What was going on when I was born?

Prosecutors at the trial of City Councilman Luis A. Olmedo played a videotape yesterday that they said showed Mr. Olmedo conspiring to get kickbacks from detectives posing as construction executives. The secret tape was played at the trial of Mr. Olmedo, Democrat of Brooklyn, and two others in Federal District Court in Brooklyn. They are charged with conspiracy and attempted extortion.

''It is a living hell. We have rockets coming down on us one a minute.

Owning a home has always been considered the American dream, and largely because of this, tax benefits have been generous. This year, while those benefits have been left unchanged by Congress and the Internal Revenue Service, several Federal court decisions have established important precedents that could affect millions of taxpayers. Specifically, the courts have provided both victories and defeats for individuals who want to write off a room in their home as a business expense. Vacation homeowners, meanwhile, were handed another favorable ruling on the amount of rental expenses they can write off. For many years, the Federal Government has helped subsidize the cost of home ownership by means of deductions for mortgage interest and real estate taxes as well as preferential tax treatment when a primary residence is sold.

AMERICAN college professors have always been free to retire to their studies, write textbooks and other scholarly works and pocket the revenues they generate. But when Sharon Dugdale writes course materials for math classes in elementary schools, she does so on the multimillion-dollar computer system of the University of Illinois at Urbana-Champaign. Does this mean that the university should share in the profits? Under a new policy, still to be formally approved by the faculty, the answer is yes and no. Dr. Dugdale, a full- time researcher in the university's Computer-Based Education Research Laboratory, will keep the first $10,000 of profits, but after that she will share the income with the university on a sliding scale. Above $100,000, the university gets three-quarters of the revenue.

SUDDENLY, psychology is excited again about the unconscious. For decades mainstream research psychologists suppressed the notion that crucial mental activity could take place unconsciously. Indeed, through the 1950's, these experimental psychologists largely ignored any such entity as ''the mind,'' focusing instead on observable behavior. Even in the 1960's when the resurgence of cognitive psychology legitimized the study of how the mind registers information, the unconscious was still slighted outside psychoanalytic circles. But now, in what one researcher calls ''a silent revolution,'' experimental psychologists are taking the unconscious seriously in the wake of new and compelling evidence that the unconscious is the site of a far larger portion of mental life than even Freud envisioned. The main studies show that the unconscious mind may understand and respond to meaning, form emotional responses and guide most actions, largely independent of conscious awareness. And the research evidence extends beyond the laboratory to such real-life situations as an operating room: Researchers have verified, for example, that what patients hear while under anesthesia can affect their subsequent behavior and, ultimately, their health. The findings imply that, despite the subjective experience of being in conscious control of feelings and thoughts, decisions and actions, people are piloted far more than they know by the unconscious mind.

Shiite and Druse gunmen demanding the resignation of President Amin Gemayel took over virtually all of West Beirut today. By early this morning, according to Lebanese Defense Ministry sources, the Lebanese Army had been driven out of that section of the capital, and the continuing small-arms clashes were the last pockets of army resistance to the anti-Government forces. ''What we had feared most has happened,'' one of the sources said. ''Whole units have left the army.'' City in Chaos As the fighting Monday plunged the city into chaos, the United States Marine contingent at Beirut's international airport came under fire, and American fighter planes and naval gunners bombarded the bases of anti- Gemayel militias in the hills overlooking the capital.

In 1976, when Salomon Brothers Inc. set up shop in Asia, it decided for several reasons to locate in Hong Kong: The colony was centrally situated in the region, it was relatively free of regulations and it was bilingual. Clearly, the firm's executives concluded, Hong Kong was the financial heart of Asia. Then, over the next few years, they decided they had missed something in arriving at their decision. ''It became apparent to me and my colleagues,'' said George P. Hutchinson, managing director of Salomon Brothers Asia Ltd., ''that Japan was the future. It had the infrastructure, the economic size and the capital.''

Beirut was in chaos as Shiite and Druse gunmen demanding the resignation of President Amin Gemayel took over most of West Beirut. As groups of Moslem youths attacked key Lebanese Army bases, some army officers and soldiers put up fierce resistance, while others broke and ran. As the fighting raged, the United States Marine contingent at Beirut airport came under fire, and American fighter-bombers and naval gunners responded by bombarding the bases of anti-Government militias in the hills overlooking the capital. (Page A1, Columns 3-6.) The use of U.S. air and naval forces against positions of anti-Government militiamen near Beirut was ordered by President Reagan as a show of support for President Amin Gemayel and as a warning to Syria and its Lebanese supporters, Administration officials said. (A1:3.)

Benno C. Schmidt Jr., a constitutional scholar and authority on First Amendment press freedoms, has been named dean of the Columbia Law School. Mr. Schmidt, 41 years old, will be among the youngest deans at the 125-year-old institution. The appointment was made by the university's board of trustees and announced yesterday by Michael I. Sovern, Columbia's president. He called Mr. Schmidt ''a first-rate teacher, a leading scholar and an outstanding human being.''

Despite the accidents that have beset the mission so far, the Challenger astronauts were ready to go ahead with plans Tuesday morning for their most daring venture, jet-powered excursions outside in orbit and free of any link to the spaceship. It will be one more moment in the space age when science fiction comes true. Never before have spacewalking astronauts been without a safety line or been able to move about under jet power. This will be a dress rehearsal for the shuttle mission in April to attempt to repair an ailing scientific satellite.

The chief Federal advisory committee on gene-splicing policy today endorsed a proposal to grow in the laboratory genetic material that produces an important bacterial toxin. The research was described as important for development of vaccines against major causes of dysentery. The proposal has been the source of controversy because of fears that the research could potentially be applied to biological warfare. The toxin is called shigella-like toxin because it is similar to one produced by shigella bacteria. The toxin- producing genetic material, which may be one gene or two, will be grown in a special laboratory strain of Escherichia coli, a common experimental bacterium.

The second satellite deployed by the space shuttle Challenger misfired this morning and strayed off course in an orbit too low for it to serve as a useful communications relay outpost. It thus apparently met the same mysterious and disquieting fate as the first one launched three days ago. It was the third major failure of the mission, following the explosion of a target balloon Sunday and the loss of the first satellite, the Westar 6. Nonetheless, space officials said the mishaps would not alter plans for two astronauts, Capt. Bruce McCandless 2d of the Navy and Lieut. Robert L. Stewart of the Army, to conduct untethered spacewalks Tuesday (Science Times, page C1).