What was going on when I was born?

Artillery explosions thundered throughout this city of 600,000 today and rockets shrieked overhead as rival Palestinian factions battled for the Beddawi refugee camp to the north. The shells began falling over a wider area of Tripoli late Friday and by today no section of the city was being spared, the police said. They said the shelling was slightly more intense on Friday but that it was concentrated in a few neighborhoods, particularly those on the north edge of Tripoli, adjacent to Beddawi, and around the port, where Mr. Arafat's men have been active with their rocket launchers. ''Last night was terrible,'' said a prominent lawyer. ''Many people slept in stairwells. Women and children are losing their nerves. They are becoming crazy and taking pills. I went to two pharmacies near my office and they said they had sold all their tranquilizers. You cannot even find aspirins.''

Secretary of State George P. Shultz said today that the outcome of the struggle within the Palestine Liberation Organization was certain to have ''major implications'' for the future of the American- sponsored peace efforts in the Middle East. Mr. Shultz pointed to a recent statement by King Hussein of Jordan, who said that if the P.L.O. fell under Syrian domination there was a legitimate question of whether it could continue to speak for the Palestinian people. Mr. Shultz's remarks were in a speech delivered tonight before the Council of Jewish Federations and Welfare Funds in Atlanta. King Hussein declined earlier this year to enter American-sponsored talks with Israel because he could not gain the endorsement of Yasir Arafat, the P.L.O. chairman who is fighting for survival in northern Lebanon against a group of Syrian-backed rebels. Some State Department officials have said King Hussein might take courage from the P.L.O. struggle and decide to enter negotiations without waiting for a P.L.O. endorsement. But Mr. Shultz avoided going that far in his assessment of the possible results of the P.L.O. strife.

RUSSIA Broken Idols, Solemn Dreams. By David K. Shipler. 404 pp. New York: Times Books. $17.95. BENEATH the guessing game played by Western observers about who's on top in the Soviet leadership - it is not worth much, but it pays the rent - is another and more serious level of speculation about long-term trends in the Soviet system and society. Those trends are obviously fateful for the world, but questions about them are difficult to answer more than impressionistically. The Soviet Union is too big and complex, and the data are too hard to come by. And, for that matter, how definite can anyone be about long-term trends in any society, including our own?

The experts had predicted that the result would not be close. Unlike the final of the National Collegiate Athletic Association tournament last spring, when North Carolina State defeated Houston by 2 points, this game more or less figured to be a showcase for Akeem Olajuwon, Houston's 7-foot center and the basketball fraternity known as Phi Slama Jama. Well, the experts were right about one thing - the score wasn't close today. But it was North Carolina State that won, 76-64, in the Tipoff Classic game that signals the opening of the college season. And if Jim Valvano, the Wolfpack coach, was pleasantly surprised, then his counterpart Guy Lewis was somewhat embarrassed by his team's performance.

AWEEK after losing his comeback attempt, former Democratic Mayor John C. Mandanici of Bridgeport was preparing for another fight. He is planning a court challenge to a state law that prevents him from being a Democrat for two years because he ran on the Taxpayers Party ticket this time. ''This is America,'' Mr. Mandanici said. ''To oust me from the party for two years infringes on my Constitutional rights.''

Steve Smith, Michigan's senior quarterback, made up for a lot of past mistakes today when he threw for two touchdowns and ran for another to lead the Wolverines to a 24-21 victory over Ohio State and into the Sugar Bowl game Jan. 2. Smith had been blamed quite a bit for Michigan's losses to the Buckeyes in 1982 (24-14) and 1981 (14-9). But this time the Michigan quarterback excelled before 106,115 fans in Michigan Stadium. The result left Michigan with a 9-2 record and a berth against Auburn in the Sugar Bowl game while Ohio State (8-3) earned a trip to the Fiesta Bowl game against Pittsburgh on Jan. 2.

