Interesting example about maps as models from a NYker profile of Paul Krugman. Larger point concerns the making of models in economics. Despite the potential gain in explanatory or predictive power of a more formal model, there is a potential loss as well. Greater rigor can mean that useful–and correct–information that doesn’t meet the criteria for rigor is banished, for a couple of centuries in the cases of maps of Africa. Models giveth, and taketh away.
Again, as in his trade theory, it was not so much his idea that was significant as the translation of the idea into mathematical language. “I explained this basic idea”—of economic geography—“to a non-economist friend,” Krugman wrote, “who replied in some dismay, ‘Isn’t that pretty obvious?’ And of course it is.” Yet, because it had not been well modelled, the idea had been disregarded by economists for years. Krugman began to realize that in the previous few decades economic knowledge that had not been translated into models had been effectively lost, because economists didn’t know what to do with it. His friend Craig Murphy, a political scientist at Wellesley, had a collection of antique maps of Africa, and he told Krugman that a similar thing had happened in cartography. Sixteenth-century maps of Africa were misleading in all kinds of ways, but they contained quite a bit of information about the continent’s interior—the River Niger, Timbuktu. Two centuries later, mapmaking had become much more accurate, but the interior of Africa had become a blank. As standards for what counted as a mappable fact rose, knowledge that didn’t meet those standards—secondhand travellers’ reports, guesses hazarded without compasses or sextants—was discarded and lost. Eventually, the higher standards paid off—by the nineteenth century the maps were filled in again—but for a while the sharpening of technique caused loss as well as gain.