111: The Infinite Book by John D. Barrow
111.6: Barrow, John D. The Infinite Book: A Short Guide to the Boundless, Timeless and Endless. New York: Pantheon, 2005. 274 pp. ISBN 0-375-42227-7.
When you start reading about philosophy (100s), you have to start with the basics. Philosophy is study of general and fundamental problems, including existence, knowledge, language, and morality. But, before you talk about these things, you have to talk about what “things” are (and also what “talking” is), which is metaphysics. You also have to define what “is” is—this is the study of being, or ontology. One of the many fundamental questions of ontology is that of infinity; can you begin to discuss the idea of an infinite quantity?
John Barrow’s Infinite Book discusses the history of infinity and its implications for how we interact with the universe around us. Infinity is more a concept than an actual thing. Things have to have edges, distinctions, boundaries, etc. Much of the early work on the concept of infinity was in conjunction with proving the infinite power and nature of God. In order for God to be omnipresent and omnipotent, you first had to ensure that infinity existed, and just how infinite it would be.
Later work on infinity yielded some interesting results. In the 1800s, Georg Cantor’s work on infinities and set theory led to the discovery of transfinite numbers (numbers that are impossibly large, but not quite infinitely large) and that there are an “infinity of infinities.” Needless to say, this confused and angered other mathematicians of the day and they sought to undermine his work (I’m starting to notice this as a pattern throughout history).
Modern conceptions of infinitely have to do with the nature of the universe. There are really two schools of thought: the universe is infinite is size or the universe has a finite boundary. One of the problems faced in this debate is the limits of our own observation, so we have to make a distinction between the actual universe and the observable universe (which has NO EDGE!). The implications of an infinite universe include how all that matter got to be where it is (or where we see it is), what will happen when there is infinite space between the infinite entities in the infinite universe, and so on.
This book is a great book to start into the discussion of ontology. I enjoyed the early history of the thinkers behind infinite concepts. Barrow does a very good job of guiding the reader through the various facets of infinity (even though it can make your eyes cross at times). Once he gets into the nature of the universe and its properties, it becomes less a discussion about infinity and
more a treatise on modern cosmological thought. And the last bits about infinitely long life spans and time travel felt a little forced. All in all, however, this was a neat book.