Friday, November 14, 2008

Serious numbers

Endless Conversation


By TONY EVANS

Mathematics and religion were one and the same for the Pythagoreans of ancient Greece, a cultish group of geometers known as mathematikoi, who formed the earliest Western monastic tradition in the sixth century B.C.

Pythagoreans worshipped numbers and formulas. They believed that numbers were either male or female and were always equal to a ratio between two whole numbers. They also believed that the underlying mathematical patterns of harmonious music were a reflection of the "harmony of the spheres" of celestial bodies in outer space. Pythagoras, their leader, devised the Pythagorean Theorum, proving that "the square of the hypotenuse of a right triangle is equal to the sum of the squares on the other two sides." He was also a strict vegetarian, believed in reincarnation and claimed to recall four of his own previous lives. Triangulating distances and heights would not be possible without Pythagoras.

Yet when one of Pythagoras' disciples, Hypassos, discovered the existence of irrational numbers (like Pi and the square root of 2), this discovery undermined the Pythagorean worldview, which held that all numbers in the universe could be expressed as fractions of whole numbers, and that numbers were inseparable from geometric shapes.

One story holds that Hypassos, now branded a heretic, was thrown from a ship and drowned by his fellow Pythagoreans for making this discovery. But Hypassos' discovery of incommensurable ratios led to the study of infinitely reducible magnitudes and opened new explorations in the study of geometry.

Three centuries later, a Greek mathematician by the name of Archimedes was tinkering with the notion of infinity. His drawings and texts, including those for calculating infinitely small and infinitely large numbers, were passed down and eventually copied by a scribe during the 10th century in Constantinople.

Then a great religious passion overtook Europe, which set aside the notion of infinity in mathematics and replaced it with the idea of eternity in the Christian tradition; eternity was spent in either heaven or hell, based on the choices you made as a mortal.

During the Fourth Crusade in 1204, the book containing Archimedes' work was taken by religious zealots to Jerusalem, where its parchments were scraped of Archimedes' text and diagrams and rewritten with orthodox liturgical texts and paintings. The book was then kept for centuries in a fortress monastery in the Holy Land and at a library in Turkey, before it surfaced in the 1920s when it was purchased by a book collector who recognized the Greek lettering under the Christian writing and pictures.

Known as the Archimedes Palimsest, this book is now being studied with the latest X-ray photography to decipher its text and bring to light Archimedes' lost works.

Dr Chris Rorres, who is working with the text at the Walters Art Museum in Baltimore remarked recently on the significance of the text: "Not only was Archimedes coming to terms with the profound subject of infinity, he had taken the first crucial steps towards calculus, a branch of mathematics that had to be reinvented after the Renaissance, and which is today used to describe every physical phenomenon from the movement of the planets to the construction of a skyscraper. Who knows what human minds could have achieved if they had only known what Archimedes already knew?"




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