# A Literary Flyover of Math Frontiers

'COMPUTERS, mathematics, and freedom - three words which may never before have appeared together in a single sentence."It's hard not to like a book that starts like that. "Computers and the Imagination" is all about computers and math and how they create the freedom to think about - and see - new areas of learning. Want to learn about numeric palindromes (numbers that are the same whether read backward or forward)? This is the book. Care to dip into chaos theory or speculate about what would have happened had a personal computer appeared at Harvard University in 1900? This is where you'll find the answers - or at least some of the answers. And always more questions. Clifford A. Pickover, an associate editor for Computers and Graphics and author of "Computers, Pattern, Chaos and Beauty," infuses this book with a spirit of adventure. He's happy to let readers pick and choose what they're interested in. The chapters are self-contained and most of them contain a section called "Stop and Think." The result is a kind of literary flyover of the frontiers of mathematics. Pickover lets the reader delve into the insides of the Mandelbrot set, instead of its much better-known borders. (The Mandelbrot set is a set of complex values discovered around 1980 that creates intricate computer-generated pictures.) He wrestles with twisted-mirror worlds and confronts the Gleichniszahlen-Reihe Monster (a special number sequence). The book has a heavy graphic and artistic bent. Many chapters deal with visualization - using a computer to draw the results of a complicated formula. The book includes color plates of some of the more intricate results, such as goggle-eyed worms, digital monsters, and a three-dimensional representation of a lava flow. My personal favorite is the visualization of the Cantor Cheese Construction. To make Cantor Cheese, you draw a circle, then two circles that fit inside it (in other words, their radius is slightly less than half the radius of the original circle). Then draw two circles within those two circles and so on. Expand the circles into three-dimensional cones, with various colors and cross-sections to differentiate them, and the effect can be quite pleasing. As you might suspect, this is not a book for math-avoiders. Artists with little or no programming knowledge and novices like me who are interested in computer issues will have fun sampling the book. But Pickover's literary flyover is really for those who have the programming expertise to get out of the plane and explore for themselves. I think he realizes this. He twice asks the question: "If Leonardo da Vinci were alive today, would he forsake canvas and brush for a computer terminal?" Pickover's answer is an unqualified "yes!" And if nothing else, "Computers and the Imagination" can inspire a new generation of da Vincis to build unknown flying machines and create new Mona Lisas.