When it comes to peace, the gap between the most that any Israeli government can offer, and the least that any Palestinian administration can accept, has never been bridged.
But never, since the Oslo peace process began, has that gap seemed wider. And it's still growing. Two weeks ago, the Palestinian prime minister, Salam Fayyad, resigned. Fayyad was one of the last remaining Palestinians with whom Israeli security chiefs had some chemistry. Working behind the scenes after the second intifada, Fayyad assisted Israel in thwarting a resurgent Hamas in the West Bank, and he got the Palestinian Authority security forces to rein in several hundred Fatah militants.
Personal chemistry matters when nothing else seems to work. It can keep a peace pulse beating, however faint. I think of the chemistry between the former Israeli leader Yitzhak Rabin and Jordan's King Hussein. Those who witnessed their private meetings speak of a genuine bond - they both even smoked cigarettes the same way. It is said that even the erratic Yasir Arafat had a grudging respect for Rabin as a man whose word could be trusted.
Those days are gone. With Fayyad out of the way, Hamas has made a renewed effort to draw Fatah into its orbit in a new unity pact, while asking Europe to annul its designated status as a terrorist organisation. Hamas hopes the European Union will be open to persuasion because Hamas hasn't launched a suicide bombing since 2004. I guess Hamas don't count rockets fired at civilian targets, or a laser-guided, anti-tank missile fired at a school bus killing a 16-year-old in 2011.
Will Hamas succeed? Probably not. But who is to say they might not eventually if nothing changes?
What President Obama politely referred to in his empathetic speech to young Israelis in March was the imperative for Israel to reverse what he called "an undertow of isolation" because of the "frustration in the international community about this conflict". For "undertow" read: "If the status quo in the West Bank continues, and religiously inspired settlements continue to grow, you will one day be staring at global isolation."
Obama's tough love may succeed in giving a resuscitating jolt to the near lifeless body of Oslo. But very few seem to think it will succeed in saving the patient's life.
As Ireland and South Africa remind us, the leaders of both sides in a conflict really have to want a settlement to the exclusion of all else, in order that they find the words and the leadership and the political courage to take their people with them.
And yet, today, the growing fusion between religion and politics on both sides in the Holy Land risks putting the conflict beyond any sort of resolution.
Does any rational Palestinian seriously believe that, never mind the Israelis, the rest of the world is ever likely to accept that the entire Holy Land has been a sacred Islamic endowment since Muslim conquerors consecrated it in the seventh century, with never one inch of it to be ceded by an Arab ruler? By the same token, is the world - let alone the Palestinians - ever seriously likely to expect Palestinians and Arabs to accept that there exists for Israelis an inviolate right to settle on the whole of the ancestral biblical homeland, irrespective of the impact this might have on others who have lived there for generations?
And does any rational Israeli - and most Israelis I know are very rational - seriously believe that scores of checkpoints, entry permits to Jerusalem, the construction of settlements, restrictions on the movements of tens of thousands of Palestinians, can continue in perpetuity without some sort of violent outlet, sooner or later?
The majority of Israelis do not. They have no desire to oppress Palestinians. But then they shrug: what to do?
If you are an optimist, you have to believe, as former director of Mossad Efraim Halevy believes, that ultimately there will be ideological burn-out on both sides and a settlement of sorts will emerge. But this will not happen any time soon because, Halevy told me, both sides will continue to claim rights to the whole of the Holy Land, right up until "one minute to midnight".
Only then will they look into the abyss and accept that, since neither side can sustain permanent conflict, life for both sides will become intolerably wretched. Do things really have to get that bad before they get better?
Every year about now, the gloom lifts for a day or two as Israelis and Jews around the world celebrate the birth of the world's only Jewish state. In London, hundreds of guests of the Israeli embassy are plied with good sushi, salt beef, smoked salmon and wine, and the truly remarkable stories of what the state has achieved in such a short time. The tone is irrepressibly upbeat - and infectious.
So this year, as Israel celebrates its 65th birthday, perhaps I, too, can strike an optimistic note even though the future seems so gloomy.
In January, I travelled around Israel making a documentary for BBC 2. Israel: Facing the Future was broadcast last week.
