What was going on when I was born?

The Board of Estimate, rejecting the last-minute appeals of neighborhood residents, gave final city approval yesterday for construction of a garbage-burning incinerator at the old Brooklyn Navy Yard. The incinerator - the first of a network of up to 10 planned across the city at a cost of $2.5 billion - was approved by a 6-to-5 vote after more than five hours of testimony before the board. ''It is a major first step for us in solving our waste-disposal problems,'' Sanitation Commissioner Norman Steisel said moments after the vote. #3 Oppose Plan While all board members said they supported the idea of the incinerator, which would burn garbage to produce energy, City Council President Carol Bellamy, Comptroller Harrison J. Goldin and Borough President Howard Golden of Brooklyn voted against it. Miss Bellamy and Mr. Goldin have two votes; Mr. Golden has one.

''I am not prepared to lead white South Africans and other minority groups on a road to abdication and suicide.'' - President P. W. Botha of South Africa. [A1:6.]

The Economy Industrial production rose a slight 0.2 percent in July, providing little evidence of the second-half economic rebound predicted by the Reagan Administration and most private analysts. But economists found some consolation in the Federal Reserve report, since it showed at least some growth for the seventh straight month. [Page A1.] Americans took on $6.79 billion more in installment debt than they paid off in June, the smallest rise since November. [D2.] Defense Secretary Weinberger said he would support changes in the way the Pentagon buys weapons in order to restore public confidence in the military. Officials said that at a closed meeting he advocated a stricter review of new weapons before they are approved for full-scale development and tighter limits on specifications that make weapons more complex and expensive. [B4.]

A series of underground electrical fires erupted in lower Manhattan yesterday, blacking out a half-dozen office buildings and leading Mayor Koch, fearful of a larger power failure, to ask all businesses south of Canal Street to send home nonessential employees. The power interruptions - which affected thousands of office workers, stranding some of them in elevators -came in the middle of the hottest day of the year, as the temperature soared to 95 degrees and the demand for electricity reached a record level. Officials of the Consolidated Edison Company said the fires had almost certainly been caused in part by the high demand. And other utilities in the metropolitan area reported that their capacity had been stretched to its limits.

New York State taxpayers would save $588 million a year under President Reagan's tax-change plan, the State Comptroller said today. The finding by the Comptroller, Edward V. Regan, disagreed with earlier claims by Governor Cuomo that New Yorkers would lose $2 billion a year under the President's plan. But Mr, Regan stressed that even with the gain, the state would be ''badly hurt'' by the proposed changes. He said New Yorkers overall would save less than residents of any other state under the plan, and middle-income New Yorkers probably would have to pay higher Federal taxes.

UNTIL a few weeks ago, New Yorkers with a passion for walking across bridges had reason to feel unwelcome. They saw new crossings built without pedestrian paths and old walkways lost to vandalism, neglect or the automobile. In recent years, as if some demonic timetable were being followed, three of the great remaining walks were carved up at the same time for repairs. The Queensboro had been closed for five hours every weekday, starting in November 1982. The north walk of the George Washington was closed completely in November 1983, the south walk three months later. The Brooklyn Bridge path stayed open but ever since August 1982, one had to be half-mountain goat to navigate the repair zones. But now there is good news. A lot of it. The south walk at the George Washington and the pedestrian path of the Queensboro both reopened full time in late July. And much of the work on the Brooklyn Bridge path has been finished.

Prime Minister Rajiv Gandhi, declaring that India had overcome another threat to national unity, today announced the settlement of a bitter dispute that has led to thousands of deaths in the northeastern state of Assam. Although Assam has been relatively peaceful recently, a sharp dispute over the rights of half a million foreign immigrants has simmered ever since an estimated 5,000 people were killed during a state election in 1983. Most of the immigrants were Moslems fleeing poverty in neighboring Bangladesh, formerly East Pakistan. The population of Assam is largely Hindu.

Mayor Koch called Council President Carol Bellamy ''a disaster.'' Miss Bellamy called Mr. Koch ''a fraud and a phony.'' And Assemblyman Herman D. Farrell Jr. compared both of them to Ralph and Alice Kramden, the bickering television couple, during the first mayoral debate of the season. The recriminations and the one-liners overshadowed the issues during the debate yesterday, which the Mayor called ''an hour of rhetoric and street theater.'' And, with their cheers, catcalls and chants, 2,000 spectators helped make the event one of the most unruly political confrontations in years.

A Washington dispatch July 24 about Vice President Bush's reflections on his role as Acting President during President Reagan's surgery included an incorrect report from the White House about the number of interviews he had given since the event. The Times's interview was Mr. Bush's third; he had also spoken with Michael Globetti of The Boston Herald and James Wieghart of the Scripps-Howard News Service.

Production by the nation's factories, mines and utilities rose a meager two-tenths of 1 percent last month as the economy displayed little evidence of the second-half rebound predicted by the Reagan Administration and most private analysts. ''The anemic rise in industrial production continues to reflect a yearlong stagnation in industrial activity, with no meaningful signs of pickup,'' said Jerry J. Jasinowski, chief economist for the National Association of Manufacturers. Consumer Debt Figures Today's report, compiled by the Federal Reserve, follows various other recent lackluster or worrisome figures for automobile sales, retail sales, business inventories and employment. The Federal Reserve also said today that consumer installment debt climbed $6.79 billion in June, well under May's $9.04 billion and the smallest gain this year.

President P. W. Botha, in defiant and sometimes belligerent tones, today rejected foreign and domestic calls for major concessions to South Africa's black majority. He also said he would not soften his terms for the release of Nelson Mandela, the jailed black leader. Addressing 1,800 whites in Durban's City Hall at the opening of the Natal Provincial Congress of the governing National Party, Mr. Botha said: ''I am not prepared to lead white South Africans and other minority groups on a road to abdication and suicide,'' He Foresees Strife and Chaos He continued: ''Listen, my friends, listen. Destroy white South Africa and our influence in this subcontinent of southern Africa, and this country will Excerpts from speech, page A6. drift into factions, strife, chaos and poverty. ''We have never given in to outside demands and we are not going to do so. South Africa's problems will be solved by South Africans and not by foreigners. We are not going to be deterred from what we think best, nor will we be forced into a position of doing what we don't want to do.''

The Federal Reserve announced a $5.3 billion increase in the nation's basic money supply yesterday, roughly twice as large as expected, The news stunned the credit markets. Although interest rates rose only modestly after the Fed's announcement, economists and traders expressed bewilderment over the combination this week of statistics showing a lackluster economy, but robust money supply growth for the week ended Aug. 5. Fed officials quietly asked bankers if there are any special explanations for the rapid money supply growth, while market participants wonderedwhat action the Fed might take to slow the growth of money held in currency and checking accounts. ''The large increase means that any moves to ease monetary policy will be put on hold,'' said Irwin Kellner, chief economist at the Manufacturers Hanover Trust Company. ''Even though the economic numbers have been weak, the Fed can't afford to ignore the tremendous growth in money supply.''