The Self-Reproducing robots would arrive in spaceships fueled by hydrogen bombs, traveling at 6.7 million miles per hour--1/100 the speed of light. * We would know they were here because they would want it that way. Their mission, after all, would probably be the search for a colony a safe distance from their own planet, sure to burn up in their sun's imminent supernova death. They would be obvious--maybe landing their probe, for instance, on the White House lawn--and they would be everywhere. They would appear not just on Earth, but in every solar system in every galaxy. * At least that's what Frank Tippler says.

Tippler, a professor of mathematical physics at Tulane University, says this scenario is highly probable if intelligent alien life forms exist. The only catch, he says, is that they don't.

"I think the evidence is overwhelming that we're alone," he says.

But just northwest of Boston, Harvard physics professor Paul Horowitz looks for extraterrestrial beings millions of miles away. He's sure they're out there.

Eight years ago he pointed an antenna up into the sky, hoping to find something, anything, to indicate that we are not alone. Since then he's been waiting. And waiting. And waiting.

At the end of each year, he and his staff review the data on the five or six signals that appear promising. Looking for some type of repetition, they point their telescope toward the indicated places in the sky and wait again.

If it's a usual finding, they probably won't be able to make any conclusions about its origin. If Horowitz and his team are especially unlucky, they'll find out that they've tracked a "mundane" object like a satellite. Their "first discovery," back in June, 1983, was an "incredibly big signal... the right profile, but not the right frequency." It took them about 30 minutes to figure out that it was the sun.

Welcome to the search for extraterrestrial life, a highly speculative science that is, by nature of its almost complete unprovability, one of the most widely debated--and tantalizingly popular--areas of study around. Some are drawn to the search by interest, some by fear, and some (according to their enemies)by the desire for media publicity. There are as many opinions about the matter as there are imaginations.

"Everybody's interested, aren't they?" muses Horowitz, with a little laugh.

The Harvard physicist can afford to chuckle a little bit, since the type of program he endorses--known as SETI, which stands for Search for Extraterrestrial Intelligence--is enjoying a comfortable share of scientific and governmental support. In fact, on October 12, 1992, exactly 500 years after Christopher Columbus's New World landing, NASA is planning to begin its SETI Microwave Observance Project (MOP) at Ames Research Center in Mountain View, California. The program will be the most comprehensive and systematic search that has ever been attempted... by humans.

The project's estimated budget is $100 million for the decade, about $14.5 million for fiscal year 1992.

Research assistant Bob Arnold explains the reasoning behind the ground-based search:

"The sun is one of the run-of-the-mill, garden variety stars, and planets are a natural by-product of star formation, and planets like Earth should be numerous," he says. "We're finding many complex molecules in space... the conditions for biology are widespread. We infer that since animals have evolved here, life could be a common phenomenon, just like stars. There should be hundreds of sites.

"You can speculate, or you can do a test--and this has been identified as the most useful approach," he claims.

SETI operates on a set of assumptions about the motives of extraterrestrials and about the development of knowledge. First, it assumes that intelligent beings will understand radio technology, no matter where their position in the universe.