The electronic dawn came precisely at 9 a.m., bathing the Orange Julius stand in a cool fluorescent glow and glistening off the designer frames in the counters at Royal Optical. Along three miles of hallway, 195 store managers began raising their Roll-O-Matic auto-shutters, and a platoon of cookie, corn dog and KarmelCorn purveyors lit their ovens.

To the swelling strains of "Oh, What a Beautiful Morning" on the Muzak, a new day was breaking at Southwest Plaza, an enormous pentagonal shopping mall that floats above a vast sea of suburban homes like the battleship New Jersey at a convention of canoes.

Before the end of the shopping day 13 hours later, about 30,000 people would pass through the Plaza, staying an average of 2.3 hours apiece. They would fill all 6,928 spaces in the sprawling asphalt parking lot, drop 150 pounds of pennies into the fountains around the mall's central "performance center," eat 1,000 Super Pretzels and purchase a half-million dollars' worth of goods and services ranging from diamonds to doorknobs, dental checkups to divorce settlements.

It was, in short, just another August day at the shopping mall, the place where much of America spends -- literally and figuratively -- its summer.

It is established sociological lore by now that giant shopping centers such as Southwest Plaza, a concrete hulk built in a style that might be called early airplane hangar, have become the social center of American life, the new Town Hall and Main Street, although Main Street would have to be 30 blocks long to hold all the shops and offices this center provides.

But to the retailing and service industries -- the fastest-growing sectors of the American economy -- the shopping center is first of all an amazing money machine, the most powerful marketing mechanism ever devised.

The ingenious secret of the American shopping center -- if anything that happens 30 million times a day can be said to be secret -- is a phenomenon deliberately designed into every mall. It has been called the "Gruen transfer" in honor of retailing visionary Victor Gruen, who conceived the notion 30 years ago, and it was visible on a recent morning at Southwest Plaza minutes after the center opened for the day.

A young woman wearing pink pedal pushers and tugging two small children marched rapidly down the corridor, resolutely ignoring the petting zoo, the Dairy Cream, the Radio Shack and the House of Suede as she headed directly for Kinney's Shoes.

In marketing parlance, she was clearly a "destination shopper" -- a consumer who had come to the mall with a specific purchase in mind.

But the woman could not find all the shoes she needed at Kinney's. So she set off toward one of the mall's other shoe stores -- a trip that took her past dozens of other merchants.

Suddenly, she veered into Hickory Farms; from there, she moved down the corridor to Waldenbooks. By the time she arrived at the next shoe store, her arms were full of purchases, and each child was lapping at an ice-cream cone. Setting Up the 'Impulse' Gantlet

Just as Gruen intended, the woman had been transformed from a "destination shopper" to an "impulse shopper" -- precisely the metamorphosis about which mall designers dream.

"See, we put one shoe store here and another way over there," explained Marcella Cain, Southwest Plaza's exuberant young operations manager. "We want you to pass 35 more stores between the two. Hopefully, you'll drop 30 or 40 more bucks along the way . . . . A destination shopper turns into an impulse shopper."

Until very recently, it was all but holy writ in the shopping-center business that the key to this phenomenon was size: big malls with long corridors lined with lots of stores to create and feed the shopper's appetite.

The apotheosis of that theory is represented by the malls known as "super-regionals" -- White Flint and Tysons Corner are Washington-area examples -- with three or more major department stores as "anchor" tenants and more than 150 shops and service outlets.

"Bigger is better" is clearly the watchword here at Southwest Plaza, a super-regional with five major department stores, five movie theaters, 190 other retail outlets, an office tower housing dozens of lawyers, doctors, dentists and social workers and a string of three smaller peripheral malls that have sprung up on the edge of the 123-acre complex like suburbs sprawling outward from a city's limits.

It offers about 1.5 million square feet of shopping area -- roughly equivalent to 108 floors of the Empire State Building.

It has not two, not 10, but 18 shoe stores -- "I can't believe it, but every one of them is making a profit," said mall manager Dale Flowers -- and well over two dozen women's clothing outlets. Its 31 eateries offer such novelties as a cookie the size of a hubcap for $14.

