If there’s one thing that makes maps so seductive, it’s their godlike perspective on our domain. With the exception of pilots and window washers, humans are afforded only a worm’s- eye view of the continental landscape. With maps, we rise above our earthbound existence, imagining our frontiers from a skyward perch.

It’s a logical thesis for an author whose last work was the cheeky (and, for a geography book, hot-selling) How to Lie With Maps. In that volume, Monmonier used hypothetical scenarios to highlight common imperfections in map design. In Drawing the Line, he sets out to make these ideas more accessible by sketching a dozen historical cases in which maps played decisive roles. It’s a clever idea, carried off amiably and with a commendable absence of jargon. But although maps offer a fertile floodplain of information, Monmonier visits too many dead-end inlets.

The author places his strongest example first—the familiar but nonetheless instructive tale of the late German cartographer Arno Peters, who set out in the 1970s to convince the industrialized world that misguided Mercator map projections were shrinking the size, and thus downplaying the importance, of the developing countries of the Southern Hemisphere. His solution, evangelized heavily in the media, was the Peters projection. Unlike Mercator, the Peters projection displays land areas consistently—but unfortunately distorts continental shapes so they look, as one wag put it, like “wet, ragged, long winter underwear hung out to dry on the Arctic Circle.”

The Peters yarn benefits from an ideological tiff (left-leaning church groups were among Peters’ most ardent supporters); conflict between a technical cartographic elite and an angry map-using constituency; and the flagrant scientific illiteracy of the media. It also presents a welcome opportunity to educate the reader about the pros and cons of various map projections. While Monmonier tears apart Peters’ misguided grasp of cartographic principles, he also argues evenhandedly that the tussle was constructive: It demonstrated that the Mercator projection—initially designed only for navigation—is widely misused in such everyday contexts as a network-news backdrop or T-shirt design.

Unfortunately, Drawing the Line only intermittently lives up to this compelling introduction (notable exceptions being an examination of siting hazards such as nuclear dumps, and a telling chapter on how Yale University was suckered into buying and widely promoting a forged map of “Vinland” that purported to predate Columbus’ discovery of the New World). Monmonier might have advised editors and mapmakers on how to handle the shifting boundaries of Eastern European and Central Asian countries. And he might have provided a more systematic user’s guide on the new-generation electronic maps that he suggests will replace the old-fashioned paper jobs.

Instead, he merely restates his observation that geographical representations carry great importance: Renaming conquered territory, he points out, is a good way to assert authority, and zoning disputes and legislative redistricting often hinge on maps. Such pedestrian conclusions undermine this exploration of how uneasily we relate to our our environment.