In the 1920s, the modern city seemed to hold nothing but promise: order, cleanliness, rapid movement, economic growth and technological progress. But disaffection grew as neatly planned metropolises sprawled and outpaced themselves. In the 1950s, urban planners recommended more order, urban renewal and slum clearances. Dutch artist Constant Nieuwenhuys offered a different alternative in the 1960s: a city of linked megastructures called New Babylon that would drift high over the regimented city and provide a place without order—a place “for playing, for adventure, for mobility.”

Since then, plenty of urban planners have taken up the quest to improve our cities. Among the most intriguing strategies is the linear city, an orderly slice of metropolitan energy dominated by a single pat...