The Jungles of Randomness: A Mathematical Safari

Description

We use the word random as though we understood what it meant, but, of course, its superficial meaning only betrays our deep ignorance of what is really going on. Random is mostly used to label anything we can't predict, from the roll of a die to our spouse's next major purchase, but what's actually happening to cause the unanticipated results? Ivars Peterson makes this complexity simple in The Jungles of Randomness.

As the mathematics and physics editor of Science News, Peterson knows his topic thoroughly and writes with a flair that stimulates the imagination. Whether telling about snowflake-shaped drums; brilliant, eccentric Paul Erdös's geometrical fantasies; or unbreakable and nearly unbreakable codes, he knows just when and where to open a topic a bit further to provoke greater insights. The eight gorgeous color plates and dozens of illustrations are well chosen and complement the text without overwhelming it.

Inevitably, The Jungles of Randomness touches on subjects as diverse as molecular biology, engineering, and entomology, but it stays rooted in the field from which our understanding of complexity first arose: mathematics. A fascinating and underreported field, math is finally getting the mainstream attention it has always deserved, and it's not hard to understand why with exciting books like this pointing the way. Where this will lead us is anyone's guess, but the die is cast. --Rob Lightner

From Scientific American
From a purely operational point of view, mathematician Mark Kac once said, "the concept of randomness is so elusive as to cease to be viable." Peterson examines a number of processes that seem random but may not be. In flipping a coin, he points out, "we know from experience (or theory) that we're likely to obtain an equal number of heads and tails in a long sequence of tosses. So if we see twenty-five heads in a row, it might be the legitimate though improbable result of a random process. However, it might also be advisable to check whether the coin is fair and to find out something about the fellow who's doing the flipping." Peterson looks at randomness in rolling dice, human concourse, slot machines, the synchronous flashing of fireflies in Southeast Asia and several other fields, presenting the mathematics imaginatively and clearly. Discussing the electronically manufactured random numbers that govern the operation of slot machines and other casino games, he says: "The trouble is, just as no real die, coin, or roulette wheel is ever likely to be perfectly fair, no numerical recipe produces truly random numbers. The mere existence of a formula suggests some sort of predictability or pattern."

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