Remember that amusing little scene at the start of the Camp David peace summit in July? Before whisking them away into two weeks of seclusion, a smiling President Clinton, dreams of Middle East peacemaking glory still intact, took his guests, the Israeli Prime Minister Ehud Barak and the Palestinian Authority President Yasser Arafat, for a brief stroll in front of the cameras.
And when he tried to lead them back inside through the narrow open half of a double doorway, Mr Barak and Mr Arafat indulged in what, at first glance, appeared to be a bit of playful wrestling: After you, said Mr Arafat. No, after you, insisted Mr Barak.
Neither was giving way. They pushed and shoved each other, still smiling. And Mr Clinton, who had made the inexcusable error of leaving them unsupervised for all of five seconds, had to come back and retrieve them, saving the day by opening the other half of the doorway.
Viewed from the Middle East's current parlous perspective, that apparently inconsequential, apparently good-natured battle of wills takes on a certain added significance. There, then, were two men utterly unprepared to give way to each other - even over something as trivial as entering a room. Here, now, are two men utterly unprepared to give way to each other - even at the cost of regional conflagration.
But as far as Mr Barak is concerned, there is one crucial difference between them.
No, he was not ready to capitulate in peace negotiations with Mr Arafat - to bow to the Palestinian leader's demands for a "right of return" to sovereign Israeli territory of hundreds of thousands of refugees, to withdraw Israeli troops from the entire West Bank and Gaza Strip, to allow full Muslim sovereignty over the Temple Mount, the Haram al-Sharif, in Jerusalem's Old City. But he was prepared to compromise on all those issues, and Mr Arafat was not.
Mr Barak won power in Israel 17 months ago as a would-be peacemaker, a moderate contrast to the Arafat-sceptic, Benjamin Netanyahu. He is adamant that, at Camp David, he offered the Palestinians a fair deal - a mechanism for limited refugee return, withdrawal from almost all of the occupied territory, some kind of shared sovereignty at the Temple Mount, and support for independent Palestinian statehood - a deal he had no guarantee his own people would endorse.
When Mr Arafat balked at the terms, and the Camp David talks broke down, the Prime Minister told his colleagues he thought the Palestinians had made a historic mistake - passed up the opportunity for statehood, in partnership with Israel, with international support, with American financial backing.
And everything ugly that is now unfolding, he believes, is a consequence of that missed opportunity.
He offered to give ground, but Mr Barak won't give way. And so, when Palestinian rioters, with gunmen in their midst, charge army positions in the West Bank and Gaza, his soldiers fire back.
AND when international diplomats note the imbalance in the death toll - the handful of Israeli dead and the 90 or so Palestinians - he stresses that his troops are reacting to, not initiating the clashes, and they're well trained, and well armed, and so sustain few casualties.
And even when two of his soldiers - reservists, family men in their 30s - are stabbed and bludgeoned to death in a Ramallah police station - he orders only what he says is a symbolic response, a series of pinpoint missile strikes on what he notes are military and communications targets, injuring a few dozen Palestinians, killing no one.
He is utterly convinced of the rightness of his position. Israel, he assures CNN, is telling "the truth" about this conflict. Mr Arafat is to blame. And it is only because of the need for diplomacy that the hordes of visiting foreign statesmen are refraining from telling Mr Arafat as much to his face.
The trouble is, of course, that the Palestinians are equally convinced that all the blame lies with Mr Barak.
Like his mentor, the late Yitzhak Rabin, Ehud Barak (58), was a peerless military man first, an awkward politician second. He was Israel's most highly decorated soldier - rising to chief of staff, having commanded Mr Netanyahu in an elite commando unit, dramatically thwarted an airline hijacking in 1972, plotted the Entebbe airport rescue four years later, played a leading role in the 1988 assassination in Tunis of Abu Jihad, Mr Arafat's deputy.
But he is unusually well-rounded for a military man - an avid reader, a good English-speaker, a pianist, a master's graduate in mathematics and systems analysis.
And he has a strong and warm family background - doting kibbutz parents, a likeable wife, Nava, and three grown-up daughters.
Like Mr Rabin, he always doubted that Israelis and Palestinians could live happily alongside each other, with open borders, in the foreseeable future, but realised that Israel's best interests were served by a negotiated separation, neighbourly coexistence, however wary.
Though no match for Mr Netanyahu as a communicator - his campaign strategists, borrowed from Mr Clinton, flatly refused to let him debate against "Bibi" on TV in the election run-up - Mr Barak won power because he promised to try to heal secular-religious divides inside Israel, and because he offered to work with, rather than against, Mr Arafat towards Palestinian independence, and thus to safeguard Israel's security needs.
He can claim one significant achievement in office - the withdrawal of Israel's troops from Lebanon in May, although that too will count against him if the northern border now heats up.
But Israel's domestic rifts have widened under his tenure. A major push to peace with Syria ended in failure. And now his Palestinian peace conception has fallen apart as well.
He beat Mr Netanyahu by 56 to 44 per cent in last year's elections; yesterday's newspaper opinion polls show his popularity at 30 per cent, compared to 46 per cent for Mr Netanyahu, who is no longer even a Knesset member.
His critics, and there is no shortage, would say he has only himself to blame. On the Israeli right, the current crisis is seen as proof that Mr Barak, and Mr Rabin for that matter, always had it wrong, proof of the long-standing contention that Mr Arafat never set his heart on peacemaking, never renounced terrorism, sought only to gain what he could through negotiation and push for the rest of Palestine by force.
On the Israeli left, there are those who feel Mr Barak moved too slowly, gave too little, and pushed too hard on the ultra-sensitive issue of Jerusalem.
And even among his more loyal supporters, there is dismay that he is running Israeli affairs almost single-handedly, with little delegation, little consultation. Amnon Lipkin-Shahak, Mr Barak's successor as army chief of staff, and now one of his senior government ministers, for instance, was allowed no input whatever on the decision to order air strikes on Ramallah and Gaza after Thursday's murder of the soldiers.
His fellow generals always regarded Mr Barak as the brightest among them. His own Labour party knows it has no one of his calibre to succeed him.
But he now heads a minority coalition, and will be voted out of office when the Knesset reconvenes next month unless he cements a "unity" coalition with, of all people, his hardline opponent, Ariel Sharon, the man whose walkabout on Temple Mount last month sparked this crisis.
The only man who can now save Mr Barak the politician, the only man who, with Mr Barak, can now save the Middle East from prolonged, futile conflict, is, of course, Mr Arafat.
But the playful wrestlers are now warring in earnest. And Mr Clinton is finding it difficult to widen the doorway.