GROUP THEORY IN THE BEDROOM

A selection of “Computing Science” columns by American Scientist magazine’s former editor-in-chief aimed at the numerate—or at least mathematically curious—reader.

While you don’t have to be a geek to appreciate Hayes’s lively, self-effacing style (complete with afterthoughts), it helps to understand that computer science relies on a field of math called numerical analysis and uses algorithms—rules for generating solutions to problems through an iterative process (the way you learned to do square roots in high school). The first essay explains how clockmakers developed the gears and linkages that enabled fabled medieval clocks to reach remarkable accuracy, as well as predict the day Easter would fall on. Other essays celebrate the notion of random numbers and why they are so hard to achieve. Numerical analysis also plays a role in economic models based on the kinetic theory of gases or simplified markets involving iterations of buying and selling. Hayes goes on to explain how statistics have been applied to compute which quarrels—from interpersonal to world wars—are the deadliest (surprising results here). Also, he looks at how algorithms have been developed to determine ways to divide a random series of numbers into two parts with equal sums, or nearly equal sums if the series total is odd. Gears appear again in the form of algorithms, which yield practical tables of numbers to enable engineers to make gear trains to approximate complex ratios. A couple of essays probe areas only professionals might ponder, such as computing the location of the Continental Divide or why base 3 arithmetic is better than base 10 or binary systems. But the pièce de résistance is the title essay, which explains why there is no algorithm whose repetitions would cycle through all four possible mattress positions that would assure equal wear and tear over time.

Challenging but rewarding for anyone intrigued by numbers.