What was going on when I was born?

Change is taking place these days in the midblock buildings west of the property on Fifth Avenue where W. & J. Sloane's once had its store. The midblock buildings once used by Sloane's - a 12-story structure at 5-9 West 37th Street and two structures of 8 and 12 stories sharing a common facade and a single address, 8 West 38th Street - are being transformed into office space.

As the most important Soviet visitor in 15 years left for home today, officials on both sides asserted that an important watershed had been passed in the long struggle to re-establish good relations between the two Communist powers. Attention among Soviet and Chinese officials here focused less on the economic and technical agreements reached during the nine-day visit of First Deputy Prime Minister Ivan V. Arkhipov than on the warm atmosphere that prevailed throughout his stay. One Soviet official recalled the situation after President Nixon visited here in 1972, a trip that he said was important more for the fact that it occurred, and for its friendly atmosphere, than for any notable political breakthroughs. 'Atmosphere Has Been Changed' ''Now,'' the official said, ''our side has come, and although we haven't overcome the big problems, the atmosphere has been changed.''

HOUSTON OFFICIALS of the Transco Energy Company still shudder at the memory of that bitter 1976- 77 winter when, facing a harrowing shortage of natural gas supplies, they had to cut off service to as much as 45 percent of their pipeline's market. Despite desperate attempts to make good on delivery commitments, scarcely any industrial customers of the company's Transcontinental Gas Pipe Line Corporation subsidiary were unaffected, and some had to shut down plants. Fears were rife that the shortage would spread to higher priority customers all along the East Coast - schools, homes, even hospitals. ''We were a prime example,'' recalled Brian E. O'Neill, the pipeline's president, ''of a pipeline that developed a substantial shortage problem.'' Eight years later, the situation is reversed. Transco and the rest of the industry face a prolonged glut - more technically described as ''excess deliverability'' - brought on by deregulation, recession and price-induced conservation of gas and oil. Competition and price have become dominant considerations, a change that has been beneficial to consumers, but that is causing upheaval throughout the gas industry, particularly for pipeline companies.

Through most of its first eight basketball games this season, St. John's carried the weight of national recognition like a man with bogus credentials, treading softly for fear of being exposed. Suspicions from without combined with nagging doubts from within to create an unspoken feeling among the Redmen that before the Big East Conference season began, they needed proof that they were one of the country's elite teams. The unequivocal proof came yesterday at Madison Square Garden as the Redmen defeated North Carolina State, 66-56, to win the Eastern College Athletic Conference Holiday Festival tournament for the seventh time in its 33-year history. It was the eighth victory in 10 games for St. John's and the second loss in nine games for the Wolfpack.

IN sports, 1984 produced some of those memorable moments that will always be seen in the instant-replay of our minds - Mary Lou Retton's vault, Doug Flutie's pass, Kirk Gibson's home run, Billy Johnson's downhill, Martina Navratilova's loss, Dwight Gooden's fastball, Fuzzy Zoeller's putt, Mary Decker's fall. For anyone aware of those moments, the performer will never be separated from what happened. In that flash of memory, the athlete will be automatically accompanied by what he or she accomplished, or failed to accomplish. It's been that way for many others in many other years - Bobby Thomson, Joe Namath, the Olympic hockey team, to name a few. When moments such as those occur, the personality is forever attached to it, if not shaped or haunted by it.

-year history of the State Council on the Arts, two recipients of grants have rejected their awards. Julie Maloney of West Caldwell, founder and director of the Julie Maloney Dance Company, has returned a $2,000 general operating support grant, and Lillo Way of Montclair, founder and director of the Lillo Way Dance Company, has given back a $1,000 choreography fellowship. The women contend that forgoing public financing was more than an acknowledgement of dissatisfaction; it was a matter of principle, they say. Because the Arts Council received a substantial budget increase this year - from $3.5 million to $5.6 million - modern dancers had hoped for more money, but there was little. Although the council granted a record $373,000 to dance, only $30,000 went to modern dance, while $343,000 went to ballet.

