Supreme game: making sense of the emotions surrounding sports; Sport: A Cultural History, by Richard D. Mandell. New York: Columbia University Press. 340 pp $24.95.

Watching the Olympics last week, as the American men's gymnastic team won the gold, I was uneasily aware of the chauvinism of my emotions. After all, it was the Chinese who had to give up the gold - noble losers. But the modern ecumenical religion of sport allows for these kinds of emotions. That the ABC-TV cameras have caught individual athletes praying before or after events suggests that the sports and the religious ecumenes reinforce each other.

Richard D. Mandell, professor of history at the University of South Carolina, explains that the force behind sport in our times (though his book goes back to prehistory and is especially strong on the Greeks) is ''the democratic accomplishment principle.'' An individual often subordinating his or her ego to the ends of the team triumphs against the limits established by the history of the game. Progress, though anticipated with excitement, appears to be inevitable , at least in sports.

The social and political elements are essential to sports today. The fact that the principle is democratic does not overshadow the role sports play in the modern ecumene, which includes totalitarian states as well as democratic ones (if they wish to play along, as the United States didn't in the '80s Olympics and the Soviets didn't this year). When Olga Korbut, on her way to gold medals for floor exercises and the high beam for the Soviets at the 1972 Olympics, broke down and cried because she had blown ''an especially daring maneuver on the high bars,'' she proved the case, only negatively. Even Soviet athletes are individuals: They cry, too.

Olympic stars, according to Mandel, are ''the new universal heroes of specified individualism, the new beautiful gods and goddesses of selfless preparation and symbolic accomplishment.'' That Mandel, whose value as a historian ranks with other generalists, such as David S. Landes and William McNeill (both of whom he praises in this book), should write with such a combination of irony and insight qualifies him as a privileged observer of our emotions as fans, and we come close to understanding them in this book.

Mercifully much of the book is about times past. The ''practical justification'' of sports, East and West, is Mandell's theme. Greek sport called forth an orgiastic response; the winners were considered favored by the gods and brought fame to their city-states. Of Byzantium, Mandell writes: ''In a society where there was considerable wealth, energy, and idleness, horse races are remarkable for the attention and importance placed on them.'' He is thinking of England as well. Later in the book it comes out: What thoroughbred racing gave the English was ''a new abstract value: something exquisite and worthy of a noble quest. It was a dynamic abstraction of pure time and pure space to produce visible fleetness - speed.'' One of the pleasures of this book is the obvious relish its author takes in discussing the beauty of horses and other bodies in motion.

That relish does not extend to the use made by politicians, bureaucrats, and communicators of the terms of sport experience. Of Richard Nixon, Mandell remarks: ''Nixon's public and private life was weirdly colored with, perhaps molded by, the sports page and locker room rhetoric of 'team play,' 'playing the game,' strategy, and, above all, winning. It is possible that some aspects of the recent disappointments that Americans have endured can be attributed to a tendency among those at the highest levels of American society to permit sports rhetoric, metaphors of winning and losing and game dramaturgy to supply patterns for dealing with issues that are in deadly earnest, that have a logic rooted in the real world, and are not games at all.'' Indeed, sport, though central to the American experience of democracy, is based on artificial rules that do not ''play'' in the world at large.

Real play is something else altogether. I would suggest that in writing this book - a supremely charming and yet completely serious endeavor - Mandell himself has mastered the supreme game: that of making sense of modern emotions. All the claims he makes for the spiritual significance of sport, even when seen in the context of the democratic-achievement principle, pale when compared to the spiritual significance of the freedom of thought of a good, scholarly, yet fully humane book. ''Sport: A Cultural History'' is such a book, that, for all its importance to us, is essentially a wise man's plaything. Read it, even if it means giving up a month of the Mets.

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