The latest burst of optimism that we might be a few inches closer to a formula for resolving the 37-year-old Palestine problem brought to mind a story I once heard about Yasser Arafat. It involves the runaround he gave a hapless reserve colonel in the Egyptian Palestine Liberation Army who had gone to Lebanon from Cairo in the summer of 1982 to help in the fight against Israel.

When thieves broke into the colonel's Beirut hotel room and absconded with his $200 in savings, he took his problem to Arafat. The PLO chairman grandly wrote out and signed a note authorizing reimbursement and sent the colonel off to the guerilla organization's finance office.

But the clerk there, after closely scrutinizing the piece of paper, said Arafat had no power to authorize such a large expenditure and the matter would have to be approved by the PLO's executive committee, which would not meet for another month -- in Damascus. The colonel waited patiently, then returned to the office after the Damascus meeting -- only to be told by the clerk that unfortunately his case had not made it onto the agenda.

Penniless and confused, the colonel showed the Arafat note to a friend and told him of his problems with the PLO bureaucracy. The friend's response was to tell him the note had only Arafat's "third signature" and that he should seek another audience with the wily leader and ask him for a note signed with his "first signature."

This the colonel did. Arafat is said to have laughed uproariously, asking the colonel: "You son of a dog, how did you know?" He then penned another note, which the colonel is said to have taken immediately to the finance clerk, who reimbursed him on the spot.

The point made by the well-connected Arab banker who told me this story was that for Arafat and for others in the Mideast, mere words on a piece of paper -- for example, Arafat's agreement with Jordan's King Hussein on peace talks and whatever notes Hussein and Secretary of State George Shultz may have exchanged last week -- should not be understood to be invested with the same sacredness as such contracts may be for the United States or Israel.

Does this mean there's no hope for an agreement? Not at all. The United States and Israel can make progress toward some kind of a deal with Arafat, but they must be willing to break tradition and begin a dialogue with him.

The idea that talking has advantages is rooted in the experience of U.S. diplomats and intelligence operatives in Beirut before the summer of 1982. These people did maintain private contact with the PLO -- for the purpose of protecting U.S. diplomats and installations.

The intriguing tale of how this backdoor channel worked has been best told in an article in The Wall Street Journal. According to reporter David Ignatius, Arab sources cited a series of specific examples of cooperation, including a tip that there might be an attempt on the life of Henry Kissinger, who was then secretary of state, when he planned a trip to Beirut in late 1973. Kissinger's plane was diverted to an eastern Lebanon air base, and he escaped harm during the trip because a top Arafat aide had marshaled a force of 6,000 to protect him during the visit, according to Ignatius' account.

Some well-informed observers believe that ironically when U.S. Marines helped escort the PLO out of Beirut in 1982, they sent out the United States' best source of protection and intelligence.

The obstacles to any direct dealing with Arafat stem from an agreement Kissinger made with Israel 10 years ago, a prohibition that was more strictly interpreted later by President Carter. Once out of office, Carter, presumably no longer bound to the promise, had contacts with Arafat confidantes, but by then he was no longer in a strong position to influence the course of events.

Many Americans wonder why neither Hussein nor Arafat will step forward and make the pilgrimage to Jerusalem as the late Egyptian President Anwar Sadat did. That view fails to understand the weakness of the PLO and Jordan when compared with Egypt, the main weight of Arab civilization. But it also ignores the fact that Sadat was later assassinated by forces within his own military and remains even today a man vilified and scorned in memory, in large measure because he was believed to have negotiated a separate peace at the expense of the Palestinians.

Any move toward direct U.S. talks with Arafat and the PLO will no doubt bring an initial outcry from Israeli hard-liners and their potent lobbies in the United States who have tended to paint Arafat as the devil incarnate.

But in view of the death and destruction that accompanied Israel's invasion of Lebanon in 1982, no one in the Middle East can exactly claim to enter this period with clean hands.

After Islamic fundamentalists with their corps of suicide bombers replaced the PLO in southern Lebanon, Israel learned the hard way that there are worse things than having Arafat at your borders.

Frankly, I don't know what might come out of talks between Arafat and the United States, but I do feel strongly that as the forces of extremism gain momentum in the Middle East, the search for the magic formula, or the alternative strategy of "benign neglect" counseled by some Washington savants, is foolhardy.

And I do not believe that Arafat, after fighting a bloody rear-guard battle in Tripoli to keep the Palestinian card out of the hands of the Syrians, will now turn around and acquiesce in some scheme put together by the Americans and Jordanians. If you think that, you would probably sit around a hotel room clutching a voucher with his "third signature" and waiting for the PLO executive committee to meet.