According to traditional shopping mall theory, the second key to impulse sales is a proper "tenant mix." The International Council of Shopping Centers, a New York-based trade association, issues detailed formulas telling mall managers how many jewelers, book shops, pet stores, candy counters and whatnot to put on each floor. Tinkering With the 'Tenant Mix'

Maintaining the right mix means keeping up with constantly changing public moods.

When Southwest Plaza opened two years ago, video arcades were the hottest thing going. The mall added two big arcades where kids lined up for the privilege of pouring their money into such games as "War of the Bugs" and "Revenge of the Beefsteak Tomatoes."

Today, according to Flowers, the mall manager, "the arcade business is way off all over the country." The plaza is seeking replacement tenants -- perhaps a specialty sporting goods store, a field in which sales are booming.

The trend of the 1980s in shopping centers, reflecting the general shift from a manufacturing to a service economy nationwide, is the arrival of what the industry calls "nontraditional tenants" -- service outlets selling expertise instead of merchandise.

At Southwest Plaza, as at malls everywhere these days, a consumer can visit his banker, broker and bookkeeper. He can lease a car for a year or "check a child" for the afternoon. "You can come in here, get your car fixed, have your teeth checked, get your taxes done, pay your insurance premium, make your plane reservation, rent your skis, get your watch cleaned and settle on your new house," said Cain, the mall's operations manager.

Murray Turner, leasing manager for the development company that built this mall, said he has been inundated with rental applications from medical professionals: The plaza's office tower houses seven dentists, a dozen physicians and chiropractors, a psychologist and four licensed social workers.

For all of its emphasis on being big and inclusive, however, the super-regional mall does not have everything. The absence of bread and butter is as much by design as the presence of record stores and popcorn stands.

"Maybe five, 10 years ago, you wouldn't think of building a mall this big without a supermarket," Flowers said. "Now hardly any developer wants one."

For one thing, industry experts say, grocery stores have such a low profit margin -- often less than one cent per dollar -- that they cannot afford the rent in fancy mega-malls. Mainly, however, the grocery shopper usually is not susceptible to the Gruen transfer.

"We want our customers to stroll past our stores for two hours or more, Flowers said. "It's what they used to call window shopping. Well, if mama's got the ice cream melting in her shopping bag, she's not going to spend her time walking the mall."

If Southwest Plaza and the hundreds of other super-regionals represent the culmination of the drive for size in shopping centers, there is also a strong body of thought that these mega-malls may be dinosaurs. The burning issue these days in the pages of trade publications such as "Shopping Center World" and "Modern Mall Monitor" is a revolutionary theory that, even in the shopping center business, small can be beautiful.

With land and energy prices going up and shoppers' tolerance for jammed parking lots and jostling crowds going down, many developers are building new malls that spurn three decades of accepted wisdom.

Among the most popular new species is the "specialty mall," which features a relatively small number of stores, many of them nonchain outlets, with no major department store as anchor.

Such malls can be found not only in city centers, where land prices preclude a large mall -- such as Washington's Old Post Office -- but also in the suburbs, often alongside the leviathans.

Directly across the access road from Southwest Plaza is a small shopping strip with seven furniture stores side by side. Industry analysts say such "unit centers" are succeeding, evidently precisely because they are so different from the multifaceted mall that shoppers have known for years.

The "unit center" concept is a gross violation of the gospel according to Gruen, an Austrian refugee from the Nazis who was to shopping centers what Henry Ford was to cars. As an architect with the Dayton-Hudson retail chain, Gruen realized that the postwar American phenomenon called the "suburb" eventually would need the kind of social and commercial nucleus that had been provided by the downtown hub in the cities. This seminal insight has since been enshrined in sociology texts as "metro-nucleation."

In the mid-1950s, Gruen brought his concept to life in two suburban shopping centers: Northland outside Detroit and Southdale at the edge of Minneapolis. There Gruen created a new shopping experience: the fully enclosed mall.

Fully enclosed meant, of course, that all the stores were under one roof. But it also had deeper meaning.

In his suburban wonderlands, Gruen shut out such downtown nuisances as traffic, weather and poor people. Americans who had flocked to the suburbs to avoid living with urban problems now found that they could also avoid shopping with them.

