The Buddhists in Love article that I linked to yesterday has got me thinking about models. So allow me to pontificate a bit.
During my first term at university, I came to the realization that science is about creating models. This idea struck me during Economics 101. It was a strange class—unlike most Econ 101 classes I’ve ever heard about. The professor had written a book in which he tried to distill the low-level principles of microeconomics into very simple definitions and axioms about preference: an Economics version of Russell and Whitehead’s Principia Mathematica. Ultimately, he hoped to derive all of microeconomics from these elementary propositions, just as Russell and Whitehead derived arithmetic and set theory from symbolic logic.
I don’t think the professor ever succeeded. If he had, he would have become famous, at least in Economics circles. And frankly most of the class was baffled. What did these weird little formulas about transitivity of preference have to do with running a business or managing inflation?
I was baffled myself, until I realized that he was trying to make an abstract model of thought processes that we usually take for granted. He wanted to state explicitly the principles underlying how a person makes choices. He invented a symbolic notation for preference, indifference, etc., with the hope that once he wrote down the obvious in an abstract form, he could start manipulating the symbols and discover ideas no one had ever noticed.
This kind of process happens all the time in pure mathematics, dating back to Euclid or before. It’s also what Newton brought to physics in the other Principia Mathematica: first, you use math to model physical processes, then you play with the math to learn new things and to see how different phenomena are secretly related.
In other words, you use math as a model for real world things. Typically, you start with very simple models (for example, ones that ignore factors like friction and air resistance), then you make the models more sophisticated so that they can deal with more complex phenomena.
But scientific models don’t have to be purely mathematical. Biology, for example, often makes use of the kind of models you see in the Wikipedia entry for Mallard Ducks. The entry contains such information as a mallard’s average size, how many eggs a female lays each year, usual habitat, and so on. Such a description constitutes a model: what a typical mallard is like. It’s an abstraction, based on observing a lot of mallards. It isn’t true for every mallard ever, but it gives you a good mental picture that’s reliable most of the time.
Other sciences use other types of models. Social sciences often use statistics and graphs. Some sciences use case studies; for example, an observer goes to live with a group of people for a while, then writes down a description of what their lives are like. This description is another type of model: an abstraction from real life.
My point is that collecting specific data may be part of scientific activity, but what science actually aims toward is production of a model, a summary, an abstraction: getting beyond individual specifics to derive something with wider applicability.
Often this is a good thing. We all know what good things science has given us. But there’s a downside too, and I’ll talk about that in the next post.
(Picture of mallards realized by Richard Bartz by using a Canon EF 70-300mm f/4-5.6 IS USM Lens [CC BY-SA 2.5 (https://creativecommons.org/licenses/by-sa/2.5)%5D, from Wikimedia Commons”)