Euclid’s Window by Leonard Mlodinow
(from the book jacket)
Through Euclid’s Window Leonard Mlodinow brilliantly and delightfully leads us on a journey through five revolutions in geometry, from the Greek concept of parallel lines to the latest notions of hyperspace. Here is an altogether new, refreshing, alternative history of math revealing how simple questions anyone might ask about space – in the living room or in some other galaxy – have been the hidden engine of the highest achievements in science and technology.
Mlodinow reveals how geometry’s first revolution began with a “little” scheme hatched by Pythagoras: the invention of a system of abstract rules that could model the universe. That modest idea was the basis of scientific civilization. Nut further advance was halted when the Western mind nodded off into the Dark Ages. Finally in the fourteenth century an obscure bishop in France invented the graph and heralded the next revolution: the marriage of geometry and number. Then, while intrepid mariners were sailing back and forth across the Atlantic to the New World, a fifteen-year-old genius realized that, like the earth’s surface, space could be curved. Could parallel lines really meet? Could the angles of a triangle really add up to more – or less – than 180 degrees? The curved-space revolution reinvented both mathematics and physics; it also set the stage for a patent office clerk named Einstein to add time to the dimensions of space. His great geometric revolution ushered in the modern era of physics.
Today we are in the midst of a new revolution. At Caltech, Princeton, and universities around the world, scientists are recognizing that all the varied and wondrous forces of nature can be understood through geometry – a weird new geometry. It is a thrilling math of extra, twisted dimensions, in which space and time, matter and energy, are all intertwined and revealed as consequences of a deep underlying structure of the universe.
Mlodinow tackles what some people would think would be a dry topic and manages to infuse some wit into it. You can tell that he really loves his topic and wants the reader to as well. He explains the math and gives you examples to help you understand. And they are very helpful (although I must say that his examples using his sons start to get a little annoying after a while.) He explains the beginnings of geometry and how it progressed and reasons why it was, at times, held back due to politics and religion and other things (which puts a lot of history in the book that you normally wouldn’t think of as having anything to do with math.) It starts out with things I learned in school, like the Pythagorean Theorem and coordinates on a x/y graph and other things I recognized and then moved on to more complex things like string theory which I had no prior knowledge of. I started out fine and could follow well enough but as the book went on and the theories got more complex I had a harder and harder time keeping up and often had to reread a passage to understand it (and sometimes never totally did.) It is obviously a book for a particular audience and is not for everyone but if you are interested enough to pick up the book in the first place I don’t think you will be disappointed. It is well written and Mlodinow knows his stuff and his love of the topic comes through and infects the reader.