Proofiness - Charles Seife [8]
If you listen carefully enough, numbers tell you that they’re only approximations. They reveal their limitations—better yet, they tell you how far to trust them. This information is encoded in the way we talk about numbers; it’s already second nature to you, even though you might not recognize it. When someone declares that a pencil is 150.112 millimeters long, you automatically assume that the measurement is extremely precise. On the other hand, if he says it is 150 millimeters long, you would assume that the measurement is much rougher. Nice round numbers are sending a subliminal signal that their associated measurements have large errors—the numbers are announcing that you can’t trust them very far because they’re crude approximations. Long, ultra-specific numbers send exactly the opposite message: that they come from measurements that are more trustworthy and closer to absolute truth. All real-world numbers behave like this. When someone tells you that his car cost $15,000, you automatically assume that there’s quite a bit of slop in the figure—the real cost was somewhere in the ballpark of fifteen grand, give or take a few hundred dollars. Yet if someone says that his car cost $15,232, you then assume that this was the precise amount he paid, give or take a few pennies. Similarly, if someone tells you that he’s eighteen years old, you expect that he’s somewhere between eighteen and nineteen years of age. If he says that he’s eighteen years, two months, and three days old, you know that his answer is good to within a few hours—and that he’s probably a bit obsessive. The roundness of a number gives you clues about how precise the number is, and how seriously you can take it.
This is the key to the dinosaur anecdote. When a scientist says that a dinosaur skeleton is sixty-five million years old, it’s a signal that the number is a fairly rough approximation; the measurement error is on the order of tens or hundreds of thousands of years.9 In reality, the skeleton might be 64,963,211 years old; perhaps it’s 65,031,844 years old. However, the paleontologist’s measurements weren’t precise enough to reveal that truth. When he said that the skeleton was sixty-five million years old, he was admitting that his measurement had large errors—it was sixty-five million years old, give or take tens or hundreds of thousands or even millions of years.
The museum guide screwed up when he took the sixty-five-million-year figure too literally. He ignored the errors inherent to the measurements of the dinosaur’s age—the errors signaled by the roughness of the figure—and instead assumed that the skeleton was exactly sixty-five million years old when he began work at the museum. Only then would his hyper-precise figure of 65,000,038 years make sense. But since the errors in measurement absolutely dwarf the time he spent working at the museum, his figure of 65,000,038 years is ridiculous. The skeleton is still sixty-five million years old—as it will be a hundred or a thousand years in the future. The guide erred because he trusted the measurement beyond the point where it should be trusted. He committed an act of disestimation.
Disestimation is the act of taking a number too literally, understating or ignoring the uncertainties that surround it. Disestimation imbues a number with more precision than it deserves, dressing a measurement up as absolute fact instead of presenting it as the error-prone