Gödel, Escher, Bach

At the turn of the 20th century, mathematics took an introspective turn when its practitioners attempted to organize reasoning itself into an axiomatic system of theorems and definitions. The results were provocative and ended in a kind of paradox when logician Kurt Gödel proved that all formalized logical systems would necessarily contain some unprovable truths. Reading Douglas Hofstadter's Gödel, Escher, Bach, we will discover the connections among seemingly disparate fields of mathematics, visual arts, and music. Our journey will pass through the philosophical worlds of Lewis Carroll, Artificial Intelligence, non-Euclidean geometry, Zen Buddhism, and crash head-on into questions about the nature of human consciousness and creativity. 3 hrs. sem.