THE GOLDEN RATIO: The Story of Phi, The
World's Most Astonishing Number, by Mario Livio, (Broadway Books, New
York: 2002), p.30-31
“Today, while we may be amused by
some of the Pythagorean fanciful ideas, we have to recognize that the
fundamental thought behind them is not very different from that
expressed by Albert Einstein (in Letters to Solovine):
“Mathematics is only a means for expressing the laws that govern
phenomena.” Indeed, the laws of physics, sometimes referred to as
the “laws of nature,” simply represent mathematical formulations
of the behavior that we observe all natural phenomena to obey. For
example, the central idea in Einstein's theory of general relativity
is that gravity is not some mysterious, attractive force that acts
across space but rather a manifestation of the geometry of the
inextricably linked space and time. Let me explain, using a simple
example, how a geometrical property of space could be perceived as an
attractive force, such as gravity. Imagine two people who start to
travel precisely northward from two different points on Earth's
equator. This means that at their starting points, these people
travel along parallel lines (two longitudes), which, according to
plane geometry we learn in school, should never meet. Clearly,
however, these two people will meet at the North Pole. If these two
people did not know they were really travelling on the curved surface
of a sphere, they would conclude that they must have experienced some
attractive force, since they arrived at the same point in spite of
starting their motions along parallel lines. Therefore, the
geometrical curvature of space can manifest itself as an attractive
force. The Pythagoreans were probably the first to recognize the
abstract concept that the basic forces in the universe may be
expressed through the language of mathematics.”
