While his aides munched tuna bagels thoughtfully provided by the Israeli military, a shirt-sleeved Tony Blair peered intently at a map showing the two main cargo crossing-points that will function between the West Bank and Israel once the 450-mile separation barrier between them is complete.
Why, Mr Blair wanted to know from his host, an Israeli general in civvies, couldn't goods also be moved directly across the border from the nearby Palestinian industrial park that he is pressing Israel to approve?
"Why can't they go straight through?" Ah, that would be difficult, the general explained, requiring a whole new expensive security apparatus to check goods going into the park.
We are a long from way from No 10. At Tarqumia to be precise, just inside the West Bank and one of those crossing points – a forbidding grey antenna and camera-studded complex of checkpoints still under construction. Mr Blair is on the road, grappling with the mind-numbing complexities of how the physical security infrastructure of the occupation has squeezed the Palestinian economy.
It is a theme reinforced for him in Hebron, the Palestinian city whose core was once the thriving commercial hub of the southern West Bank. Its mayor, Khaled Osaily, briefs him extensively about how much of its old city is boarded up, stripped of Palestinian life because of the presence of some 800 Jewish settlers, and their military protectors.
As Mr Blair's convoy threads out of the city through the afternoon Ramadan traffic afterwards, Mr Osaily compliments Mr Blair on his thirst for facts. No, they had not talked much about the prospects for the forthcoming US-convened Annapolis conference on which hopes of any revival of a peace process have no been vested by the international community and in the preparations for which Mr Blair is intimately involved. "He is a practical man," said Mr Osaily. "He asked many questions about daily life here. We talked about the economy, about movement, about security. He wanted to know details."
Mr Blair gave the Israeli daily Yedhiot Ahronot his stock answer yesterday to questions about what he has learnt since taking the job. "I have learnt the depth of Israel's concern for security, and I have learnt the depth of the Palestinians' distress caused by the occupation."
Certainly he accepts Israel's view that Palestinians should not have a state until it can reasonably guarantee its neighbour's security. Hence the importance he attaches to the efforts that US General Keith Dayton is making to beef up Palestinian security forces. Indeed he has been telling diplomats and others that the emergency Palestinian Prime Minister, Salam Fayad, does not enter Nablus because he will not make the deal with the militias needed to guarantee his security.
He was shocked by what he was told about conditions in Hebron and diplomats say he was genuinely taken aback by his trip to the West Bank sector of the Jordan Valley – where Palestinians are allowed to dig wells only a third as deep as Israelis – at the exploitation of resources by the rich Jewish agricultural settlements at the expense of closed in Palestinian farmers. And he has been privately dismissive – rather more so perhaps than he was as Prime Minister – of the argument by some Israelis that security comes first, with economics and a political deal well behind it. "All three have to happen together" he has told diplomats – which is what he sees Annapolis as being about. This week he has been concentrating on the economics and is pressing Israel to permit job growth in the West Bank's Area C, where it has direct as well as total control – including a Japanese government plan for an "agro-industrial" park in the Jordan Valley.
A key purpose of all this, of course, is to try to give the Palestinian President, Mahmoud Abbas, something tangible to show for the outline political accord that he and the Israeli Prime Minister, Ehud Olmert, are under pressure to reach before Annapolis and which Mr Blair sees as a " stepping stone" to full negotiations for a final resolution.
Some of the possible contours are beginning to clarify: a land swap to preserve the big West Bank Jewish settlements and, possibly, Israeli agreement in principle to East Jerusalem as a future Palestinian capital.
But the obstacles could hardly be more potentially terminal. Mr Abbas, at least as much as Mr Olmert, will have to make concessions without yet having a final deal in return. And this at a time when a totally excluded Hamas will have every opportunity to sabotage any process.
Yet none of this seems to dent Mr Blair's almost heroic optimism that it is " do-able." He accepts in private that settlement expansion will soon make a Palestinian state unrealisable, increasing the urgency of a solution. But he is said to believe that Mr Olmert sees a two-state solution as necessary in Israel's interests and accepts time is short.
He thinks the similarities with Northern Ireland are as great as the differences but since it irritates Israelis for him to say so, he doesn't. But that doesn't stop him recalling how Ian Paisley told him early in his premiership there would never be an agreement in Northern Ireland.
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