It's like that literary moment that sent Victorian London into mourning, when Arthur Conan Doyle decided that enough was enough, and dispatched Sherlock Holmes by having him topple over the Reichenbach Falls in a death-grip with his arch-enemy, the Napoleon of crime, Dr Moriarty.
That is where Israel and Palestine now seem to be, grappling on some hideous brink. Israelis feel they must enforce a solution now, before Arab demographics and Arab nuclear scientists shift the balance of power. Palestinians feel they must react now against the enormous pressures of an occupation that has been driven into cruelty by Israel's own fears.
There seem to be only two ways. There is the Ariel Sharon belief in a military victory, or at least a settlement based on Israel's overwhelming military might. And there is the Palestinian extremist view that Israel can be terrorized out of the West Bank and Gaza, and maybe even out of existence. Each of those solutions is wrong, cruel, and doomed to disaster.
Maybe, just maybe, the glimmering of a third way is starting to emerge. A group of 52 Israeli reservists is vowing not to serve in the West Bank or Gaza, although they will loyally defend the Israeli homeland whenever called. Israeli journalists and politicians are complaining of the cruelty of an Israeli blockade system of Palestinian villages that have women in childbirth barred from reaching hospitals.
And on the Palestinian side, a handful of intellectuals, backed up by some brave Members of the European Parliament and NGO activists, are trying to revive a non-violent peace movement. Dr Mustafa Barghouthi, president of the Palestinian Medical Relief Committees, who despises the corrupt autocracy of Arafat's foul little regime is trying to rally a democratic alternative through (his words) "the growth of public participation in a struggle for freedom from Israeli occupation which focuses on non-violent resistance.
"Participation in such a struggle will simultaneously re-energize the Palestinian people with the hope that peace, security and independence are possible," says Barghouthi.
And he still speaks this way, even after Israeli troops broke up his attempted press conference in East Jerusalem earlier this month, smashing his knee with rifle butts, and arresting him on spurious charges of disturbing the peace.
The point that Barghouthi, and his friends and supporters in the U.S. and Europe all understand is that even when poised on the brink of Reichenbach Falls, there are certain societies where non-violence can work.
Let us not be romantic about this. Non-violence has too often been clubbed into submission and silenced. But in democracies like Great Britain, when faced with Gadhi's movement for Indian independence, or the Deep South of the United States when faced with the Civil Rights movement of the 1960s, it can work.
In countries where there is a free press and free speech and brave TV cameramen and a kind of public conscience about what the police and troops do in a society's name, non-violence can be a hugely potent weapon.
Israel is that kind of society, or at least most Israelis want it to be even as suicide bombings bring out the inevitable instincts of vengeance and retaliation. Israel is a society with a conscience, a sense of right and wrong, and so is the Jewish diaspora.
"In their final attack, when they arrested me, Israeli soldiers physically assaulted two members of the European Parliament, and several European participants," says Barghouti. "The Israeli authorities clearly fear the growing strength of this movement -- not only for its representation of a real and solid democratic alternative for Palestinians, but also because it brings direct international attention to the reality of Israeli occupation, and the Israeli violence accompanying it."
Edward Said, the Columbia University professor who is probably the best-known Palestinian after Arafat, is a friend and backer of Barghouthi who thinks the political space may just be available for this mind of non-violent movement.
"Recent polls show that between them, Arafat and his Islamist opponents (who refer to themselves unjustly as the resistance) get somewhere between 40 and 45 percent popular approval," Said writes in The Nation. "This means that a silent majority of Palestinians is neither for the Authority's misplaced trust in Oslo (or for its lawless regime of corruption and repression) nor for Islamist violence."
Maybe they are right. Maybe there is the glimmering of a third way. And anything is better than Israelis and Palestinians taking the death plunge over the Reichenbach Falls.