PYTHAGORAS: MORE THAN JUST THE SQUARE ON THE HYPOTENUSE

Kitty Ferguson. Pythagoras: His Lives and the Legacy of a Rational Universe. Icon Books, 2010

To most people, Pythagoras is probably known only for his theorem about right-angled triangles, but Kitty Ferguson shows us that his name has been involved in many other contexts throughout the 2,500 years since his lifetime. This is despite the fact that he and his devotees were very secretive about their work and that, so far as is known, he left no writings at all. The earliest written evidence about him consists of six short fragments of text from about a century after his death, referring to earlier writings.

🔻

Pythagoras was born on the Aegean island of Samos, which he left in about 530 B.C. and went to live in Croton, on the southern coast of Italy, where he gained a reputation as a teacher and religious leader. He also became involved in politics and made enemies, so that, after about 30 years in Croton, he fled to another coastal city, Metapontum, where he died.

The work of Pythagoras and his followers was important for their discovery of the importance of numbers, their "recognition that numbers are a pathway from human ignorance to an understanding of the deepest mysteries of a universe that on some profound level makes perfect sense and is all of a piece". This discovery was made in music. As Ferguson notes: "It is well established, as so few things are about Pythagoras, that the first natural law ever formulated mathematically was the relationship between musical pitch and the length of a vibrating harp string, and that it was formulated by the earliest Pythagoreans."

This discovery also inspired Pythagoreans to look for other examples of mathematical relationships, and the author discusses how the application of these ideas to astronomy gave rise to the notion of the "music of the spheres", which in turn inspired astronomers such as Joannes Kepler, whose investigations of an apparent lack of harmony in the movements of the planets eventually led him to the realisation that their orbits were not circular, but elliptical.

Pythagoreans already knew that constructing a triangle with sides in the ratio 3-4-5 would produce a right angle, and that 5 squared was equal to 3 squared plus 4 squared. However, most right-angled triangles, the simplest example being a square with a diagonal drawn across it, produced the problem of incommensurability, because if the sides of the square are 1 unit, then the diagonal must be the square root of 2 units, which is an irrational number, having an infinite number of digits after the decimal point. This might seem trivial to some people, but academics today are still working on the logical and philosophical problems posed by the concept of infinity, for example, the discovery by Georg Cantor, in the 19th century, that one infinite collection can be bigger than another.

Bertrand Russell regarded Pythagoras as having been the most influential man in the sphere of thought. He wrote: "Pythagoras was intellectually one of the most important men that ever lived, both when he was wise and when he was unwise." Russell considered him "unwise" because of what he saw as his mystical tendencies, which led Plato to develop his idea of Forms, giving rise to the idea of intellect as superior to direct observation of the world.

Kitty Ferguson's account of the pervasive influence of Pythagorean thought on the development of science, philosophy, religion and culture through 25 centuries is impressive and should appeal to anyone interested in history, particularly the history of science .

• John Harney