Six years after invading Cambodia and establishing a friendly Government in Pnom Penh, Vietnamese forces seemed intent last week on delivering a knockout blow against rebel forces holding out in camps along the border with Thailand. The large number of civilians killed and injured by artillery and tank guns led Washington to describe the attacks as ''contemptible.'' Bangkok, which has to deal with thousands of Cambodian refugees, called the Vietnamese onslaught ''cruel, savage and brutal.'' Whatever hopes there were for a settlement of the civil war seemed more distant than ever.

White House officials said today that preliminary planning for the arms talks with the Soviet Union had produced a consensus that the United States would not agree to limit research for a long-range defense against missiles. This apparent agreement, contained in the papers being flown to California today for President Reagan's perusal, was made known by officials who sought to end confusion over the Administration's position. The officials said the Administration was prepared to be more flexible on procedural issues that are the ostensible reason for the meeting between Secretary of State George P. Shultz and Foreign Minister Andrei A. Gromyko in Geneva on Jan. 7 and 8. Flexibility on Another Weapon It is also ready, they said, to live up to President Reagan's commitment last September to discuss restraints on testing a new antisatellite weapon if negotiations on both offensive and defensive weapons resume.

TSixty-five years ago, a rich and aristocratic Indian lawyer named Motilal Nehru renounced the grandeur of his Western-style life to join Mohandas K. Gandhi in the leadership of the struggle for independence. In the subsequent years, he gave to the nation not only his devotion, including terms in British colonial jails, but also his family - his son, Jawaharlal, became the first Prime Minister of independent India and then his granddaughter, Indira Gandhi, held the job for most of the last two decades. Last week, the fourth generation came into its own, as Rajiv Gandhi, Indira's 40- year-old son, was swept back into office in a landslide parliamentary election victory that gives him a five-year term and a solid mandate to govern.

Rarely in their history have the Miami Dolphins been so forced to prove something to themselves. But today's 31-10 divisional-playoff victory over the Seattle Seahawks erased any lingering frustration they felt over being eliminated in last season's playoff against Seattle. The decision today was marked by a superbly coached, balanced combination of offensive firepower, highlighted by Dan Marino's three touchdown passes, and a clinging defense. The triumph lifted Miami to the American Conference championship game. They will appear in it here next Sunday , for only the second time since the 1974 season, against the winner of Sunday's playoff game in Denver between the Broncos and Pittsburgh Steelers. Before today, the Dolphins had been 1-5 in their last six first-round playoff games.

A Government study has raised serious objections to a proposal to improve benefits for women by changing the decades-old formula used to compute Social Security pensions. The study, by the Social Security Administration, focused on sharing earnings: The earnings of a husband and wife would be split equally for the purpose of computing the benefits. The study concluded that such a formula would reduce many people's benefits, would be expensive to put into effect and would not mesh well with the current system unless there was a long transition period. But critics of the study say it was biased against the concept of sharing earnings and did not present a balanced assessment.

HE is usually outgoing and effervescent, but on that spring day in 1982, E. Gerald Corrigan was subdued. The elegant Washington office of Paul A. Volcker, the chairman of the Federal Reserve Board, had been converted into a war room of sorts, where an unmistakable tension gripped some of the most powerful men in the central bank. It had just been learned that an obscure securities firm in New York - the Drysdale Government Securities Corporation - would not be able to pay millions, perhaps hundreds of millions of dollars, that it owed to a number of brokerage firms. No one knew just how much was involved or who all the players might have been. But one thing was clear: It was a giant crisis that threatened to wreck the world financial system. The Fed needed someone who could find out exactly - and quickly - what was going on and who could mediate among the warring financial institutions, each of which argued that the others should take the loss. That go-between would also have to reassure the big New York banks that the Federal Reserve would provide whatever liquidity might be needed to keep the system afloat.