Proofiness - Charles Seife [3]
The cold and crystalline world of numbers gives us the rarest of all things: absolute certainty. Two plus two is always four. It was always so, long before our species walked the earth, and it will be so long after the end of civilization.
But there are numbers and there are numbers. Pure numbers are the domain of mathematicians—curious people who study numbers in the abstract, as Platonic ideals that reveal a higher truth. To a mathematician, a number is interesting in its own right. Not so for the rest of us.
For a nonmathematician, numbers are interesting only when they give us information about the world. A number only takes on any significance in everyday life when it tells us how many pounds we’ve gained since last month or how many dollars it will cost to buy a sandwich or how many weeks are left before our taxes are due or how much money is left in our IRAs. We don’t care about the properties of the number five. Only when that number becomes attached to a unit—the “pounds” or “dollars” or “weeks” that signify what real-world property the number represents—does it become interesting to a nonmathematician.
A number without a unit is ethereal and abstract. With a unit, it acquires a meaning—but at the same time, it loses its purity. A number with a unit can no longer inhabit the Platonic realm of absolute truth; it becomes tainted with the uncertainties and imperfections of the real world. To mathematicians, numbers represent indisputable truths; to the rest of us, they come from inherently impure, imperfect measurements.
This uncertainty is unavoidable. Every unit represents an implied measurement. Inches, for example, represent an implied measurement of length; when someone says that a coffee table is eighteen inches wide, he’s saying that if we were to take the table and measure it with a ruler, the table would have the same length as eighteen of the little hash marks we call inches. When someone says he weighs 180 pounds, he’s saying that if you measured him with a bathroom scale, the number on the dial would read 180. Every number that has a real-world meaning is tied, at least implicitly, to a measurement of some kind. Liters are tied to a measurement of volume. Acres imply a measurement of area. Watts imply a measurement of power. A measurement of speed is expressed in miles per hour or in knots. A measurement of wealth is in dollars or euros or yuan. If someone says that he has five fingers, he’s saying that if you count his digits—and counting objects is a measurement too—the answer will be five fingers.
It’s universal; behind every real-world number, there’s a measurement. And because measurements are inherently error-prone (they’re performed by humans, after all, using instruments made by humans), they aren’t perfectly reliable. Even the simple act of counting objects is prone to error, as we shall see. As a result, every measurement and every real-world number is a little bit fuzzy, a little bit uncertain. It is an imperfect reflection of reality. A number is always impure: it is an admixture of truth, error, and uncertainty.
Proofiness has power over us because we’re blind to this impurity. Numbers, figures, and graphs all have an aura of perfection. They seem like absolute truth; they seem indisputable. But this is nothing but an illusion. The numbers of our everyday world—the numbers we care about—are flawed, and not just because measurements are imperfect. They can be changed and tinkered with, manipulated and spun and turned upside down. And because those lies are clad in the divine white garb of irrefutable fact, they are incredibly powerful. This is what makes proofiness so very dangerous.