Brandeis Magazine

In a scene from Woody Allen’s futuristic comedy “Sleeper” (1973), two scientists size up the behavior of a health-food storeowner, played by Allen, who must adapt to a new world after spending 200 years in a deep freeze.

Dr. Melik: This morning for breakfast he requested something called wheat germ, organic honey and tiger’s milk.

Dr. Agon (chuckling): Oh, yes. Those were the charmed substances that some years ago were thought to contain life-preserving properties.

Dr. Melik: You mean there was no deep fat? No steak, or cream pies, or ... hot fudge?

Dr. Agon: Those were thought to be unhealthy ... precisely the opposite of what we now know to be true.

Dr. Melik: Incredible.

You don’t have to awaken from two centuries of cryogenic slumber to feel a bit shaky when bedrock facts — any number of steadfast bits of broadly accepted knowledge — start crumbling beneath you.

For decades, scientists believed the human cell contained 48 chromosomes, not 46. Until a few years ago, Pluto was a planet. Brontosaurus was the beloved herbivore of the Jurassic period — until it turned out to be an apatosaurus, complete with a differently shaped skull.

Facts change all the time. The fact is, facts have an expiration date, says Sam Arbesman ’04, an applied mathematician and network scientist at the Ewing Marion Kauffman Foundation in Kansas City, Mo., and a fellow at Harvard’s Institute for Quantitative Social Science.

Arbesman is a young Turk in the quantitative study of science known as scientometrics. A polymath in an era when much of science is siloed, he is deeply conversant in physics, biology (he holds a PhD in computational biology from Cornell), chemistry, computer science and, of course, mathematics. He spends much of his time at the Kauffman Foundation figuring out how to put science in the service of practical problem solving.

In a new book, “The Half-Life of Facts: Why Everything We Know Has an Expiration Date” (Current, 2012), Arbesman argues that knowledge evolves predictably and systematically — in a nutshell, mathematically. Luckily, you don’t need to be a mathematician to understand his explanation of how facts are tossed out or plowed under to fertilize yet more discoveries.

Knowledge, like radioactivity, has a half-life, says Arbesman. In fact, the best way to think about how knowledge evolves is to start by pondering a chunk of uranium. You can’t predict when a single atom among trillions in a block of uranium will decay — it could be in a fraction of a second or in millions of years. But if you consider all the atoms in the piece of uranium, “the unpredictable becomes predictable,” Arbesman explains, thanks to a rule of probability known as the law of large numbers. (Half of the uranium will break down in 704 million years.)

In the aggregate, facts also have half-lives of sorts. If you consider the body of facts that, say, make up particle physics, or medicine, or computer science, using applied mathematics you can determine when half of the facts in that field will be overturned. The rate of knowledge decay in each field varies. The half-life of information in a physics textbook is about 13 years; the half-life of information in an economics textbook is a bit more than nine years.

“If we can understand how knowledge grows and changes, we can get a better handle on how the world changes,” Arbesman says. For instance, if we understand how medical knowledge evolves, we can better keep up with the latest research. (Warning to medical students: Almost everything you learn about medicine will likely be jettisoned or will need updating in just five years.)

“In the world of business, there’s a lot of rapidly changing information — people often have out-of-date information, and that can affect how they make decisions,” says Arbesman. “For example, there’s a story that the makers of the BlackBerry didn’t believe that the first iPhone was even possible, due to their outdated technological information, and that caught them flat-footed.”

There is broad consensus about what constitutes a fact. “Many of us know a fact when we see one,” Arbesman likes to say, paraphrasing Justice Potter Stewart’s famous comment about pornography. Nevertheless, many, maybe all, of us suffer from some degree of factual inertia — a tendency to ignore information that does not fit into our worldview — or its flip side, a penchant for accepting only facts that confirm our outlook.

Several examples in “The Half-Life of Facts” give the “facts are stubborn things” saying a deadly dimension. For instance, Ignaz Semmelweis, a young obstetrician in 1840s Vienna, observed that women who had their babies in a hospital, attended by obstetricians who also conducted autopsies, suffered greater rates of childbed fever than women who delivered at home or used midwives in the hospital. Patients of obstetricians who did not perform autopsies also had lower rates of the often-fatal disease.

The eagle-eyed physician suggested that doctors performing autopsies and deliveries scrub their hands before undertaking the latter task. “It lowered the cases of childbed fever to one-tenth the original number,” writes Arbesman.

In return for this stunningly simple yet brilliant suggestion, Semmelweis was ostracized by his fellow doctors, who still subscribed to the miasma theory of disease. The germ theory of disease wouldn’t gain currency for several decades.

“Skepticism is good, but when it overwhelms your ability to examine things critically, it can be dangerous,” notes Arbesman.

An optimist by nature, Arbesman believes our exploding knowledge, fueled in part by colossal, growing computing power, is leading to a deeper understanding of the world.

“That said, anytime someone says that we’re finished learning new things, they’re almost certainly wrong,” he asserts. “There always seems to be more to learn, and if we can understand the regularities behind this fact, we’ll be better prepared for dealing with the rapid change around us.”