What was going on when I was born?

BOSTON SITTING with Nina Fletcher Little is a bit like sinking gently into history. One discovers a young America. The mullioned windows of her sitting room, framed when the Massachusetts farmhouse that is her principal home was built in 1812, look out on snowy woods, gray and white in the dusk of winter. The tall clock by the door chimes softly and then ticks on, as steadily as it has since her great-greatgrandfather, a Salem clockmaker, built it around 1820. Thomas Jefferson would have approved of her desk. A fall-front model of shiny brasses stamped with the third President's profile, it was made in 1790, 36 years before he died, and was passed down to Mrs. Little by a cousin. Some of the lamps and glassware would have seemed old to Thomas Alva Edison. Alexander Graham Bell would have recognized the telephone, which was installed in 1921, the year before he died.

Governor Carey proposed today a broad program to change the way public education is financed in the state. It would include a one-cent increase in the state sales tax, now 4 cents on the dollar, and would call for $8.6 billion in new state education aid over the next five years. If approved by the Legislature, the increase would raise the total sales tax to 9.25 percent in New York City and Yonkers and 8.25 percent in Nassau, Suffolk and Westchester Counties. Its impact would be partly offset through a new income tax rebate to low-and middle-income residents that would eventually return $300 million a year to New Yorkers whose income is below $25,000 a year.

''Europe is in greater danger than the Americans have understood so far.

The executive director of New York State's Financial Control Board warned yesterday that New York City's finances were in their most perilous shape since the crisis of the mid-1970's. In addition, a report from the board's staff said, there is ''an unusual degree of uncertainty'' in city plans to balance the budget for the coming fiscal year. ''The city has not had to face challenges of such magnitude in half a decade,'' said Comer S. Coppie, executive director of the Control Board. As the principal fiscal watchdog of the city, the board must approve all budget proposals and contracts.

David A. Stockman, the budget director, indicated some flexibility in the Administration's plans for cutting the budget. Testifying under heavy criticism before the House Budget Committee, he said that some portions of last year's tax cuts could be scaled back or repealed to increase Government revenues. (Page A1.) Industrial production fell 3 percent in January, the largest decline since May 1980, the Federal Reserve Board reported. The decline resulted from industry's efforts to work off inventories in the face of a worsening economy and poorer sales, as well as bad weather. (D1.) Housing starts fell 0.6 percent in January, after rising slightly in December, the Commerce Department reported. (D1.)

An item in Business Day on Wednesday incorrectly reported the value of an acquisition by the Hughes Tool Company. The transaction was valued at $60 million.

Chancellor Helmut Schmidt contends that West European society is in danger of political and social destabilization as a result of the world's continuing economic crisis. The United States has not fully understood this, he said today in an interview.Mr. Schmidt also criticized the projected American budget deficits as being likely to lead to higher interest rates, worsening economic problems for the rest of the world. Without significant steps in the next two years, Mr. Schmidt warned, every nation could tumble into depression. But in Washington, President Reagan told another Western European leader today that his economic policy, intended to foster noninflationary growth in the United States, was the best way to deal with the world's economic ills. ''We think it will work,'' he told Prime Minister Wilfried Martens of Belgium, who as current president of the Council of the European Community visited Mr. Reagan to argue the European case that American interest rates are too high and are intensifying Europe's economic difficulties. (Page D3.)

Banks across the country raised their prime rate by half a point, to 17 percent, yesterday, touching off new fears of further increases that would drive the economy deeper into recession. Bankers regarded the half-point increase as conservative and argued privately that the rising cost of money justified an even bigger increase. The march to higher ground began shortly after 10 A.M., when the Chase Manhattan Bank, the third largest in the country, said it was raising its rate to 17 percent from 16 1/2. Following soon after were the Morgan Guaranty Trust Company, the National Bank of Detroit, the First National Bank of Chicago, the Chemical Bank and Continental Illinois. By 2 P.M., the new rate had become general nationwide.

Because of an editing error in an ar- ticle about baseball contracts on Tues- day, the name of one baseball player was incorrectly substituted for that of another. The player who will earn $100,000 for each season he wins the most-valuable-player award and a maximum of $300,000 annually in at- tendance bonuses is George Foster of the Mets.

International A two-day police sweep in Poland found 145,000 people to have been violating martial-law regulations, the authorities announced. As punishment, they said, 128,000 people were issued warnings, 3,500 were detained for questioning, 7,000 were fined a total of $29,000 and 4,000 were given court summonses. (Page A1, Column 6.) Zimbabwe's unity regime broke apart as Prime Minister Robert Mugabe dismissed his partner, Joshua Nkomo, from the Cabinet and accused him of plotting to overthrow the Government by force. The dismissal of Mr. Nkomo and three members of his party effectively ended the coalition that was established 22 months ago when Rhodesia became independent. (A1:5.)

Most of Mayor Koch's closest friends and advisers think he should run - and will run - for the Democratic nomination for governor. ''He's getting a lot of input from people, and I think most of them are telling him to run,'' said David Garth, who would be the chief strategist in a Koch state campaign. Mr. Garth was one of a dozen associates of Mr. Koch who were interviewed in the last two days, a week before the Mayor is scheduled to announce his decision on whether to be a gubernatorial candidate. ''Most think he's running,'' said John LoCicero, the Mayor's patronage dispenser at City Hall and his campaign manager in the mayoral election last year.

There is some flexibility in the Reagan Administration's stance on taxes and military spending, David A. Stockman, the budget director, suggested today in Congressional testimony. In its budget for the fiscal year 1983 and in statements since it was presented last week, the Administration had until now rejected all proposals to reduce the projected $91.5 billion deficit either by significant changes in the President's tax cuts, approved last year, or by reducing the proposed 18 percent rise in military spending. In five hours of heavy criticism of the proposed $757.6 billion budget by the Democratic-controlled House Budget Committee, Mr. Stockman suggested that some portions of last year's tax cuts, including a provision that allows companies to sell unused business depreciation tax credits, could be scaled back or repealed to increase Government revenue. And while he argued against military budget cuts in the range of $20 billion to $30 billion, Mr. Stockman did not reject the suggestion of a $10 billion cut in 1983 military spending made by Representative Les Aspin, Democrat of Wisconsin.