What was going on when I was born?

The United States formally announced today that it intended to withdraw from Unesco in a year's time. But at the same time, it said that it would strengthen its participation in the United Nations and other international agencies. In a letter to Secretary General Javier Perez de Cuellar, Secretary of State George P. Shultz said, ''We wish you to understand that our withdrawal from the United Nations Educational, Scientific and Cultural Organization does not presage any wider disengagement from the United Nations or its other specialized agencies.'' Gregory J. Newell, the Assistant Secretary of State for International Organizations, said at a news conference this afternoon that the United States ''not only remained committed but would redouble its efforts'' in the other organizations. The decision to withdraw from Unesco, he said, was made only after the group refused to adjust its policies to meet American and other Western complaints.

Earlier this month, on the sixth night of Hanukkah, about 150 Jews and Arabs gathered in the lobby of a building at Hebrew University for the lighting of the candles and the singing of the Jewish prayer. The Jews then sang Hebrew songs; the Arabs stood respectfully, watching and listening. It was a rare moment of concord in the broad sweep of Arab-Jewish conflict, a fleeting symbol of the increasing effort being made in Israel by small groups of Jews and Arabs to struggle against the tide of hatred and suspicion. The group had assembled between classes at the Martin Buber Institute for Adult Education, where the Jews were studying Arabic and the Arabs Hebrew. The Jews come mostly out of an idealistic attitude that one should know the language of one's neighbor; the Arabs come out of a pragmatic conviction that one should speak the language of one's rulers.

A dispatch yesterday on the press in Suriname incorrectly described Interpress Service, an international news agency specializing in coverage of third world countries. It is an unaffiliated, nonprofit cooperative and opposes all restrictions on the press.

A fire that killed two children and a workman in an East Side brownstone home late Wednesday erupted when paint remover was accidentally ignited, the Fire Department said yesterday. A third child and a baby sitter were injured in the blaze. They are expected to recover.

The Government's index of leading economic indicators fell four-tenths of 1 percent in November, the first decline in 15 months, the Commerce Department reported today. But the Administration and independent economists expressed little concern about the dip in the index, which is intended to forecast future swings in economic activity. Some analysts said they expected the figure to be revised to a small gain when more complete data are available, while others said that the decline was a positive development.

The New York Times today publishes an interview with Senator Alan Cranston, another in a series of interviews with candidates for the Presidency. In the interview, Senator Cranston made these major points: Arms Control - A summit meeting would be sought on the arms race.

A caption with an article from Memphis yesterday about the establishment of the Benchmark Hotel incorrectly identified the two men pictured.

In recent months the United States and its allies have become the targets of what Arab and Israeli security experts describe as terrorism sponsored by sovereign nations. State-sponsored terrorism, they say, is exploiting an anti-American atmosphere in the Middle East and the willingness of some activists to commit suicide for a cause, and has become a potent form of political violence that is extraordinarily difficult to prevent or root out. Although the hard evidence is fragmentary - because of the professionalism of the operations and the ease with which plotters can disappear across Lebanon's open borders - the overwhelming opinion among diplomatic and security sources in the Middle East is that the Governments of Syria and Iran are ultimately involved in some way. They said both Syria and Iran had the resources and ample political motives for supporting these attacks as an adjunct to their foreign policies in the region. Bombing of Marine Compound When Secretary of Defense Caspar W. Weinberger declared that the bombing of the Marine compound in Beirut on Oct. 23 was carried out with the ''sponsorship, knowledge and authority of the Syrian Government,'' he was only giving public voice to what Western diplomats and Arab officials had been saying privately.

Federal prosecutors are planning to open inquiries into whether crimes were committed during an investigation of Paul N. Thayer, the Deputy Secretary of Defense, according to Justice Department officials. The apparent widening of the investigation, begun by the Securities and Exchange Commission, is said to be causing concern and embarrassment to the Administration, which has so far been silent on the matter. Two other officials have resigned this year after reportedly being investigated by the S.E.C. The United States Attorney in Washington, Joseph DiGenova, is looking into whether witnesses made false statements or obstructed justice during the investigation of Mr. Thayer by the S.E.C., the Justice Department sources said. If false statements were made under oath, they would constitute perjury.

''WHAT are you doing New Year's, New Year's Eve?'' the old Frank Loesser song asks. New Yorkers, well known and little known, who answered that question in an unscientific poll, responded with characteristic individuality and diversity. What follows are some of the more original plans, a few grand and expensive, others costing nothing at all. What they share is involvement with New York. There may even be useful ideas here for New Yorkers who haven't made their own plans yet. As she has done for the last couple of years, Carol Bellamy, City Council President, will go with friends to hear Bach's Brandenburg Concertos at Bargemusic near the Brooklyn Bridge, then dine at a restaurant. She may be home for a special fanfare. ''The great thing about living where I do, near the Brooklyn waterfront,'' she said, ''is that all the boats sound their horns at midnight. I find it exciting.''

''We're saying, you can't run programs that aren't safe for kids.'' - Michael Willie of the State Education Department on order to Yonkers schools. (A1:2.)

The State Department of Education has ordered the Yonkers public school system to suspend all winter interscholastic sports until the state is satisfied that the Yonkers athletic program is being run properly. The Education Department's report, which has not yet been made public, follows an investigation of the death last September of a 17-year-old junior varsity football player with a long history of heart disease. Yonkers officials have acknowledged that the youth should not have been permitted to play. State officials said it was the first time that the Department of Education had taken such strong action against a school system. The move by the state is meant to send a message to all New York school districts, according to state officials.