Sunday, July 15, 2007
The Eight - Cinq (Philidor's Tale Continued)
Philidor’s Tale continued (Page 171) Euler and I complimented the aging composer upon the cleverness of his work. I was then requested to play three games of blindfold chess simultaneously against the king, Dr. Euler, and the kapellmeister’s son Wilhelm. Though the older man did not play chess himself, he enjoyed watching the game. At the conclusion of the performance, where I won all three games, Euler took me aside. "I’d prepared a gift for you," he told me. "I’ve invented a new Knight’s Tour, a mathematical puzzle. I believe it to be the finest formula yet discovered for the tour of a Knight across a chessboard. But I should like to give this copy to the old composer tonight, if you don’t mind. As he likes mathematical games, it will amuse him." Bach received the gift with a strange smile and thanked us genuinely. "I suggest you meet me at my son’s cottage tomorrow morning before Herr Philidor departs," he said. "I may then have time to prepare a little surprise for both of you." Our curiosity was piqued, and we agreed to arrive at the appointed time and place. The next morning Bach opened the door of Carl Philipp’s cottage and squired us inside. He seated us in the small parlor and offered us tea. Then he took a seat at the small clavier and began to play a most unusual melody. When he’d finished both Euler and I were completely confused. "That is the surprise!" said Bach with a cackle of glee that dispelled the habitual gloom from his face. He saw that Euler and I were both totally at sea. "But have a look at the sheet music," Bach said. We both stood and moved to the clavier. There on the music stand was nothing other than the Knight’s Tour that Euler had prepared and given him the prior evening. It was the map of a large chessboard with a number written in each square. Bach had cleverly connected the numbers with a web of fine lines that meant something to him, though nothing to me. But Euler was a mathematician, and his mind moved faster than mine. "You’ve turned these numbers into octaves and chords!" he cried. "But you must show me how you’ve done it. To turn mathematics into music – it is sheer magic!" "But mathematics are music," Bach relied. "And the reverse is also true. Whether you believe the word ‘music’ came from ‘Musa,’ the Muses, or from ‘muta,’ meaning mouth of the Oracle, it makes no difference. If you think ‘mathematics’ came from ‘mathanein,’ which is learning, or from ‘Matrix,’ the womb or mother of all creation, it matters not…" "You’ve done a study of words?" said Euler. "Words have the power to create and kill," Bach said simply. "That Great Architect who made us all, made words, too. In fact, He made them first, if we may believe St. John in the New Testament." "What did you say? The Great Architect?" said Euler, growing a little pale. "I call God the Great Architect, because the first thing He designed was sound," Bach relied. "’In the Beginning was the Word,’ you remember? Who knows? Perhaps it was not only a word. Perhaps it was music. Maybe God sang an endless canon of His own invention, and through it, the universe was wrought." Euler had grown paler yet. Though the mathematician had lost the sight of one eye by studying the sun through a glass, he peered with the other eye at the Knight’s Tour that sat upon the clavier stand. Running his fingers over the endless diagram of tiny numbers inked across the chessboard, he seemed lost in thought for several moments. Then he spoke. "Where have you learned these things?" he asked the sage composer. "What you describe is a dark and dangerous secret, known only to the initiated."