(correction on February 27th, 2009)
It was Lord Kelvin who wrote, "To measure is to know." This is one of those tiny quotes that carries a heavy load of meaning. The central point of Kelvin’s comment was the realization that quantification is the root of a deeper knowledge of the world. Yes, it’s nice to say that a boulder is heavy, but to measure its weight, to declare that it weighs 892 kilograms, that’s a better kind of knowing. Kelvin’s comment implied that knowledge comes in degrees. The lowest degree of knowledge is unmeasured knowledge: "The boulder is heavy". Higher up comes a rough measurement: "The boulder weighs about 900 kilograms." A better measurement implies better knowledge: "The boulder weighs about 890 kilograms."
The important point, though, is that when we make the transition from a nonquantitative form of knowledge to a quantitative form, our knowledge suddenly changes for the better in a fundamental way. Without quantitative measurements, we can kinda sorta know about the world, but to really know, we must quantify.
Of course, these higher levels of knowledge may have no practical value. A bunch of medievals lugging a boulder out of a field don’t care how much it weighs; all they care is that it’s heavy! But as humankind has advanced, the value of more precise knowledge has increased. A road builder confronting the same boulder may well want to take some quick measurements before deciding whether to push it aside or blow it up. And a prospector determining the value of the platinum ore in the rock will want to make very careful measurements before deciding whether to break it up for ore.
Observe, however, that Kelvin was thinking solely in terms of knowledge. Knowledge is only half of our appreciation of the world; the other half is understanding. Knowledge allows us to appreciate what the world is, but understanding lets us appreciate how it works. Knowledge answers questions with simple numbers. How long is the rock? How much does it weigh? But understanding requires more complex answers: What holds the rock together? Why is its surface pockmarked?
Thus, understanding constitutes a completely different kind of mental process than knowledge. This prompts us to ask, "what is the analogue of Kelvin's dictum for knowledge?" In other words, if "to measure is to know" then (what?) is to understand?
The central idea of Kelvin’s dictum is that quantification of knowledge propels us into a higher level of knowledge. Therefore, quantification of understanding should propel us into a higher level of understanding. But just what do we mean by "quantify understanding"? Quantified understanding is really nothing more than the use of mathematics. We can say, "Things move when you push them", or we can say with greater understanding, "F = ma". To express an idea in quantitative terms, we must understand it at a deeper, more profound level.
Some might object that quantification is a denial of spiritual truth. Many, for example, would object to the notion of writing equations for human behavior. I have no such qualms. So long as we understand that the equation is an approximation, we need not be bent out of shape by its quantitative nature. Did the nonquantitative description of Captain Ahab’s character in Moby Dick provide us with a complete image of his personality? Of course not; Melville gave us an approximation of Ahab’s character, leaving out many details. In the same way, a set of equations for human behavior are approximations. Just as Melville could have expended more effort and given us a better image of Ahab, so too could a more assiduous artist expend more effort on the governing equations to obtain a better approximation.
In seeking a verb to describe this concept of quantifying how the world works, I settle on "process". This includes direct formulae as well as multi-step algorithms and other extended techniques. It’s also what computers do. Thus, Crawford’s extension of Kelvin’s dictum reads "and to process is to understand."