In the 1981 preface Rucker writes, “This book discusses every kind of infinity: potential and actual, mathematical and physical, the ontological and the mundane.” The main line of argument is mathematical. Rucker uses physics, philosophy and theology as illustrations and examples of mathematical concepts. He also uses mathematical formulas, diagrams and cartoon to illustrate concepts in other disciplines. The five chapters all conclude with a collection of puzzles and paradoxes. This assumes that if the reader has followed and understood the concepts so far you have another chance to exhaust your reasoning powers on these, because with infinities there are things that cannot be logically, mathematically or scientifically described fully. Rucker argues that many of the ideas about infinity are not rationally and deductive, but mystical an intuitive. This makes a book that is an active and entertaining mental wrestling match. It also makes it a stimulating, thought provoking, and potentially mind expanding read. ( )

The contents of this book is best used in 50 lb bags, available at most lawn & garden stores. You would get a better grasp of infinity by overdosing on dextromethorphan than by reading this tripe. The basic concept of a true infinity escapes Mr. Rucker throughout the whole book. ( )

I read this book over a longish evening. At the end my mind was so expanded I had difficulty in going to bed! if you are at all curious about infinity, the concept, which, according to Borges "Contaminates and destroys all others", then a look at this book wil satisfy you. Some concepts still elude me, but if Rucker can't make them plain, then probably no-one else can. Perhaps I might suggest a book on flower arranging?

To Rucker I owe the following proof of the falsity of the statement "in an infinite universe, anything is possible". Ti disprove this, we only have to show that something is impossible in our (imaginary) infinite universe. Let's say a planet where everyone has green hair. Now imagine a guide to the planets in the universe. This book has an infinite number of pages. Now imagine that we put green-haired planets every other page, with noral planets in between. We can remove the GHP from our guidebook, and it is still infinite. So now we can imagine an infinite universe with no GHPs. So many things are not possible in our infinite universe. This proof is oddly satisfying. Thank you Mr. Rucker. ( )

The concept of infinity is one that many people banter around without really grasping its meaning. People use the word almost blithely, but few realize what an astounding, frightening idea it really is. Imagine the largest number you can. Add one to it. Think of the smallest unit imaginable. Cut it in half. Try to grasp your insignificance based on a universe that simply never ends. It's a little scary. In this book, Rucker (best known for his science fiction writing) attempts to explain infinity in terms that laymen can understand. While he often gets bogged down in complex mathematics and occasionally drifts in to New Age territory, there are enough interesting ideas and concepts presented here to make the book a must read for those interest in the idea of infinity. Rucker occasionally has a way of explaining this that makes them just click. Despite its flaws, an interesting read.

(This review originally appeared on zombieunderground.net) ( )