Mathematical Digest Short Summaries of Articles about Mathematics in the Popular Press "A Lucid Interval," by Brian Hayes. American Scientist, NovemberDecember 2003, pages 484488. As accurate as digital computers are, roundoff errors are hard to avoid when performing arithmetic computations with noninteger numbers. Include division, and approximation is almost inevitable. Floatingpoint arithmetic can't avoid roundoff errors either: if a number cannot be exactly represented using this notation, it must be approximated by its closest floatingpoint neighbor. The author, Brian Hayes, suggests that interval arithmeticusing intervals instead of single numbersmay be a way to determine more accurate answers, or at least a more accurate range of results. For example, a number x could be represented by the interval [a,b] consisting of the two floatingpoint numbers x falls between. While certain aspects of interval arithmetic present challengesincluding possible division by zero, or comparing intervalsHayes points to people who suggest ways to solve or manage these problems. Currently, the computer hardware needed to support interval arithmetic has yet to be developed, and acceptance of intervalarithmetic standards has not been adopted by any standardssetting organizations. In spite of this, interval methods have been successfully applied to a number of problems, including research relating to Newton's gravitational constant. And while perhaps not the best solution to practical problems requiring a single result, Hayes suggests that interval arithmetic could be at least part of the means to more accurately solve realworld problems.  Claudia Clark
