Barrow, John D. The Infinite Book. New York: Vintage Books, 2005. ISBN 1-4000-3224-5.
Don't panic—despite the title, this book is only 330 pages! Having written an entire book about nothing (The Book of Nothing, May 2001), I suppose it's only natural the author would take on the other end of the scale. Unlike Rudy Rucker's Infinity and the Mind, long the standard popular work on the topic, Barrow spends only about half of the book on the mathematics of infinity. Philosophical, metaphysical, and theological views of the infinite in a variety of cultures are discussed, as well as the history of the infinite in mathematics, including a biographical portrait of the ultimately tragic life of Georg Cantor. The physics of an infinite universe (and whether we can ever determine if our own universe is infinite), the paradoxes of an infinite number of identical copies of ourselves necessarily existing in an infinite universe, the possibility of machines which perform an infinite number of tasks in finite time, whether we're living in a simulation (and how we might discover we are), and the practical and moral consequences of immortality and time travel are also explored.

Mathematicians and scientists have traditionally been very wary of the infinite (indeed, the appearance of infinities is considered an indication of the limitations of theories in modern physics), and Barrow presents any number of paradoxes which illustrate that, as he titles chapter four, “infinity is not a big number”: it is fundamentally different and requires a distinct kind of intuition if nonsensical results are to be avoided. One of the most delightful examples is Zhihong Xia's five-body configuration of point masses which, under Newtonian gravitation, expands to infinite size in finite time. (Don't worry: the finite speed of light, formation of an horizon if two bodies approach too closely, and the emission of gravitational radiation keep this from working in the relativistic universe we inhabit. As the author says [p. 236], “Black holes might seem bad but, like growing old, they are really not so bad when you consider the alternatives.”)

This is an enjoyable and enlightening read, but I found it didn't come up to the standard set by The Book of Nothing and The Constants of Nature (June 2003). Like the latter book, this one is set in a hideously inappropriate font for a work on mathematics: the digit “1” is almost indistinguishable from the letter “I”. If you look very closely at the top serif on the “1” you'll note that it rises toward the right while the “I” has a horizontal top serif. But why go to the trouble of distinguishing the two characters and then making the two glyphs so nearly identical you can't tell them apart without a magnifying glass? In addition, the horizontal bar of the plus sign doesn't line up with the minus sign, which makes equations look awful.

This isn't the author's only work on infinity; he's also written a stage play, Infinities, which was performed in Milan in 2002 and 2003.

September 2007 Permalink