(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.
