In old-fashioned carnivals, the final act of the night was known as "the blowoff." It was the big finish, the supposedly naked lady or death-defying feat that the customers paid to see.

Needless to say, the blowoff usually wasn't as titillating as the hype promised, but it managed to come close enough that the customers felt foolish demanding their money back.

Amir Aczel's Probability 1, just released in paperback, leaves its readers with much the same feeling.

Aczel, a professor of statistics at Bentley College, claims that his book, subtitled "Why There Must Be Intelligent Life in the Universe," contains definitive proof that intelligent life must exist in the universe.

Furthermore, he promises to back up this claim using the mathematics of probability.

Drake suggested figuring out how many habitable planets there are in the galaxy, how many are likely to develop life, how likely that life is to develop civilization, and so on. If you can figure out the right numbers and plug them in, you'll have a pretty good idea how many civilizations are out there.

The difficulty, of course, is in figuring out what the right numbers are.

Aczel spends most of Probability 1 going through each of the factors in Drake's Equation, presenting what astronomers now know about how common planets are and how likely life is to develop.

His writing is clear and engaging, and Drake's Equation is so broad in scope that Probability 1 becomes an excellent general survey of current astronomy. Fans of Asimov, Sagan and other science writers will find much of the material familiar, but Aczel also presents a lot of exciting new developments in the field.

The most interesting chapter, however, focuses on mathematics. Aczel presents a fascinating discussion of how probability and psychology interact, showing why you always seem to wait longer than normal for the bus and how the same math may explain why we haven't found aliens already.

Unfortunately, the final "proof" that appears in the book's final chapter wastes this survey of astronomy and math, using almost none of it.

Instead, Aczel simply makes the point that even using arbitrarily tiny values for the factors in Drake's Equation, the number of stars in both our galaxy and the greater universe is so vast that it's impossible for the equation not to return the practical certainty of alien life.

Therefore, he announces triumphantly, it's certain there's at least one other civilization somewhere in our galaxy.

That's good news. Unfortunately, the information is useless when arrayed to prove a point that wasn't even under serious dispute in the first place.

As Aczel points out, our galaxy is huge. While there might be a civilization on the other side of it -- as far as 100,000 light years away -- we aren't likely to be communicating with it any time soon.

The real question is how far away the nearest civilization is likely to be. What are the chances there's somebody close enough to talk to?

It's a question Drake's Equation was designed to answer, but while Aczel brings up the issue of distance at the beginning of the book, he completely ignores it when formulating his "proof."

That's too bad. There's nothing wrong with a good survey of astronomy, but the death-defying stunt we really want to see is conclusive evidence that aliens are closer than we think.