Television is not the friendliest medium in which to unravel complex subjects. It suffers from what the BBC's former director-general John Birt once called the "bias against understanding". What Birt meant was that television tends to cleave to polarity and in a conflict as complex and visceral as this one, finds it hard to grapple with the nuances that can be vital to a proper understanding.
Because this conflict arouses such huge passions, we attempted, where possible, to paint a picture of the country in some of the colours that we felt showed how Israel actually is rather than the way its often portrayed.
With so much ground to cover in a limited time, inevitably some impressions couldn't be accommodated. But they're worth retelling because to me they show there are still signs of life in the search for peace and reconciliation in everyday events.
Take the Palestinian entrepreneur Bashar Masri, whom I met in the West Bank. He is risking much of his personal fortune to build a new city at Rawabi. As in Israel, there is a shortage of housing in the West Bank, only chronically so. Masri is building homes for 40,000 Palestinians, schools, mosques and a commercial centre. American architects and engineers helped get the project started, but now it's almost exclusively run by Palestinians.
Rawabi gave me a glimpse of a possible future, a mini Palestinian state in the making, free of the religious ideology that has done so much to fuel hatred and mutual mistrust. Masri and his team just want to make a better life for Palestinians. He speaks eloquently about the disaster that will ensue in the absence of some kind of two-state solution - a disaster, he stresses, not just for Palestinians but also for Israelis. "We'll be killing each other throughout time and throughout the next 100 years, which I would hate to think about," he says.
Adjacent to this project is a settlement, legal under Israeli law, but whose members, according to Masri, have been generally obstructive, holding demonstrations, refusing to co-operate over access roads, and even resorting to legal action. Masri says he's had a stream of Israeli visitors - rabbis, MKs, IDF top brass, including chief of staff Benny Gantz. After a tour of the site, Gantz turned to Masri and said: "Any man who can build a place like this is a man of peace. How can I help?" Masri explained his difficulties with the settlers. Gantz said he would sort it, and that is what Gantz did. The hostility has stopped.
Although distrust is the very heart of the Israel-Palestinian conflict, between them Gantz and Masri showed how to build it.
Masri has also built strong cross-border relationships with Israeli entrepreneurs and philanthropists. And although ordinary Israelis and Palestinians have had negligible contact since the second intifada, in the restaurant of one Israeli hotel I saw a large group of Israel and Palestinian businessmen eating together, joshing with each other, talking earnestly - and laughing together. Again, I could glimpse a future.
And then I read that, on the eve of Yom Hazikaron, some Palestinians from the West Bank who'd had relatives killed by the IDF were given permits to travel to Israel to meet Israelis whose relatives had been killed by Palestinians. A hall with 2,000 seats is reported to have been filled, mostly with young people. This cannot have been easy for either side. Yet it happened.
And what about the last election - the one in which almost everyone forecast Israel would take a big lurch to the ideological right? It didn't happen. In fact Israelis recoiled from it. The country's ideological right may still be the largest single voting bloc in the Knesset, and within it, members seem to be moving ever further to the right. But the Israeli electorate has stayed stubbornly around the centre - as it has for several elections now.
Predictions about Israeli-Arabs disengaging from the democratic process also defied expectations. While the most exhaustive polls point to deepening tensions with their fellow Jewish citizens, Arab-Israeli turnout showed the biggest rise since 2000. And while there are disturbing signs of xenophobia in some sections of the Jewish-Israeli population, here's one more snapshot of Israel that these days, rarely seems to see the light of day.
Having heard all sorts of racist horror stories about Beitar Jerusalem FC, I went to watch then play at home. Sure enough there were extremists - a gang of about 200. Furious that Beitar had just signed two observant Muslim players (from Chechnya as it happens), they raised a sign saying: "Beitar - pure for 70 years."
But was this permitted? Was it applauded? Was it even tolerated? No, it was not. The police moved in to arrest the mob and some have been charged with racist behaviour. The club has been fined, the stand was closed for several matches, and the club's owner has said he wants nothing to do with racists. None of the fans I interviewed on the opposite stand supported them. One or two intimated that they were off their heads.
This peace business is so easy to aspire to and waffle warm words about - and so very difficult to do. None of these events should be overstated. Yet to me they indicate there is a peace pulse, on both sides, that still flickers. And while there's life there must always be hope.