FINALLY, after 16 years of hostile noncommunication, high-pitched shouting and - finally - contacts through intermediaries, the United States and Cuba are now talking directly and quietly to each other about problems of mutual concern. The first talks opened the other day in New York on fishing rights and maritime boundaries, an issue forced upon the two physically near but politically remote countries by their recent assertion of 200-mile fishing zones, which overlap. Talks on the control of terrorists, both those who hijack American airplanes to Havana and those who launch attacks on Cuban citizens and properties, evidently are next on the agenda. After that, if these immediate matters go reasonably well, discussions may proceed to the difficult political issues that now block normalization of relations between Washington and Havana.

Fidel Castro has been ready for some time to go down this path. He has had his eye on the substantial benefits - in trade, in physical safety, and in the satisfaction of having the United States accept the Cuban revolution - that normalization would bring. Presumably he also would appreciate the resulting gain in political distance from the Soviet Union. Previous American Presidents, however, regarding Cuba as a spearpoint of international communism and an affront to American sensibilities, could not bring themselves to consider reconciliation. Thriving on American antagonism, Mr. Castro responded by intensifying precisely those policies of foreign adventure and domestic repression of which Americans disapproved. The result was, in bad years, a cold war including, on the American side, efforts to unseat and even murder Fidel Castro. In "good" years the result was a stalemate serving the interests of neither side.

President Carter, it seems to us, is trying to break that stalemate. He has accepted the notion that both the United States and Cuba have something to gain from improving their relations, and that negotiation rather than confrontation provides the best framework in which the United States can bring about some alteration of the Cuban policies to which it objects. Understandably, Mr. Castro would like to see the trade embargo lifted without his having to pay any political price. But this is unlikely to happen all at once, though a lifting of the embargo on food and medicine might at some point help the process along; and it is unlikely to happen at all without some Cuban changes of heart in relation to both its political prisoners and its African military expeditions.

In any event, the Carter administration has shown good faith by lifting restrictions on American travel to Cuba and by entering unconditional talks with the Castro government. As a close student of American politics, Fidel Castro surely knows that the best way he can get the embargo lifted is to offer balancing neighborly moves of his own.