JERUSALEM - A Palestinian businessman was crossing the border from Jordan into an Israeli-controlled section of the West Bank not long ago, and he got to talking to a Canadian who was making the same trek.
After a while, the Palestinian began to muse about what he sees as the solution to the conflict between his people and Israel.
According to this man's blueprint for the future, the Palestinian Authority that now holds a tenuous grip on power in the West Bank should unilaterally dissolve itself, obliging Israel to take over civil administration in the territory, as used to be the case - an arrangement that would blur the borders between Israelis and Palestinians.
In a matter of decades, the man said, the total Arab population of Israel and the West Bank would outnumber the Jewish population, and the state of Israel would collapse beneath the combined weight of demographics and international censure.
In other words, the one-state solution.
For most Israelis, the merest mention of this term is like a dose of ethnic poison, a premonition of their demise as a nation.
Among Palestinians, the idea has long been out of fashion. But in recent weeks, the notion of a single bi-national state for Arabs and Jews has experienced something of a revival among Palestinians, most notably when Sari Nusseibeh, a respected intellectual and president of Al Quds University in East Jerusalem, spoke favourably about the concept in a lengthy interview with an Israeli newspaper.
"I think one should maybe begin, on the Palestinian side, to begin a debate, to re-engage in the idea of one state," Nusseibeh said, in remarks published last month by Haaretz.
The main point of Nusseibeh, 59, was that the search for a two-state solution - an independent Palestine dwelling alongside Israel - is now floundering so badly it may never recover.
After many years of failed negotiations, the two-state vision is still far from reality, and few expect current peace talks between Israel and Fatah - the more moderate Palestinian political faction - to change matters by much, if at all.
"We have failed in the last 15 years to create the world we wanted to create," Nusseibeh said. "So it is time, maybe, to rethink."
Like the businessman at the border crossing with Jordan, he suggested the Palestinian Authority should simply pull the plug on its own existence.
"The PA has no use," he said. "The whole thing is a mess."
For most Israeli Jews, the prospect of dwelling among millions of Palestinians in a single bi-national state would be far worse than a mess. It would be the fulfillment of their darkest nightmares.
Either they would be obliged to hold sway in an ethnic dictatorship, where only Jews would be entitled to vote and exercise full civil rights - like whites in South Africa under apartheid - or the Jewish character of their country would eventually be overwhelmed by a faster growing Arab population.
Either way, Israel as a Jewish state would be unlikely to survive.
It was mainly to help forestall this dilemma that former Israeli prime minister Ariel Sharon engineered his country's unilateral withdrawal from the Gaza Strip in 2005.
Since then, Israel has been walling itself off from the West Bank, partly for security reasons but also to fortify its own identity as a sovereign Jewish state - whatever becomes of the Palestinians.
Nusseibeh's remarks have excited debate among Palestinians, but the one-state concept has not exactly gained unanimous approval.
"This is not the logical step," said Hassam Khader, 47, a reform-minded Fatah leader recently released from an Israeli-run prison, who thinks Palestinians should continue to pursue a two-state solution with Israel.