CHICAGO ALITTLE more than a year ago, Martin S. Feldstein, Chairman of the President's Council of Economic Advisers, vetoed the Reagan Administration's evolving economic forecast. He told his fellow Presidential advisers that the United States economy would not grow at a 4.4 percent clip over the next 12 months - 3 to 3.5 percent was more likely. Many of Mr. Feldstein's fellow economists agreed with his caution. High interest rates, the looming budget deficit, sickly foreign economies - all mitigated against a strong recovery. Or so they warned. But they were wrong. The economy came roaring back, so strongly that only a firm tug on the monetary reins by the Federal Reserve has held real growth to an annual rate of 6.5 percent since the recovery began last winter - which tracks with virtually every economic recovery since World War II. The recession of 1981-82 may have been the worst by many measures since the Great Depression, but this first year of recovery has been remarkably average. If it were to continue average, the recovery would last another two to four years.

Nine years ago, backed by Turkish troops who had just seized the northern third of Cyprus, Rauf Denktash threatened to set up an independent Turkish Cypriot state if the Greek majority on the island did not accept a more equitable political arrangement. Last week, with the situation essentially unchanged from 1974, the Turkish Cypriot leader made good his threat. Mr. Denktash's declaration of independence concerned about 150,000 people occupying little more than 1,300 square miles and without many friends to help them out of their poverty. But the move set off minor tremors in the world. Turkey was once again at odds with Greece, its nominal NATO partner. Athens threatened to end all discussions with Turkey unless it withdrew its recognition of the new state. Britain, the former colonial power and a guarantor of Cyprus independence, condemned the move, as did the United States. President Reagan sent his new Middle East envoy, Donald Rumsfeld, to confer with the Turks and prepared to receive President Spyros Kyprianou of Cyprus tomorrow. At the United Nations, which has maintained a peacekeeping force on the island since 1964, the Security Council denounced the move as illegal and called on Turkish Cypriots to withdraw it.

As the rock generation approaches middle age, it has become the pop cultural establishment. The old intergenerational battles that pitted rock hipness against pop squareness - the Beatles and the Rolling Stones against Frank Sinatra - have receded into the past. After a long period in which pop was so rigidly formatted on the radio that one had to switch stations in order to hear different musical styles, the barriers separating sounds have begun to crumble. More important, the artists themselves have begun to push across the lines dividing records from other popular art forms. Along with records, the pop marketplace has begun to be flooded with video music software, much of it rock concert footage. The best-selling full-length musical video program to date has been ''The Compleat Beatles,'' with sales of over 65,000 video cassettes and video disks. But the music industry will be closely watching the sales performance of Michael Jackson's hour-long video program, ''The Making of the Thriller Video,'' which hits the marketplace Dec. 14.

The Reagan Administration has drafted a plan requiring the Census Bureau to share the personal information it collects about the American people with a number of Government agencies. Officials in the Office of Management and Budget contend that sharing the information, which is prohibited by law, would improve Government efficiency by reducing the cost of making surveys and eliminating overlapping studies by different agencies. 2 Agencies Oppose Proposal The officials add that a provision in the draft legislation prohibiting the use of such information for law enforcment, national security or administrative purposes would improve the protection surrounding the millions of statistical files maintained by the Government. But officials in both the Census Bureau and the Internal Revenue Service are fighting the Administration's proposal. They argue that any tinkering with the law, no matter what the intent, might undermine the willingness of Americans to fill out census forms and pay their taxes on what is essentially a voluntary basis.

AWOMAN whose job was final inspection grabbed something resembling a bracket for wall bookshelves that for some reason had a shiny doorknob stuck on the end. It was actually an artificial hip. ''Here's a shoulder,'' remarked a co-worker, plucking what looked like a skinny faucet out of a rack. ''I believe this is a wrist.''

At the height of the civil rights movement in 1965, when a quarter of black families with children were headed by women, Daniel Patrick Moynihan wrote in a report to President Johnson that this growing matriarchy was an important cause of poverty among black Americans. Mr. Moynihan, then a White House aide, created a furor, accused by many of blaming the victims for their distress. Today, 18 years later, virtually half of black families are headed by single women, and 55 percent of black babies are born to unmarried mothers. Gun-shy from the Moynihan experience, authorities for years were reluctant to speak out about the problem. But now, politicians and scholars - black and white, liberal and conservative - openly agree that the situation has reached such proportions that it threatens to undo the black economic gains of the past three decades. Growing Alarm Among Blacks The breakdown of traditional family structure is, they say, one of the underlying causes of black poverty, not only because there is no man to provide family income but also because women on the average earn much less than men.