Pantometry is one of the neologisms that appeared in increasing numbers in the languages of Europe in the first half of the second Christian millennium, words summoned into being by new tendencies, institutions, and discoveries. Milione and America are others. A general surge of more in the 1200s rendered the awkward and seldom-used a thousand thousand obsolete and inspired a convenient replacement: milione. Columbus and Amerigo Vespucci and the like created the need for America two centuries or so later. These words were sparks thrown off by the wheels of Western society veering and grating against the sides of old ruts. The veerings and gratings are the subject of this book, but first we must examine the ruts, that is to say, the view of reality that most medieval and Renaissance Western Europeans accepted as correct.