What was going on when I was born?

Claudio Arrau's piano recital at Avery Fisher Hall this afternoon will celebrate his 80th birthday and, at the same time, bestow a twofold gift on his listeners. For every so often, nature produces a musician who achieves great age without relinquishing his powers of communication, and events like today's not only compress 70-odd years of practical performing experience into two hours of music; they tell us in fascinating ways how age can transform how we think and how we hear. Few of the living can see Mr. Arrau's career as a whole - it stretches far too far into the past. But clearly this long musical life - begun in Chile in 1903 and nurtured in Berlin before World War I- serves as connective tissue between the emotional generosity of the Romantic era and the respectful restraint of mid-20th century interpretive philosophy. Mr. Arrau's teacher in those Berlin years was Martin Krause - a pupil of Liszt. Yet it has been in the 1950's, 60's and 70's - an age of new classicism among performers - that Mr. Arrau's major recording projects have taken place. Rarely have two separate traditions been so successfully bonded together in one man, and for those who cannot share today's concert, there is the phonograph to assure us that all these qualities are really there.

ticket brochure proclaims, ''Billy's back!'' Bumper stickers shout, ''Billy's back!'' Billboards blare, ''Billy's back!'' And everyone asks, ''For how long?'' The contract that Billy Martin signed Jan. 11 says for five years; the skeptics say contracts between Billy Martin and George Steinbrenner have not been completed twice before. Billy and George. They are perhaps a more widely discussed couple than Elizabeth Taylor and Richard Burton ever were. They have forged a link that makes them as familiar a pairing as Abbott and Costello or Roy Rogers and Trigger. They are so well known they transcend the sports pages. They have wound up, for example, on the comic pages.

WITH divorce so common and New York City apartments so hard to find, the question of who keeps thea partment when a couple breaks up has taken on new importance. An additional element is added to the situation when there is a p rospect of a conversion to a cooperative. Whoever gets the a partment may be able to buy it at a bargain insider price in a c onversion. There are many other questions involving real estate thatp arting couples may quarrel over, usually when property is owned. Butr ental situations offer special complications. Lawyers offer conflicting advice, but many agree that when it comes to maintaining the right to stay in possession of an apartment, there is a ''best'' position to be in, which can be determined by a few key questions: - Did you occupy the apartment before the marriage? - Is your name on the lease?

ATLANTIC CITY SINCE the opening of its first hotel-casino in 1978, this resort often has been called Las Vegas East. But if the swift growth here continues, Las Vegas may become Atlantic City West. Last year, with nine casinos its prime attraction, Atlantic City had 23.1 million visitors, double the 11.6 million for Las Vegas. The Atlantic City totals (up 21 percent from 1981) were announced last week by the city's Convention and Visitors Bureau and the New Jersey Expressway Authority.

Moshe Arens, who is replacing Ariel Sharon as Israel's Defense Minister, says that Israeli-American relations have worsened in recent months partly because of the Reagan Administration's attitude toward talks on Lebanon. Mr. Arens says the problem, in his view, is that some American officials have ''idealized notions'' about how quickly a negotiated solution can be achieved in Lebanon. In his first interview since being named to the Cabinet on Monday, Mr. Arens said the United States had benefited from Israeli military gains in Lebanon last summer. But, he added, ''You have got some people in the Administration who would like to pick up the dividends and kick us in the teeth at the same time.''

HARTFORD CONNECTICUT Republicans, the minority party in the state since the 1950's, will make a change at the top this week in a shift that could reshape the party's future. The significance of the move, in the view of some politicians, will be more than the selection of a new Republican State Chairman. It will signal a changing of the guard to a new generation of party leadership and the emergence of Senator Lowell P. Weicker Jr. as the leading figure of a party with which he had long been at odds. If everyone follows the script, as expected, the Republican State Central Committee will meet here Tuesday evening to elect Thomas J. D'Amore Jr. as the party's state chairman, succeeding Ralph E. Capecelatro, who is resigning after nearly three years in office.

WASHINGTON UNLIKE Harvard and Princeton, Yale University does not maintain a Washington lobbyist or a large on-campus staff of Federal relations experts. It says it gets along fine without them. ''Yale, as a nonprofit institution, has always been conscious of not wanting to engage in lobbying,'' said Lindsay C.Y. Kiang, the university's general counsel and its chief liaison with the Government. Nevertheless, Mr. Kiang has tried to follow a schedule of monthly ''courtesy calls,'' as he put it, with the members of Connecticut's Congressional delegation in their Washington offices. And even when Mr. Kiang or A. Bartlett Giamatti, Yale's president, have not been directly in touch with the lawmakers and Federal officials here who influence policies on higher education, the school's presence has been felt.

