EUCLID’S WINDOW

Halfway through this articulate and droll history of math and physics, you wonder: Who is this guy with the unpronounceable name you want to recommend to all your friends?

And so you discover that Mlodinow has gone from Cal-tech professor to Star Trek scriptwriter to developmental VP for an educational software firm. That would account for his knack of presenting the evolution of mathematical thought with an insider’s insight, quirky humor, and titillating facts about the great and near-great. Describing the work of Boethius (who abridged Euclid’s Elements), Mlodinow writes, “his translations might be entitled ‘Euclid for Dummies’ or sold in TV ads imploring, call 1-800-NOPROOFS.” On the foundations of quantum mechanics he quotes Erwin Schrodinger (“It has never happened that a woman has slept with me and did not wish, as a consequence, to live with me all her life”). These little fillips engage the reader as the author chronicles how our views of the universe have been informed by concepts of space. Much of the text (and human history) does indeed reflect the view from Euclid’s window—in which space is flat, filled with points, lines, and figures (like triangles) whose angles add up to 180 degrees. That works only as long as you accept as an axiom that through a point outside a line one and only one line can be drawn parallel to a given line. Much ink was poured unsuccessfully over the years to derive this “axiom” from the other Euclidean axioms as a theorem. Then during the 19th and 20th centuries, in the works of Gauss, Riemann, and Lobachevsky, the notion of non-Euclidean curved space took root and revolutionized physics. Einstein demonstrated the curvature of space in general relativity, and he needed four-dimensional space-time to develop special relativity. Mlodinow concludes with the latest wrinkles on the geometry of space, from the early formulations of string theory and now M-theory to the abstruse work of mathematicians like John Schwarz and Ed Witten.

Splendid exposition, accessible to the mathematically challenged as well as the mathematically inclined.