everyone in the world had become a scientist. Since that would be impossible, he proposed the curve would have to shift from exponential to logistic.
I don’t think that Arbesman would disagree, but the realization that these curves can change would seem to complicate the rules of mesofacts. There are even cases when one exponential rise or fall nests inside another, making it harder still to figure out what’s going on. Take last week’s publication of an important study on fraud in the scientific literature. The authors went through about 2,000 papers that had been retracted from biomedical research journals since the early 1970s, and found that the rate of scientific crimes has been sharply on the rise. In fact, cases of suspected fraud, plagiarism and duplicate publication appear to be rising exponentially, even as a percentage of the total output of scientific papers (which, of course, is also rising exponentially). So what does all this mean for the half-life of a scientific fact? Is it speeding up or slowing down? And how does knowing these relationships help me to handle the uncertainty?
Arbesman wants to calm us with the notion that the facts of how facts change are constant and predictable. It’s an appealing notion, and one he’s illustrated with an array of intriguing mesofacts. But knowing what we know, the book leaves an open question: Can you ever really trust a mesofact about a mesofact? That’s where this anxious reader starts to chew his fingernails. The Half-Life of Facts may be fascinating, but won’t it have a half-life, too?
The Half-Life of Facts: Why Everything We Know Has an Expiration Date by Samuel Arbesman. Current.