In a sense this property of infinity has been known since Galileo, who pointed out that there are just as many even numbers as there are whole numbers. Likewise there are just as many whole numbers as there are multiples of 17. The following pairing suggests why this is true: 1 - 17, 2 - 34, 3 - 51, 4 - 68, 5 - 85, 6 - 102, and so on.
Where physicist Barrow's play relies on a sort of abstract drama to get its ideas across, novelist Wallace's book has a more conventional format and covers more mathematical ground. Among many mind-bending oddities, it discusses different orders of infinity; in a quite precise sense the set of all decimal numbers is "more infinite" than the set of all fractions, which is "no more infinite" than the set of all whole numbers. Wallace also discusses Georg Cantor's unprovable Continuum Hypothesis, which deals with these various orders of infinity.
The task Wallace has chosen is heavy going, but he brings to it a refreshingly conversational style as well as a reasonably authoritative command of mathematics. Because the language is smart and inventive, the book provides enough enjoyment to induce the mathematically unsophisticated reader to slog through the many difficult patches along the way.
And this is part of the value of the confluence of these two works and of others like them. Although it's extremely unlikely that a novelist will prove a new theorem and only slightly less improbable that a mathematician will write a great novel, these attempts to span the chasm between the so-called two cultures should be applauded. Mathematical exposition is too important to be left only to mathematicians, and the wide variety of literary forms available should not be off-limits to mathematicians and physicists.
Maybe one day Heartbreak Hotel will be just down the creative block from Hotel Infinity, but right now it's time to check out.
Professor of mathematics at Temple University and winner of the 2003 American Association for the Advancement of Science award for the promotion of public understanding of science, John Allen Paulos is the author of several best-selling books, including Innumeracy and A Mathematician Plays the Stock Market. His Who’s Counting? column on ABCNEWS.com appears the first weekend of every month.