For years, Israeli politics have been frozen under the same two leaders, one now aged 77 and the other 82.
Now, in the space of little over a week, there has been a sudden thaw.
The 82-year-old has lost his leadership of the Labour Party; the 77-year-old is abandoning Likud, which he assembled back in 1973, and founding a new party altogether.
The second intifada has proved bloody for both sides
The 82-year-old is Shimon Peres: a man of remarkable grasp and ability, who has been at the centre of events in Israel for much of its existence.
In recent years, he has given Labour's support to Likud.
Ariel Sharon, who at 77 can look back on a roller-coaster career of risk and confrontation, realised his opponents within Likud would not let him make the concessions to the Palestinians and to US pressure which he now believes are necessary.
Measured alongside Palestinian hopes, his concessions of territory on the West Bank will be small, and certainly will not include sharing Jerusalem.
Yet by Likud's standards, they will be even more divisive than Mr Sharon's decision to evacuate Jewish settlements in Gaza and the northern West Bank in August.
Knowing he could not win over the hardliners in his party, Mr Sharon decided to break away and form a new group containing only his supporters.
Shimon Peres may well leave Labour and join him.
Ariel Sharon came to power with a hawkish reputation
He unexpectedly lost the party leadership last week to the charismatic Amir Peretz, who plans an altogether different approach to Israeli politics.
Mr Peretz, who was born in Morocco, is the leader of Israel's trade union federation.
Instead of concentrating on the divide between Jews and Palestinians, he wants to combat poverty and social deprivation within Israel itself.
In a country which has been obsessed ever since 1967 with its boundaries, this would represent an entirely new start.
All the evidence shows that there is a longing among most ordinary Israelis for an agreement about the future of the country which will bring about lasting peace.
But the central question has always been, peace on what terms?
Under Ehud Barak, in 1999 and 2000, there was an effort to reach out and offer a negotiated peace which seemed to most Israelis to be extremely generous, if not dangerously foolhardy.
Yet even these terms were not enough for Yasser Arafat, the Palestinian leader, to accept and be sure of keeping his job.
The gap proved too wide.
Mr Sharon represents a completely different strategy: he now accepts that a Palestinian state should exist, but he wants to deal with the Palestinians from a position of overwhelming strength.
As a result of deliberately targeting and killing the leaders of more extreme movements such as Hamas, Mr Sharon and his colleagues feel they are effectively defeating Palestinian armed resistance.
And although large numbers of Likud supporters regard Mr Sharon as a sell-out for handing back some settlements, he has encouraged the growth of settlements elsewhere, and will eventually hand back as little territory as he can when the time comes.
Shimon Peres has moved away from his own party
For Palestinians, he has a dark past.
After forcing through Israel's invasion of Lebanon in 1982, he was linked with the process which resulted in the massacre of Palestinians in Sabra and Shatila in 1982 by Christian militiamen.
An Israeli judicial commission recommended that he should never be given high office again.
His decision in September 2000 to visit the area round al-Aqsa mosque in Jerusalem, which the Israelis call Temple Mount and Muslims call Haram al-Sharif, partly triggered the second intifada and destroyed the Oslo Peace Process.
For nearly 40 years, the aftermath of the huge victory won by the Israeli army and air force in 1967 has bedevilled Israel and its politics.
Before, Israel was a small, left-leaning state, much threatened by its neighbours, and had the emotional support of large numbers of people in the West.
The capture of so much territory changed all that.
Shuffling the deck
In June 1967, the elderly David Ben-Gurion, who had been the first prime minister of Israel, was flown over the old city of Jerusalem and the captured territory of the West Bank in a helicopter by General Moshe Dayan, and shown the extent of the victory.
When they landed, Ben-Gurion gripped Dayan by the arm and told him that most of the territory should be handed back at once.
It was, he said, the only way to ensure peace.
Scarcely anyone else in Israel saw it that way, and there has been no peace since.
The old, more idealistic politics were finished.
Now, four decades later, we have a new political alignment.
The right in Israel, headed by Likud, will fight to keep as much of that territory as possible.
The centre, under Mr Sharon and with Shimon Peres' support, will try to achieve peace by handing back a certain amount of the territory.
And the Labour Party, under Amir Peretz, will concentrate on obtaining social justice within Israel itself.
The safe option has always been to assume that no peace deal can succeed between Israel and the Palestinians.
Maybe it still is; but even if most of the players are still the same, at least the cards are being shuffled now.
A new deal is in prospect.
Do you agree with John Simpson's views? What effect will Ariel Sharon's move have on Israeli-Palestinian relations and peace in the region?