So many gay and lesbian activists attended this month's rally at the state Capitol that it was impossible to count them. But that did not stop the pundits from claiming to know just how many were there.

State Police Cmdr. Dennis Williams said that "years and years and years" of experience gauging demonstrations convinced him that no more than 3,000 to 4,000 protesters gathered Oct. 11 at the building's west steps.

"Anything over 5,000 I would have to seriously challenge," Williams said. "We pretty much know what numbers will fit in here."

Torie Osborn, executive director of the Los Angeles Gay and Lesbian Community Services Center, said that after two decades of rallies she was sure 12,000 people had turned out to denounce Gov. Pete Wilson's veto of a homosexual rights bill.

"I've done so many of these, you just get a sense of it," Osborn said. "There's no way it was less than 10,000."

In an age of instant public opinion, crowd counting has become an unbelievable numbers game.

A generation after widespread protests altered the course of the Vietnam War, the ability to mass bodies has become a crucial gauge of almost any cause, whether people are welcoming home troops, debating abortion, cheering a visiting dignitary or, as in recent days, rallying for gay rights.

A huge turnout--or at least the perception of one--can capture the media's attention, sway elected officials and, ultimately, force a nation to rethink long-held assumptions. A disappointing showing can mean relegation to the radical fringe.

As a result, crowd estimates--dished out with an air of certitude--often are fabrications, wishful thinking or wild guesses. Without a turnstile to prove anyone wrong, it is usually politics--not a desire for accuracy--that most shapes the numbers.

"Telling the size of a crowd is in the same category as uttering an effective slogan," said Neil Smelser, a UC Berkeley sociologist. "As a measure of public sentiment, it's not very precise. But as rhetoric and symbolism, it matters very much."

The discrepancies occur every time people gather in the streets, whenever ideology, money or prestige is at stake.

At the beginning of the Persian Gulf War, either 2,500 or 15,000 protesters marched on Los Angeles City Hall. Earlier this month, anti-abortion demonstrators in the South Bay formed a human chain that might have had as few as 10,000 links or as many as 25,000. When Nelson Mandela visited the city last year, the crowd was initially set at 3,000, then revised to 15,000.

The Los Angeles Marathon, vying to overtake New York City's race, drew 250,000 spectators, or more than 1 million, depending on who did the counting. At Fiesta Broadway, last April's Latino street fair, estimates ranged from 500,000 to 1 million. And at the L.A. Festival last September, between 3,000 and 30,000 people attended some of the events.

In Orange County, Irvine police initially estimated the crowd at a May victory parade for Gulf troops at 200,000. However, after reviewing aerial photographs, police later reduced that number by half. "To be honest with you, I was a little liberal because of the spirit of things," Sgt. Tom Hume said when making his revision.

"It's all spin control," said Laura Myers, a reporter for the Associated Press who covered anti-war protests this year in San Francisco, where estimates at one rally ranged from 20,000 to 200,000. "If they want a bigger crowd, they just say there's a bigger crowd."

Part of the problem is the dynamic nature of a crowd. Even an objective counter must contend with a huge number of bodies, ebbing and flowing over an extended period of time, usually in a space with no fixed boundaries.

George Berklacy, chief of public affairs for the National Park Service in Washington, said he used to deal with such fluctuations by relying on the SWAG system--"scientific wild-ass guess." In fact, few police agencies have a method for calculating crowd sizes. And officers, who usually end up doing little more than educated eyeballing, often have little interest in providing the so-called "official estimate."

"There is no formula," former Pasadena Police Lt. Gregg Henderson said when asked whether crowd counts at the annual Tournament of Roses Parade were overblown. "You go up in the air and you take a look down, and it's like, 'Yep, a whole lot of folks down there, probably about a million.' "

In the absence of a formula, chaos rules. Police often are accused of low-balling the numbers, organizers are charged with inflating them, and reporters are faced with estimates so wildly disparate as to be left wondering whether those doing the counting actually attended the same event.