LIKE children of divorced parents who celebrate every holiday twice - once with their mother and once with their father - Berlin is finding that celebrating its 750th anniversary this year is not without its problems. West Berlin proposals for joint anniversary celebrations by those on both sides of the wall came to nought. And now West Berlin Mayor Eberhard Diepgen has rethought his original acceptance of an invitation to the anniversary celebrations in East Berlin. For him to attend, he finally decided, would be to grant de facto recognition of East Berlin as a separate entity and as the capital of East Germany. His acceptance of the invitation had troubled Bonn, as well as the three Western allies - the United States, Britain, and France - for whom the at least theoretical unity of Berlin has been an article of faith since the end of World War II.
If East German leader Erich Honecker had accepted the West Berliners' invitation to their party April 30, the birthday celebration could have been an opportunity for d'etente and improved understanding between East and West. Absent that reciprocity, Mr. Diepgen is doing the right thing to stay home.
In any case, there will be plenty for Berliners and their visitors to see and do during this year's celebrations. The 1980s have been a progressive and fruitful time for Berliners. The West has enjoyed a notable upsurge in young professionals coming in, many of them involved in founding new enterprises; Berlin's role as a research center is evident once more.
And in the East, particularly, there has been a rediscovery of the city's architectural glories. Both East and West have begun to come to terms with Berlin's Prussian heritage, valuing the good in it and more squarely facing up to the bad.
Renewed appreciation for their common heritage has also provided opportunities for West Berliners to work with their counterparts across the wall. In 1981 West Berlin returned to the East eight statues by the great architect Karl Friedrich Schinkel; East Berlin reciprocated by sending the archive of the Prussian state porcelain enterprise.
Still, relations between East and West are conducted according to an arcane code that by comparison would have made the court of Versailles appear positively nonchalant. On Aug. 30, for instance, West Berlin plans a major fireworks display that should be visible in both East and West. But the air space more than 200 meters up over the city is technically the jurisdiction of all four occupying powers. To forestall the risk of a Soviet nyet, the pyrotechnicians will work their magic over Tempelhof military airport, where, as one official puts it, ``the Americans can do anything they want in the air up to two kilometers.''
The Berlin Wall went up overnight on Aug. 13, 1961, but will take years to come back down. And neither East nor West is ready for German ``reunification.''
The important questions are not about how many German states there are, but about human rights, freedom of movement across borders. Let's hope this gradual warming continues - so that Berliners on both sides of the wall don't have to wait for their 800th anniversary before they can attend each other's parties.