The week that began with the first national observance of Martin Luther King's birthday ends with a stunning demonstration of the general irrelevance of the civil-rights era to the calamity currently engulfing much of black America. The demonstration will be on CBS for two hours Saturday night in Bill Moyers' "The Vanishing Family -- Crisis in Black America."

The honors accorded King are proportional to his accomplishment, and nostalgia for the clarities of his day is understandable. But the struggles of the 1950s and 1960s, against institutional barriers to blacks and for material assistance, are almost irrelevant to the catastrophe of the 1980s.

Government programs on behalf of access and amelioration for blacks are necessary. But such programs are barely germane to the growing crisis of personal behvior by millions of inner-city blacks. All other value-generating institutions -- schools, churches, youth organizations -- are unavailing if the primary institution, the family, fails.

Today nearly 60 percent of all black children are born out of wedlock. Imagine the astronomic percentages in many inner cities. Blacks girls between ages 15 and 19 are the most fertile population of that age group in the industrialized world. Half of all black teen-age girls become pregnant. The resulting "families" rarely are self-supporting. Almost half of all black children are partially supported by government payments.

As a result, social pathologies multiply. More than half of all black pupils in primary and secondary schools are in the 12 largest central- city school districts, where schools are inadequate and only one-quarter of the students are white. Blacks are about 11 percent of the population, but about 50 percent of imprisoned felons. The principal cause of death among blacks aged 15 to 24 is murder by blacks. Approximately 40 percent of murder victims are black men killed by black men. The yearly total approximates the total number of black deaths in the entire Vietnam war.

Young blacks, whose sexual recklessness produces oceans of misery, feel little of the kind of guilt that changes behavior. One reason for this is that they have been taught by reflexive "civil rights" rhetoric that they are mere victims, absolved from responsibility by the all- purpose alibi of "white racism."

When next you hear a "civil-rights leader" (probably a middle-class black selected from a small and self-selected pool of middle-class blacks important as brokers of government benefits) say that the big problem is, say, "failure to enforce the Voting Rights Act," try this:

Suppose that the act is now imperfectly enforced. Also imagine perfect enforcement. Then ask yourself: What would that accomplish?

The problem of black America is not an insufficiency of elected officials prepared to regard blacks, alone among American groups, as permanent wards of government compassion. The problem is that millions of blacks are victims of many irresponsible blacks.

Moyers begins asking a young unwed mother if she does not need a man's help. She replies, "Not really. I didn't have a father." Today most black families are headed by women. Most black children are growing up without fathers. Moyers talks with a Timothy, unmarried father of six children (not counting the abortion and the stillborn baby) by four women:

"I ain't thinking about holding up as far as no sex, my man, you know. If a girl, you know, she's having a baby, carryin' a baby, that's on her, you know. I'm not going to stop my pleasures because of another woman."

Moyers: "How did it feel to have those . . ."

Timothy: "Women?"

Moyers: "No, kids. Kids."

Try to concentrate, Timothy. The subject is kids. He laughingly says, "I'm highly sexed" and "I just got strong sperm," and he had "a lovely time" begetting the children. But he says, "I'm old-fashioned" about marriage. And he means he wants "a big wedding" with the men in tuxedos.

Moyers: "When?" Timothy: "Whenever."

The Timothys are more of a menace to black progress than the Bull Connors ever were.

There is much heroism in the ghettos. Moyers interviews a black man, a Newark detective, who tries to be a caring father for some fatherless children. He says that with Medicaid, welfare and food stamps, "a lot of the women are more married to welfare than to the guys layin' in the bed next to 'em. 'Cause he's just a physical thing. The whole backbone of the family is coming out of downtown or out of uptown offices."

Wrong. Such backbone cannot come from offices or any other mere physical thing. The detective really knows that. He says: "Freedom is a lot of times destruction (to fatherless children). . . . So I try to, you know, keep 'em in a little cage . . . keep 'em in my arms."

That is the voice of a real father. Nothing -- not laws propounding "rights," not rhetoric deploring "racism" -- can do what such a loving, protective cage can do.