Keys to Infinity

by Clifford A. Pickover

"An original and exciting exploration of how utterly weird, and utterly beautiful, the infinite can be."-Ian Stewart, author of Does God Play Dice?
What can we know about numbers too large to compute or even imagine? Do the tiny bubbles in the froth of a milkshake actually form an infinite fractal pattern? What are apocalyptic numbers and recursive worlds? These and dozens of equally beguiling mathematical mysteries, problems, and paradoxes fill this mind-bending new book.
In each chapter, acclaimed author Clifford Pickover poses a delightful brain-teasing challenge that reveals the scope and splendor of the world of infinity. Try scaling the ladders to heaven, playing a game of infinite chess, or escaping from the land of Fractalia. Along the way you will encounter a myriad of intriguing topics from vampire numbers, to abduction algebra, to the infinity worms of Callisto.
Every problem and puzzle is presented in a remarkably accessible style requiring no specialized mathematical knowledge. Over one hundred illustrations enhance the text and help to explain the mathematical concepts, and stunning color images created by the author reveal the breathtaking beauty of the patterns of infinity. A variety of computer programs offer additional ways to penetrate the enigma of infinity.
For anyone who has ever wondered just how big infinity really is, or just how small, this book will provide an endless source of insight, creativity, and fun.
Advance praise for
KEYS TO INFINITY
"In this the latest of Dr. Pickover's marvelous books, he breaks all finite chains to soar into the transcendental, mind-boggling regions of mathematical infinity. Written in the author's informal, clear style, it is a treasure trove of recreational problems, many published here for the first time, with special emphasis on computer programs and riveting graphics. As you soar, fasten your seat belt."-Martin Gardner, author of The Magic Numbers of Dr. Matrix
"Inventive, quirky, fun! Pickover presents an engaging, inspiring romp in the realm of number and mathematical thought."-Ivars Peterson, author of The Mathematical Tourist
"Join Pickover on his wonderful merry-go-round of ideas, and reach for the infinite. Keys to Infinity is an engaging book. . .a must for those wishing to explore the infinite in all its manifestations."-Theoni Pappas, author of The Joy of Mathematics
"Keys to Infinity contains a near infinity of absorbing themes: from stepladders to the moon and spiral earths, to worm worlds, random chords, and self-similar curlicues. Fascinating!"-Manfred Schroeder, author of Fractals, Chaos, Power Laws
"What could be more appropriate to the subject of infinity than a book like this one, so dense with wonderful puzzles, anecdotes, images, and computer programs that you could pore over it forever? In Keys to Infinity, Pickover has once again assembled a mathematical feast."-Carl Zimmer, Senior Editor Discover
"Cliff Pickover has produced yet another book of mathematical puzzles, weird facts, computer art, and simple programs to challenge our minds and enthrall us with the beauty of the infinite mathematical world in which we live."-Dr. Julien C. Sprott, author of Strange Attractors

Genres: Mathematics, Nonfiction, Science

360 pages, Paperback

First published January 1, 1995

About the author

Clifford Alan Pickover is an American author, editor, and columnist in the fields of science, mathematics, science fiction, innovation, and creativity. For many years, he was employed at the IBM Thomas J. Watson Research Center in Yorktown, New York, where he was editor-in-chief of the IBM Journal of Research and Development. He has been granted more than 700 U.S. patents, is an elected Fellow for the Committee for Skeptical Inquiry, and is author of more than 50 books, translated into more than a dozen languages.

Reviews

[Gerry · Rating 4 out of 5]

Stretches the mind.

In a good way.

Pity it's so out of date.

[Lionel D'Souza · Rating 5 out of 5]

The book is a collection of fascinating, thought-provoking essays on various topics which are not necessarily all concerned with infinite topics. Some may be discussions of really big numbers or
mathematical constructs, but these may or may not necessarily involve infinity.

Now I am by no means a math wizard, but this book really helped me appreciate the vastness of infinity, a concept most of us trivially take for granted.

[Kathy Elrick · Rating 4 out of 5]

I remember I enjoyed reading it when I was 12 - the chapter on fractals definitely still hangs in my imagination. Worth considering coming back to...

[Yofish · Rating 3 out of 5]

Written in '95--lots of musing about many things that are at least vaguely related to infinity. Lots of computer-related suggestions for exploration. But feels a lot like a blog, as there's plenty of suggestions from his peanut gallery (including Tim Chow!) Meant to get people interested in math-y topics. Might work, but I'm not really the target audience. A little too fragmented, maybe, for my tastes. Again, might have worked better as a blog. (Which meant nothing in '95, I suppose.)

[James · Rating 4 out of 5]

For a non-mathematician such as this reviewer, Pickover's book starts off with several interesting thought problems pertaining to the concept of infinity. From there, more mathematical angles are introduced but gradually so that one is eased into the more complex and sometimes dizzying heights of extremely large numbers. An entertaining and fascinating read, perfect for both mathematician and non-mathematician alike.

[Josh · Rating 4 out of 5]

It is a fun hodgepodge of math related problems dealing with the idea of infinity and has a lot of suggestions for fun code to write if you're into programming (like me). Great for your inner (or outer) nerd.