Flying to the mysterious Middle East, I am struck by the extreme difficulty of reading yet a new riddle: the effect of shock, show-biz diplomacy on the area.

By its sheer drama, by its capacity to touch millions, Anwar Sadat's visit to Jerusalem changed the nature of what had been a fixed pattern of politics and diplomacy. While the leap in the dark could have a happy ending, it is at least as likely to put events out of control.

The old game in the Mideast was a game of secretly saving face for bogus claims. All Israeli governments felt behind them folk memories of the Holocaust and the appeasement that preceded the slaughter, so they staked out positions of strength that Arab governments could not accept. They made even small concessions only under pressure and in return for something - usually something American.

All Arab governments worked against the background of a proud people fallen from grace. They had been humiliated in battle by a despised minority. A part of the Arab family - the Palestinians - had become stateless. So no government could publicly afford to be less hostile to the Israelis or less enthusiastic about the Palestinians than another.

These intrinsic difficulties were compounded by the Russians, who fostered local grievances and - at times, at least - poured gasoline on brushfires. In part to block the Russians, in part for more altruistic reasons, the United States tried to manage matters in a constructive way.

The upshot was an example, on the world stage, of a permissive parent dealing with unruly children. All claims were admitted as valid in principle. No one was allowed to gain a decisive edge. All parties were encouraged at all times to sort out their difficulties.

Ocassionally, when the game was played in private on a one-to-one basis, progress was achieved. President Eisenhower forced the Israelis to disgorge the conquests of the Suez War of 1956. By similar pressures, Henry Kissinger worked out limited disengagement agreements between the Israelis and the Egyptians and the Israelis and the Syrians after the 1973 war.

The latest American effort, under President Carter, asserted in public the urgency of a comprehensive settlement. Going comprehensive meant throwing indiscriminately together the parties most eager to settle, the Egyptians and Israelis, with those nursing the biggest, grievances - the Syrians and the Palestinians, heading up in the Palestine Liberation Organization.

To bring in the latter, the United States made common cause with Russia in a joint appeal for reconvening the Geneva peace conference. The Israelis saw themselves being gang-tackled by the Arabs and Russians. The Egyptians, or at least Sadat, saw himself being hustled by the other Arab states into positions that made fruitful talks impossible.

By going to Jerusalem, Sadat broke up the old game. He defied the Syrians and the Palestinians and other Arab states they had taken in tow. He surprised and disarmed the Israelis - particularly the hawks who had all along insisted on "an eye for a tooth."

He completely fooled outsiders who have made a specialty of watching the game. That includes the Carter administration, the Soviet leadership and most professional observers. Those who claim to have seen it coming all along only prove that they have been confused all along.

What will happen next nobody can say with confidence. But an indent has been made for progress. SHams have been exposed for millions of people by a kind of televised shock treatment.

Israelis are now free to make genuine concessions of a large order. Arab states who want to deal - and that seems to include Jordan and Saudi Arabia besides Egypt - have some room to maneuver.

But the old game has withstood shocks before - notably at the time of the 1973 war. Many Arab states, at least some Egyptians, and the Palestinians and Russians do not want the Sadat initiative to bear fruit. The malcontents could cause the kind of trouble in Egypt - and in such friendly nations as Jordan, Saudia Arabia and the Sudan - that would force matters out of control.

Americans can be helpful chiefly by nourishing the entente between Jerusalem and Cairo. It needs light and air and a chance to burgeon in followup actions. What is not helpful is an effort - visible in some parts of the administration and the State Department - to force the new reality back into the mold of an approach that was going nowhere.