ROME In ''A Special Day,'' the 1977 film that brought him international recognition, the Italian director Ettore Scola placed the tender and fleeting mutual recognition - perhaps love - between a worn-out and exploited wife of a domineering Fascist and a homosexual equally victimized by Mussolini's brutal regime against the background of a major event in history. The day was May 6, 1938, when Hitler was received by Mussolini in Rome disguised for the occasion as the reborn capital of a Roman Empire. In an apartment house emptied of its inhabitants because all right-thinking Romans were on the street to provide a chorus for the dictators, the two who had been pushed to the margin of their society found the time and place for the one encounter that led them to express their suppressed selves and for the first time recognize themselves in the compassionate mirror of another. In his latest film, ''La Nuit de Varennes,'' which just opened in New York, Mr. Scola has again set the self-revelation of his main characters against a great historic backdrop. The event takes place on June 20, 1791 and is the flight of Louis XVI and Marie-Antoinette from the Tuileries in Paris toward friendly armies in Metz and the royal couple's interception and capture in the small town of Varennes, from where they were returned for eventual execution.

Herschel Walker, the Heisman Trophy-winning tailback, said tonight that he had not signed a contract with the New Jersey Generals, and that he was confident he would be back at the University of Georgia for his senior year. Reports continued to circulate today that Walker had signed an agreement with the United States Football League club after meeting with J. Walter Duncan, the owner of the Generals, last Thursday night in Athens, Ga. If he did, he would be ineligible under National Collegiate Athletic Association rules to play his senior season next fall. But at an informal news conference here tonight after the Georgia Sports Hall of Fame awards dinner, Walker said: ''Like I said, I haven't seen a contract. I've heard a lot of rumors.''

WASHINGTON WHENEVER a President and his Congressional rivals work together in the spirit of bipartisan cooperation for the good of the nation, an inevitable question arises. Which side is going to be able to use the products of their compromise to advantage in the next election? By ballyhooing President Reagan's willingness to work with the Democrats on Social Security and jobs legislation, White House aides clearly hoped to provide Mr. Reagan with a record of concern for the elderly and the unemployed for a 1984 re-election campaign. At first glance, they appeared to be succeeding with the assistance of the Democrats. The party's Congressional leaders, for example, agreed to support Mr. Reagan's $4.3 million emergency jobs bill, even as they let the President get away with the contention that he was still opposed to legislation creating ''make-work jobs.'' Scarcely a Democratic protest was heard when Senator Howard H. Baker Jr. of Tennessee, the majority leader, listed House Speaker Thomas P. O'Neill Jr. as Mr. Reagan's ally in a new joint leadership venture. ''The President,'' Senator Baker concluded, ''has achieved a bipartisan approach to the major problems confronting this country.'' What, a cynic might ask, do the Democrats expect their own Presidential candidates to run on in 1984 if they let Mr. Reagan buy into their best issues? The Benfits of Cooperation

ALTHOUGH no one is able to determine how many deer roam the county, conservation and wildlife officials report a growing number of complaints - some from as far south as New Rochelle - that the animals are feeding on crops and shrubbery. The deer, which because of hunting restrictions and a lack of natural predators are older and larger than elsewhere in the state, are also increasingly cited as a hazard to motorists. ''There's really no way to count them,'' said Joseph A. Steeley, the senior wildlife biologist for the state's Department of Environmental Conservation who is stationed in Millbrook, N.Y., and is responsible for the Westchester region. ''The best index is the number of nuisance complaints we receive, and those are considerable. The number of deer in Westchester has been growing for a long time, to their detriment, and they've been causing human problems.''

IN 1940, Ward Melville, a philanthropist who built a financial empire in the shoe business, stood on a grassy stretch in the sleepy village of Stony Brook and watched his dream of rebuilding a village start to become a reality. A hodgepodge of shoddy structures built in the early 1900's shattered as easily as plastic toys, and in their place, new stores, all adhering to an Early American motif, took shape -one next to the other, complete with whitewash and green shutters, in a semicircle. A post office, with four massive columns and an American eagle waving its wings mechanically as the clock in the cupola struck each hour, proclaimed Main Street, U.S.A. Now, some 40 years later, the post office, in crisp white, still anchors the shopping village, personifying at least one man's American dream. But change is about to come to the placid shopping area, and that is causing some clouds over the dream. John Ruth, a one-time insurance man, also had a dream. Like his father, he wanted to be a butcher. And in May of 1980, standing inside his own meat market, he proudly placed plucked chickens and slabs of steak into refrigerated counters. Customers came in to introduce themselves, welcoming Mr. Ruth to the Village of Stony Brook, where he had become the fourth butcher since 1913.