The Infinite Book: A Short Guide to the Boundless, Timeless and Endless

Barrow is one of my favorite authors, and his lucid explanation of fascinating topics is always a pleasure.

This is a marvelous book. Infinity is a tough concept to wrap your mind around, but Prof. Barrow makes it as understandable as anyone possibly can. He goes deep into the subject -- this is by no means a superficial treatment -- yet never loses an attentive reader. His brilliant final chapter, dealing with the theory of time travel, will knock your socks off. Barrow has a nice wit, and as a special bonus he has seeded the text with some intriguing Briticisms that were new to me, but happily understandable from the context.

The value of "The Infinite Book" is definitely summed up in the chapter "The Madness of Georg Cantor." Believe it or not, "new math", that strange evolution of math teaching that stumped homework for a generation in the 60's was a direct result of Cantor's theories about sets, and the supposition that some infinite sets could be larger than others--which is the first thing you REALLY learn about infinity in mathematics. The other great part of this book is the coupling of mathematics theory with physics. The assertion by Einstein that a singularity would be a breakdown of the laws of physics, and that any theory involving singularities would thereby have in it, the "seeds of its own destruction." Then author Barrow moves on to a very good explanation of string theory (imagine a particle that stretches like a tube in a warm enviroment, but contracts to a single point in a cool environment.) The explanations, illustrations are so clearly written in this book. It's a valuable reference for students of physics and mathematics and a great read for the curious about these subjects. Recommended.

The infinite is one of those concepts that takes just a bit of understanding. Well, maybe more than just a bit. Infinity doesn't necessarily mean a bunch, it means, mathematically, that a number cannot be determined. Infinity is not a new idea. Mathematicians have been working on them for hundreds of years. Physicists really got involved when Einstein published the Theory of Relativity in 1905. He talked about all kinds of things happening when you approached the speed of light. Then when you actually got to the speed of light his equations went to infinity. This was a bit disconcerting. One of the real reasons for the willingness of physicists to believe in string theory is that that the equations still show valid values at and above the speed of light. But enough on infinity. If you want to know more, here's the book for you. It discusses just about everything there is to know about infinity. It would be great for the high school math/physics teacher to use for examples. Or, it's just plain fun reading to anyone that's interested.

When we get the capacity to look closer and closer into molecules, atoms, and subatomic particles, will we always be able to find something smaller? When our telescopes or probes look deeper into space, will we always find something larger? Is there a limit to the shortness of an instant, or the duration of eternity? In _The Infinite Book: A Short Guide to the Boundless, Timeless, and Endless_, John D. Barrow has invited us to look at infinities in many ways. He's competent to do so, as a professor of mathematical sciences at Cambridge, and as the author of previous books which successfully explained such concepts as nothing or impossibility. Like his previous efforts, this is highly readable stuff, but extraordinarily mysterious. The topic is something that everyone has pondered in some way; who has not, looking into the stars, wondered how far they go? It has a universal appeal, and a history within religion, philosophy, mathematics, and physics, all of which Barrow goes into here, in an entertaining summary. There are answers here, but plenty of mysteries. Consider a universe that is infinite in space; this is a possibility, for no one knows that space is not infinite. In a universe of infinite size anything that can happen does happen, and does so infinitely often. In such a universe, not only are you here, but somewhere out there is another you doing exactly what you are doing; in fact, there are an infinite number of you. There is also somewhere out there another you who has done everything you ever did, but on the day after his sixteenth birthday, wore black socks instead of brown. This has to be the case in an infinite universe, Barrow shows; it is enough to make us uncomfortable, but discomfort is not an argument that an infinite universe cannot exist. Mathematicians have had fun and frustration with infinity ever since Zeno, who "proved" that because to walk a mile, you first had to walk a half mile, and then a quarter mile more, and an eighth mile more after that, and so on forever, that you never were able to finish that mile, and if you are under the impression that you have accomplished a mile journey at some time, you are just deluded. The world as it perceived by us, with all its journeys, is an illusion. Georg Cantor solved the problems of dealing with infinities mathematically, but his work was viciously attacked and blocked from publication, but surprisingly, Catholic theologians welcomed his ideas as a way of understanding the infinite, the infinite that included God, of course. Today, mathematicians take Cantor's work for granted, and its religious implications are not the common stuff of sermons. It is a pleasure to puzzle through these matters with Barrow as a guide, at least partially because this is a general overview which skims through details in order to provide a larger picture. String theory, for instance, takes a couple of pages, and cosmology not much longer. If one flavor of infinity is just to