The Democrats convene Monday in the midst of a historic political paradox: They are deeply divided over their presidential choice, yet underneath the apparent disunity lies a source of potential strength.

Democrats are variety. If this convention shows the national television audience a diverse political party, genuinely open to all, the message could be a powerful political force in the fall. Or the message could be bedlam.

The delegates caucusing across Manhattan today represent a wide spectrum of American society. The contrast between them and their Republican rivals who assembled last month in Detroit could not be more dramatic.

Consider this. The place: the gilded splendor of the Waldorf-Astoria Hotel. The occasion: the first gathering of the California delegation. Last month their Republican counterparts from the nation's largest state were a study in similarity -- a largely all-white, predominantly male, middle-aged delegation whose members even dressed alike, wearing white cowboy hats as a gesture of proud conformity.

The Democratic version looks as if it came from a different state -- out of that sea of faces you could put together almost the picture-perfect democratic -- small "d" -- convention. Women of all ages and manner of dress, from the sensuous look to the rigorously asexual, were seated everywhere. Blacks, Indians, Chicanos, gays and lesbians filled the room (some 30 gays and lesbians are among California's 306 delegates).

They seemed to glory in their diversity.

A young woman delegate arose to ask if she could take her 1-year-old child onto the convention floor. Another stood to ask all the women present to wear white dresses -- the color of the suffragettes, she explained -- when they assemble in Madison Square Garden Monday before national television. A male delegate asked whether, if he leaves the convention floor, the alternate replacement also has to be a male. A nonsmoker took the floor to ask that all cigarettes be extinguished. a black delegate questioned the language of a platform report that spoke of minorities but failed to specify blacks.

They were vocal, noisy, emotional. The Carter delegates cheered when the president's son. Chip, urged them to hold fast on the rule that binds delegates to the candidate they backed in the primary. The Kennedy delegates stood and shouted their approval when the senator forcefully called on them to reject that rule and let all Democratic delegates vote their conscience.

And they were notably attentive and serious when the delegates leaders explained the intricacies of roll calls, procedures and how to obtain credentials. Sounds of shhhh, shhhh, swept the caucus whenever these questions were raised. Silence was immediate.

A show of hands demonstrated a majority were attending a convention for the first time.

These same kinds of scenes were being duplicated at other caucuses throughout New York today. They provided evidence of the great change that has taken place in the Democratic Party.

For the first time, half of the delegates are women. That represents a sharp increase form the 1976 convention here, when one-third of the delegates were women. Four years before that only 13 percent of the delegates were women.

The 3,331 delegates also include more blacks than in the last New York convention -- this year's figure is 14 percent. Close to 6 percent of delegates are drawn from other minority groups roughly equal to their share of Democratic voters at large.

A Washington Post sampling of 591 Democratic delegates reinforces that show of hands in the California caucus. New faces abound throughout the convention halls and hotels. The Post poll shows 70 percent are attending their first national convention.

Behind these figures stands a larger political story. The composition of this convention represents the culmination of bitter struggles among Democrats for more than a generation. Previous Democratic gatherings were rent by disputes over seating blacks and women or groups espousing causes then considered radical or politically destructive.

Now, those battles are over. The Democrats have achieved their broad representation after more than a decade of often divisive party reform efforts. r

And now, ironically, no one seems to notice.

Politically the Democrats are much more representative of the country than are the Republicans. They have another potential advantage that could help them in the future -- their age. These Democrats are considerably younger than the Republicans who convened in Detroit.

For example, 13 percent of the Democratic delegates are 30 years of age or younger. The Republicans had only 5 percent in that age group.

The demographic differences between the two parties are matched -- or exceeded -- by their ideological ones.

Democratic delegates overwhelmingly favor adoption of the Equal Rights Amendment to the Constitution. The Post sample shows 86 percent are for it and 10 percent opposed. An earlier Post survey of the GOP delegates found Repulbican sentiment exactly the opposite. Their delegates were against ERA, 70 to 27 percent.

Similar sharp disagreements are found on other major issues. The bulk of the Democrats here, 72 percent, oppose balancing the budget if that meant cutting into social programs. In Detroit, 75 percent of the Republicans said they favor balancing the budget even if it means cutting back such programs.

On national health care, Democrats, by more then 2 to 1, want the federal government to institute a national care program now. Republican delegates, by 11 to 1, oppose it.

The Democrats still express concern about the power of business, while the Republicans don't. Fifty-two percent of the Democrats here agree with the statement that "businessmen have too much power for the good of the country." Ninety percent of the GOP delegates disagreed.

And they continue to differ over the role of the federal government in providing work for Americans.

Democratic delegates by 56 to 39 percent, agree with the proposition that the government should see to it that anyone who wants to work has a job. Republicans' response to that question was the opposite -- they wanted the government to stay out of job guarantees by 85 to 13 percent.

Where the two parties resemble one another is in the wealth and education of their delegates. Both party conventions continue to represent society's elite, as compared to the public at large.

Two of every three Democrats are college graduates, while nearly 25 percent of them have annual family incomes of more than $50,000 a year. Republican delegates had even higher economic status.

But mutual affluence aside, the two parties obviously stand for different approaches to public issues and public policy.

The Democrats, after their long years of struggles over party reform, are clearly the more diverse political gathering.

And, as always there is intellecutal diversity here. The party platform speaks of budgetary restraint, fiscal responsibility and "the discipline of attempting to live within the limits of our anticipated revenues." But the party's socialist left wing lives on in the Democratic Agenda, led by the old socialist, Michael Harrington. He denounces the "no longer relevant John Kennedy tax cut liberalism" which, he says, Republican nominee Ronald Reagan has embraced

What is needed now, Harrington tells all who will listen, is greater control of the corporations, federal charters for oil companies, jobs for all and a Democratic Party that "has to go as far beyond Franklin Roosevelt as Roosevelt went beyond Herbert Hoover."

For all the divergent philosophies and lifestyles on display here, the backbone of this party remains its respectable, God-fearing middle class, best symbolized by the powerful National Education Association and its 464 delegates and alternates. They have come late in their history to party politics, but now they play the game with a vengeance and great skill. Their incomes and their careers depend on the public purse, and they are determined to have a significant vote in how public monies are spent.

There was a great gathering of Hispanics tonight at the Coliseum. The New York fire marshal ordered the doors closed after the hall filled up.

Two reporters walked up to the door and flashed their press passes to the doorkeeper, obviously nervous because of the crowd outside that had been denied admission.

One of the Hispanics denied admission tapped the reporters on the shoulder: "If he lets you in that hall I will tell you something. He will be dead. Right away. He will be dead!"

And the reporters?

"You will find out."