Proofiness - Charles Seife [7]
There’s an anecdote about an aging guide at a natural history museum. Every day, the guide gives tours of the exhibits, without fail ending with the most spectacular sight in the museum. It’s a skeleton of a fearsome dinosaur—a tyrannosaurus rex—that towers high over the wide-eyed tour group. One day, a teenager gestures at the skeleton and asks the guide, “How old is it?”
“Sixty-five million and thirty-eight years old,” the guide responds proudly.
“How could you possibly know that?” the teenager shoots back.
“Simple! On the very first day that I started working at the museum, I asked a scientist the very same question. He told me that the skeleton was sixty-five million years old. That was thirty-eight years ago.”
It’s not a hilarious anecdote, but it illustrates an important point. The number the museum guide gives—sixty-five million and thirtyeight years old—is absurd. When the guide tacks on that thirty-eight years, he’s committed a numerical sin that turns his answer into a falsehood. He’s committed an act of proofiness.
When the scientist told the guide that the dinosaur was sixty-five million years old, the answer was tied, implicitly, to a set of measurements. Paleontologists somehow measured the age of the dinosaur—perhaps by looking at the decay of radioactive materials in its skeleton or by looking at the age of the rock strata that the fossils were embedded in—yielding an answer of sixty-five million years. But that number is only an approximation; fossil dates can be off by a few hundred thousand or even a few million years. The sixty-five-million-year date isn’t perfectly accurate. Measurements never are. They always contain errors that obscure the truth.
By being very careful with your measurements, by using sophisticated and precise tools, you can drive that error down. A typical ruler makes errors on the order of half of a millimeter. If you use one to measure, say, a pencil, and you’re very diligent, closing one eye to make sure that you’re lining the pencil up with the hash marks properly, you can be confident that the answer you get (150 millimeters) is no more than half a millimeter from the truth. This isn’t the final word, though. You can get a better answer if you want. You just have to shell out money for fancier equipment. Perhaps you can use a costly engineering ruler with ultra-precise hash marks or, even better, a set of calipers or a micrometer that can measure the same object with much more precision. With that kind of equipment, you might drive the error down to even a thousandth or a ten-thousandth of a millimeter. Where an old wooden ruler says that a pencil is 150 millimeters long, give or take half a millimeter, an expensive set of calipers might be able to declare that the pencil is 150.112 millimeters long, give or take 0.001 millimeters. By virtue of their smaller error, the calipers can get you closer to the truth than the ruler can.
In the laboratory, researchers using lasers or atom interferometers or other devices can make measurements that are even more precise still, 0.0000001 millimeters and beyond. In theory, someone might be able to discover that the pencil is 150.1124835 millimeters long, give or take a tiny, tiny fraction of a millimeter. The more precise (and expensive) your measurements, the more you reduce the error inherent to those measurements, getting you closer and closer to the truth.7 However, that error never completely disappears. No matter how careful you are, the measurement is always, in some sense, a mere approximation of reality, an imperfect reflection of truth. Error obscures reality, injecting a touch of falsehood and uncertainty into our measurements. Whether that error is half a millimeter or 0.001 millimeters or 0.000001 millimeters, it is still there, obscuring the true answer just a little.
Error ensures that any measurement