What was going on when I was born?

President Reagan will begin one of the most ambitious campaigns of his Presidency on Tuesday, a drive for a new Federal income tax system that would affect the personal finances of nearly every American family and the operations of almost every business. According to his advisers, Mr. Reagan views the 15-minute speech he will deliver on television at 8 o'clock Tuesday night as the opening shot of the ''Second American Revolution'' he proclaimed in his Inaugural Address last January. After months on the political defensive on such questions as cuts in social programs, production of the MX missile, aid to the Nicaraguan rebels and his trip to the Bitburg cemetery, the President was said to relish the prospect of devoting much of his attention for the rest of the year to an issue that he believes has enormous appeal. The Plan's Basic Provisions If the President has his way, tax rates will be reduced to their lowest point since before World War II, and capital gains taxes would be cut. The personal exemption and standard deduction would be lifted to a point at which people with incomes around the poverty level and below would owe no income tax. Deductions as old as the income tax law itself, such as the ones for state and local tax payments and consumer interest payments, would be restricted or abolished.

Mikhail S. Gorbachev, the Soviet leader, gave a warm welcome today to Willy Brandt, the former West German Chancellor, and told him the Geneva arms talks had so far proved ''completely fruitless.'' After the highly publicized five-hour meeting with Mr. Brandt, a member of the West German delegation said at a news conference that Mr. Gorbachev had said he saw little hope for progress at the talks, which resume Thursday, unless the United States revises its policies. Calling Mr. Gorbachev ''harder than some believe,'' the West German spokesman said the Soviet leader, echoing an assessment he made when the first round of talks ended on April 23, had called the discussions fruitless. The West German spokesman, Egon Bahr, an arms expert in Mr. Brandt's opposition Social Democratic Party, said Mr. Gorbachev also said that contacts and preparations were under way for a summit meeting with President Reagan but that details had not been fixed.

Prodded by the Reagan Administration, mayors and county officials are increasingly paying private industry to provide a wide range of public services in a move that has redefined the role of local government. In the past local officials sought to expand their political bases by expanding services, creating new jobs and constituencies. This approach gathered momentum in the 1960's and 1970's as the Federal Government sharply increased funds for the cities; they could then increase services without raising taxes. But Federal funds are now running dry, and local officials, facing taxpayer revolts and paying union salaries and benefits they consider high, are turning to private industry to provide public services. Jails, Hospitals, Transit Some localities have begun to pay private industry to operate jails, hospitals or mass transit systems, services that local officials often consider both costly and troublesome.

THERE was a time long ago when real dragons soared over Texas, their leathery wings casting monster shadows over the drab Cretaceous landscape far below them. Those huge flying reptiles, the pterosaurs, died out with the dinosaurs some 64 million years ago, but thanks to space-age advances in aerodynamics, robotics and structural materials, a startlingly lifelike replica of one of the largest of them will take to the sky later this year. With flight tests of several prototypes behind them, a team of engineers, model makers and aerodynamicists last week began the task of meshing a host of complex gadgets into a single lifelike mechanism - one that is expected to fly well enough to seem as if it had a mind of its own. The object of building a robot pterosaur is not merely to create a convincing reproduction of a long-extinct animal. Scientists expect their mechanical creature to help solve some long-standing puzzles in paleoaerodynamics - the study of how some of earth's early creatures managed to fly. Knowledge gained along the way, they say, may even help engineers design better airplanes.

Industry reports that Norway is cutting oil prices mark a new downward trend that will persist for a few months at least, analysts said yesterday. Norway has been considered an oil-price leader since it cut prices last October, initiating a important round of declines. Its latest cut by Statoil, reported by industry sources over the weekend, lowers its North Sea crude by up to $1 a barrel, to about $26.50 for June deliveries. ''This Norwegian development reflects what has been going on in the market for five weeks,'' said Philip L. Dodge, an analyst with Donaldson, Lufkin & Jenrette. ''We are definitely in a weak phase of the price cycle.''

