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.