Proof! How the world became geometrical

A lively explanation of how geometry structures aspects of the natural and human worlds.In this bracingly enthusiastic account of geometry's role in shaping a variety of institutions, Alexander (History/UCLA; Infinitesimal: How a Dangerous Mathematical Theory Shaped the Modern World, 2014, etc.) turns to Euclid's Elements and its complete world of mathematical proofs, founded on indisputable postulates and proven through impeccable logic. (The book isn't overrun with mathematics, but when it is unavoidable, the author is clear in his language.) Geometry revealed truths stripped of anything erroneous, unessential, and transitory, truths that were deployed by such luminaries as Copernicus, Galileo, and Leon Battista Alberti, setting the scientific agenda. Geometry is everywhere, underlying the natural and human-made worlds, infusing even our social arrangements. Guided by the art and architectural works of Alberti, which demonstrated "that the seemingly limitless variety one encounters in nature was in fact governed by the fixed eternal laws of geometry," Alexander applies that thought to the royal gardens of, in particular, France. Gardens were central to the monarchy's public presentation, ideology, identity, power, and legitimacy, especially so at Versailles, where Louis XIV's hierarchical state was reflected in the layout of the vast but tightly ordered gardens. "At the apex of this universe was, inevitably, the king in his palace, whose rule was as inescapable and unchallengeable as geometry itself," writes the author. This modernizing state was governed by a rational and efficient central bureaucracy, which is how the story moves forward beyond the monarchy into city planning. "The geometrical ideal of an efficient rational state found expressionon the bustling streets of capital citiesthe homes of state bureaucracies." This is the case in Rome, Paris, St. Petersburg, and Berlin, where harmony and order reflect the organs of state. The stamp of Versailles can also be found in New Delhi and Washington, D.C., the latter being a fine example of geometry accommodating several nodes of power.A deep immersion into geometric determinism at its most entertaining. Copyright Kirkus Reviews, used with permission.