TUESDAY, MAY 28, 1985 International 10,000 Bangladeshis are missing and feared dead after a cyclone devastated the islands in southeastern Bangladesh, the authorities said as they widened search and rescue efforts. The seas were reported littered with floating bodies. [Page A1, Column 6.] Efforts to rescue Palestinians from a besieged refugee settlement in Beirut were only slightly successful. Red Cross ambulances brought out 11 wounded people from the Burj al Brajneh settlement, but the operation had to be abandoned after 30 minutes because of new fighting between the Palestinian defenders and Shiite Moslem militiamen. [A1:5-6.]

The Upjohn Company may be several years away from receiving Government approval to sell what could be a revolutionary hair-growth ointment, but thousands of balding men are said to be using a homemade version of the product. And while the company is still a long way from seeing the full financial impact of its drug, called minoxidil, Upjohn may already be realizing considerable benefits from the cottage industry that has grown up around the compound. Minoxidil has the approval of the United States Food and Drug Administration, but as a tablet taken to treat hypertension. Years ago, however, Upjohn scientists found that the drug promoted hair growth as a side effect. More recently, doctors have been putting patients on minoxidil not to fight hypertension, but to grow hair.

Talks between United Airlines and its striking pilots union broke off over the weekend, but industry analysts said that, if necessary, the giant carrier could endure a prolonged strike without serious harm. ''When you have half a billion dollars in cash and in short-term securities and a strong line of credit, you can go for a long, long time,'' Robert J. Joedicke, an analyst with Shearson Lehman Brothers Inc., said yesterday. ''Certainly, the union doesn't have a strike fund that could compare with that,'' he said. Not that the strike, which began May 17, is without cost to the airline. It would not comment on the strike's financial impact, but industry analysts estimated the airline's losses to be between $5 million and $7 million for every day of the strike.

SCIENTIFIC interest in the effects of birth order on later development, an interest that has fallen in and out of vogue several times in the last few decades, seems to be coming back again with a rush. Early findings showed that firstborns and only children had a higher proportion of successes in later life and that they tended to have higher I.Q.'s than later-born children have. Firstborns and only children were also shown to be overrepresented in such groups as those listed in ''Who's Who,'' astronauts and students in graduate and professional schools. Critics have maintained that the birth-order effect has been exaggerated and is more ephemeral than its supporters suggest. The new inquiries tend to affirm much of the earlier work, but they also significantly modify those findings. For instance, some data show that the amount of time between births in a family has perhaps as much to do with the development of a child as does that child's place in the order of births.

In the 1920's nearly 250 shoe factories dotted the landscape of Lynn, Mass., which called itself the ''shoe capital'' of the region just north of Boston. ''My dad used to tell me that at lunch time he'd go out into the central square and the people would come pouring out of the factories like ants,'' said Richard Rothbard, president of Barry Manufacturing Inc., Lynn's only surviving shoe factory. These days Lynn's largest employer is the General Electric Company, and the city has shrunk to about 78,000 people from its peak of more than 100,000. In an industry that is rapidly contracting, Barry has survived because it is small, specialized and highly automated. It makes baby shoes, about 7,000 pairs a day, using 14 computerized stitching machines. All of Barry's shoes are produced in the United States.

The trial here of eight defendants accused of plotting to assassinate Pope John Paul II opened today with an appeal by a prosecutor that the state seek evidence from suspected Turkish drug traffickers and terrorists jailed in several European countries. The session today was also marked by an episode in which Mehmet Ali Agca, the state's key witness against five Turks and three Bulgarians, began shouting: ''I am Jesus Christ! I am omnipotent, and I announce the end of the world!'' Later, Mr. Agca, a Turkish national who has been convicted of wounding the Pope in 1981, began a measured account of how he obtained the gun he used to shoot the Pope. He gave testimony until a breakdown of the courtroom's public address system forced the judge to suspend hearings until Tuesday.

TUESDAY, MAY 28, 1985 The Economy President Reagan begins his drive to change the tax system in a televised address tonight. The new system would affect almost every American family and business. [Page A1.] The plan will not include a tuition tax credit or special break for businesses in designated poor neighborhoods, contrary to an earlier report. [D9.]