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The title of [David Halberstam]'s engaging new book, \"The Next Century,\" is a shade on the coy side. One expects him to have drawn on the broad knowledge of various worlds he has stored up while writing such books as \"The Best and the Brightest,\" about America in Vietnam, \"The Powers That Be,\" about the rise of certain media giants in this country, and \"The Reckoning,\" about the eclipse of Detroit's automotive industry by Japan's. Because we have been bemused by the cold war. We have been locked in combat with the Soviet Union like \"two scorpions in a jar,\" as Mr. Halberstam paraphrases J. Robert Oppenheimer, \"each able to give a nuclear sting to the other, but only at the price of its own death.\" Yet despite the \"marvelous opportunities squandered\" and the \"unseemly national arrogance manifested by both sides\" in this struggle, \"future historians will sum up the 40-year struggle with the Soviets not harshly but in fact quite gently,\" Mr. Halberstam writes. In short, Mr. Halberstam's essay is a variation on the theme whose most pointed expression he credits to Chalmers Johnson, the Japanologist: \"The Cold War is over; the Japanese won.\" But it remains to be seen to whom the next century of Mr. Halberstam's title belongs. Judging from his tantalizing conclusion, it could be Japan or Germany, the Eastern European countries or the \"Little Tigers\" of Asia. It probably won't be the United States, unless it can finally get its act together, which Mr. Halberstam seems rather to doubt.

Although Mr. [Alan Schneider] displayed a catholicity of taste over the years -among his early efforts were stagings of such plays as Thornton Wilder's ''Skin of Our Teeth,'' Robert Anderson's ''All Summer Long'' and Clifford Odets's ''Country Girl'' - he would become best known for his more experimental work, and in one of the few passages of self-assessment in this volume he makes it clear where his affinities lay. ''I am the only American theater director who ever went from the avant-garde to the Old Guard without having passed through the Establishment,'' he writes. ''I have always favored the poetic over the prosaic, siding with instinct over reason, swayed by the power of symbols, images, metaphors, all of the substances lurking behind the closed eyelids of the mind. To me, these are more faithful signs of essential truths than all those glossy photographs that seek to mirror our external world. I've always preferred Chekhov to Ibsen, Tennessee Williams to Arthur Miller, and Dostoyevsky to Tolstoy; but [Samuel Beckett]'s metaphors reach deepest into my subconscious self.'' Having been signed up to direct the first American production of ''Waiting for Godot'' in 1955, Mr. Schneider spends a week looking for the elusive writer in Paris and finally succeeds in trying to get Mr. Beckett to answer his questions about the play. ''According to him,'' Mr. Schneider writes, ''Godot had 'no meaning' and 'no symbolism.' There was no 'general point of view involved,' but it was certainly 'not existentialist.' Nothing in it meant anything other than what it was on the surface. 'It's just about two people who are like that.' That was all he would say.''