Review of "The Infinite Book: A Short Guide to the Boundless, Timeless and Endless," by John D. Barrow

Review of

The Infinite Book: A Short Guide to the Boundless, Timeless and Endless, by John D. Barrow, ISBN 1400032245

Five out of five stars

Infinity for the masses

 The concept of infinity is both simple and extremely difficult to comprehend. That is because there are in fact so many ways the fundamental concept can be applied. The idea that there is no largest natural number is easy to understand. Nearly everyone can comprehend that one can continue to add one to positive integers with no possible ending. If it is explained the proper way, then it is also easy to comprehend that one can take the average of two numbers and get a third between them. By repeating the process, the concept of an infinite number of decimal numbers can also be understood.

 The concepts of being able to match up the positive integers and the positive whole numbers so that there are an “equal” number of elements in both sets, where one is inside the other is where some people start to get lost. The continuation to transfinite numbers with hierarchies of infinity is a difficult, but not impossible concept to grasp.

 The place where the concept of infinity really becomes difficult, even for mathematicians and people who study the universe is when the question arises whether the universe is finite or infinite in both breadth and in time. There is now little doubt that the universe as we know it began with what is called the Big Bang. In other words, elapsed time can definitively be traced back to a point where the universe popped into existence and has expanded at a great rate since then. No known laws can take us back before the Big Bang and we do not yet have enough information to determine what the ultimate fate of the universe will be.

 Barrow covers these topics in ways that are as understandable as possible for people that have not engaged in deep study of the concepts. The book is both a fun as well as informative read. All readers will come away with more knowledge about the many types of mathematical infinity as well as the current understanding of the properties of the universe and the various options for how it will evolve.