The tiny Palestinian baby, just a few weeks old, is surrounded by the best medical technology the state of Israel can provide. She is one of three Palestinian children in the eight-bed paediatric intensive care unit at the Hadassah University Hospital, funded by the Women's Zionist Organisation of America.
Unlike the other children in the ward, this baby is alone, with no parent comforting her. Dr Ido Yatsiv explains: "Her parents find it very hard to get through the IDF [Israeli Defence Force] roadblocks." I wonder, if the little girl survives, what her parents will one day tell her. That her life was saved by the generosity of the Zionists? Or that their soldiers cruelly made it so difficult for them to comfort her when she was at her most vulnerable?
The Hadassah hospital, Jeru-salem's biggest, is at the heart of the horror and the hope in the Middle East's most intractable dispute. Dr David Gillis, who emigrated to Israel from Sunderland, told me how his brother Shmuel, who also worked at the Hadassah, was shot dead by a Palestinian gunman as he came back home from the hospital late one night: "He had just been helping a Palestinian mother with a difficult childbirth," said Dr Gillis in a voice barely above a whisper.
Hence, the IDF argues, the need for the roadblocks. They are fully aware that these "fixed ambushes" cause unbearable frustration and humiliation for law-abiding Palestinians; but they also point out that such checkpoints are a vital non-violent weapon in their campaign to limit the mobility of the sort of people who murdered Dr Shmuel Gillis.
These arguments do not impress the very senior official from the Palestinian Authority whom I met in the PA's compound in Ramallah: "We thought, after Annapolis, that Israel would change their attitude on the ground; but they aren't – and it's just helping the jihadists." By this, the official meant Hamas, of course: the Islamist group which has increasingly displaced his own secular Fatah organisation as the voice of Palestinians, especially among the young.
Angry as this Fatah official is with what he sees as the unwillingness of Israel to relax its military grip on the day-to-day lives of Palestinians, it as nothing to his feelings about Hamas. "These people are crazy, deviant, horrible – and they are serious." The official's tirade is hardly surprising: Hamas seized control of the Gaza strip from Fatah with a murderous coup – and promises more of the same.
The next day I went down south to Sderot, the part of Israel which suffers most from Hamas's growing ascendancy. It is a city of about 20,000, no more than a kilometre from the Gaza strip. Every day Sderot is hit, mostly by Hamas's home-made Qassam missiles, which take a mere 30 seconds to make their brief journey. Even the efficient Israeli early warning system gives the inhabitants of Sderot no more than 15 seconds to find cover.
Geut Aragon is a 34-year-old Israeli nurse whose home was hit in January by a Qassam while she was playing indoors with her four- year-old son – the mothers of Sderot no longer dare let their children play outdoors. They both survived the attack, although Geut still has shrapnel lodged very near to her brain. When I asked her what she thought of the people who had done this she described them as "animals – I hate them" but went on to say that, "I tell my son that there are so many good people in Gaza who are not trying to kill us. We have good Arab friends in Gaza. They were so nice-they used to stay with us. We still talk on the phone. We tell each other to stay strong."
Geut is more critical of her own government: "The day Israel withdrew from Gaza, I knew it was a terrible idea, I knew we would be a target. And I know my Arab friends will suffer when the IDF goes back into Gaza." At that point the early warning system sounded and I caught a glimpse of pure terror on Geut's face before she turned and rushed for cover. Only then did I grasp what was happening, and followed her.
Many Israelis who are not as immediately at risk as Geut Aragon would share her view. Just as Hamas's immediate response to the IDF's retreat from Gaza was to use the territory to rain missiles on Sderot, so Iran-sponsored Hizbollah filled the vacuum left by the IDF's departure from south Lebanon and used it as a base to fire missiles into northern Israel.
In other words, they argue, every time Israel concedes territory, it makes life more dangerous – fatally so – for its own citizens. This makes it politically extremely difficult – impossible, in fact – for the already unpopular government of Ehud Olmert to meet the Palestinian demands for a complete withdrawal from the West Bank: to do so would guarantee that Tel Aviv itself would soon be within range of Iranian-supplied missiles.
Next week, nonetheless, President Bush arrives in Jerusalem, as part of his push for a final peace settlement between Israel and the Palestinians. It's what American presidents do at the very end of their second term, in an effort to turn a political dying fall into something glorious for posterity. But, as the most respected Palestinian pollster, Jamil Rabak, points out, this is not the way to help things along: "Every time Abu Mazen [the President of the Palestinian Authority] is seen greeting Condoleezza Rice, then Hamas's popularity shoots up."
The leader of the opposition on Jerusalem's City council, Nir Barkat, put it to me most bluntly: "Our Prime Minister is weak. The Palestinian Authority is weak. George Bush is weak. How can these people have the authority or the credibility to succeed?" It's fair to say that Mr Barkat does not want them to succeed, if "success" involves any division of Jerusalem – one of the most complex of all the problems confronting the negotiators.
So the Palestinians are forced to endure this week's celebrations marking the 60th anniversary of the founding of the state of Israel, still with no tangible prospect of a state of their own. If in 1948 the Arab world had accepted the UN-mandated partition between Israel and Palestine – rather than send in their armies to try to destroy the new Zionist state on the very day after its creation – then Palestinians too might this week have been able to celebrate 60 years of independence.
Perhaps their salvation will not have to wait another 60 years – that would be dreadful; yet I left Israel with the sinking sensation that the prospects of a final settlement are, if anything, receding. It would be wonderful to be proved wrong – but that would require a change of government not in Washington DC, but in Tehran.