But as Gruen noted in his master work, "New Forms of Community," the shopping center was much more than a retailing locus. Instead of gathering in the courthouse square, Americans would now find their community in huge concrete structures called Northland and Southdale, Westgate and Eastridge, Northeast Mall and Southwest Plaza.

As Gruen predicted, what happens in America today happens largely at the mall.

"We have what no place else in our society has today, and that's people," said Flowers, the Southwest Mall manager.

It hardly takes a survey to prove what almost every American knows, but the shopping center industry regularly surveys the public to ensure that people remain true to their malls.

In a national poll last spring, Shopping Center Age magazine found that 78 percent of Americans -- about 185 million people -- go to a large enclosed mall at least once a month. The figure was somewhat higher for smaller community and neighborhood malls.

Fully 93 percent of the population had been to a big mall at least once in the last six months. The remaining 7 percent were mainly city or country dwellers with no ready access to the suburbs.

Within those hefty figures are tens of millions of "mallingerers" -- people who go to a shopping mall virtually every day.

One large group consists of the "mall rats," age 9 to 19, who go to a mall whenever they are not in school. At the other end of the demographic spectrum is the legion of "mall walkers," elderly cardiac patients who have been ordered by physicians to exercise daily in a controlled, predictable environment.

They do so by walking through shopping malls. It is such an important part of life that Southwest Plaza, like many major malls, opens its doors at 7 a.m., two hours before store lights come on, to accommodate the mall walkers. $/ Dissecting the Social Significance

The significance of the mall in American life has not been lost on academia. Prestigious colleges offer graduate degrees in "Shopping Center Management," and every year doctoral candidates in anthropology and sociology produce dissertations on the malls, treatises called "Shopping Center Preference -- The Adequacy-Importance-Attitude Model" or "Selected Components of Shopping Center Imagery."

There is also a burgeoning body of shopping center law, ranging from minuscule commercial disputes to a raging First Amendment question: If the shopping center is the new Main Street, do Americans have the same right to picket and petition in a privately owned mall that they have on a public avenue?

The Supreme Court has considered this question four times since 1968, reversing itself twice. The current answer can best be summarized as "maybe."

The most contentious legal issue that shoppers and shopping centers are fighting over today, however, is one that has touched almost every aspect of American life: civil liability. To the mall industry, it seems that everybody ever hurt, physically or financially, in a shopping center sues the management.

At the insistence of insurance companies, the managers of Southwest Plaza, like their counterparts elsewhere, take extensive steps to guard against liability. Every few minutes during a typical day here, the careful listener will note that the Muzak has been interrupted for a coded message on the public address system:

"8-5-0 in front of Zales," the announcer will say, or "8-5-1 next to Eddie Bauer's, upper level."

These are urgent calls to maintenance or security crews to clean up a spill. An 8-5-0 means that something wet -- such as a soft drink -- was spilled. An 8-5-1 means a dry spill, such as popcorn. In either case, it must be cleaned up immediately, because the shopper who slips is thought almost sure to sue.

Southwest Plaza has a security force, uniformed men and women who carry handcuffs but no guns. One of their major tasks is policing the parking lot, cleaning up after fender-benders and helping the several people each day who have lost their cars in the vast asphalt desert, supporting columnist Erma Bombeck's theory that malls rotate slowly all day so that you always go out the door farthest from where you parked and entered.

But Southwest's security force has had to stop its former practice of lending booster cables to motorists with run-down batteries or putting some free gas in empty tanks. "We can't do that anymore because the insurance company's afraid some driver will sue us if his car breaks down," Flower said.

Marcella Cain, the operations manager at Southwest Plaza, learns anew each night how satisfied most mall shoppers are. The lesson begins at 9:30 when the public address system announces that the mall will close soon.

"It takes us a good hour to get people to leave," she said. "It's just harder than heck to convince people that they have to leave the mall and go home. The public is just nuts about coming to this place."

Perhaps the most revealing statistic in last spring's Shopping Center Age survey came when respondents were asked to list what they found "unpleasant" or "bothersome" about their favorite malls. Fifty-four percent replied, "Nothing."

Among those who did have a complaint, the two most common gripes were crowded parking lots and crowded stores. In other words, the average American in 1985 loves the shopping mall so much that his only real complaint is that everybody else loves it, too.