It is too late for Israel to solve its demographic problem and avoid becoming a bi-national Jewish-Arab state by agreeing to a Palestinian state in the West Bank and Gaza. To remain a Jewish state, it will also have to surrender big chunks of its territory within the Green Line - its pre-1967 borders.
That is the stark conclusion not only of Israeli left-wingers. It is also the basis of the policy of the hawkish Foreign Secretary Avigdor Lieberman and, it seems, of Yair Lapid, the celebrity journalist who is entering politics as a centrist determined to achieve an "efficient" divorce between Jew and Arab.
The underlying reason is that, over the past 60 years, the Arabs living in Israel proper (including annexed East Jerusalem but not the West Bank) have increased from 11 to 21 per cent of the population. Jewish immigration, however large, has been trumped by Muslim Arab fertility.
The high Muslim birth-rate has admittedly fallen in spurts over the past 40 years, most recently because of the settlement of the nomadic Bedouin in Negev towns. But, at 3.8 children per woman, it remains higher than that of the Jewish population (3.0) – and of the Arabs in nearby Egypt, Syria or Jordan. Demographers such as the eminent Hebrew University professor, Sergio Della Pergola (whose data I have used here), warn that, even if the Muslim birth-rate were to fall immediately to that of the Jews, the proportion of Arabs would continue rising for many years because they are much younger. At the same time, all the large sources of potential Jewish immigration have been exhausted.
Already, Arabs account for more than a quarter of all Israelis younger than 25. Crucially, all the large sources of potential Jewish immigration have now been exhausted – and Israel has been attracting a growing number of residents such as East Asian guest workers who are neither Jewish nor Arab. Although long-term fertility predictions are notoriously unreliable, the proportion of Jews in Israel's current borders and in the West Bank settlements is unlikely to be much more than two-thirds by the end of the next decade.
These proportions are way above the threshold at which the demands of an ethnic minority for power sharing become difficult to suppress or deny. Turks made up only 20 per cent of the Cyprus population before the enforced partition of 1974. Catholics in Northern Ireland were only one-third of the population at the start of the "troubles" in 1968. The Protestants' opposition to power-sharing was ultimately doomed by their failure 45 years earlier to hand over to the Irish state the Catholic areas in the south and west of the province and in Londonderry west of the Foyle. The analogy with Israel is striking.
Although Israeli Arabs have full voting rights, their situation is similar to that of the pre-1968 Ulster Catholics, or to the Jewish population of Poland in the decades leading up to the Second World War. The mainstream ethnic majority parties do little to appeal to them - so they vote for parties that are shunned and can never join a coalition government.
For this state of affairs, it would be unfair to blame either Jews or Arabs. Both could have done more: the Israeli government to improve Arab employment prospects and housing, the Arabs to embrace modernity and wiser, more pragmatic leaders. But, after 64 years of Arab-Israeli warfare, it is a tribute to the tolerance and good sense of both communities that there has been so little internal violence.
However, the younger generation of Israeli Arabs are less quiescent than their parents and becoming ever more assertive of their national minority rights. At the same time, as the demographic pressure mounts, even the Israeli judiciary, traditionally the guardian of Arab minority rights, has recently felt impelled to stop them bringing in spouses from the territories.
There is one solution that seems almost too neat to be true, particularly as it would solve another intractable problem at the same time. The rest of the world, including the US and the EU, have demanded that Israel give up approximately 22 per cent of mandatory Palestine to an Arab state, by withdrawing to the Green Line, while accepting the principle of limited territorial swaps around it. That would let Israel keep some areas in the West Bank with large Jewish settlements. But the Palestinians understandably refuse to accept in exchange the barren areas on offer in the north-western Negev.
If, instead, Israel agreed to exchange the Israeli Arab towns, villages and neighbourhoods that are close to, but within, its currently established borders, it would kill two birds with one stone.
The most controversial such area is East Jerusalem with some 280,000 Arabs. Although nationalist politicians talk about Israel's eternal united capital, the truth is that few Israeli Jews ever visit or have any interest in Jerusalem's Arab neighbourhoods outside the Old City.
That point applies with even greater force to the "Triangle" of Arab towns in the centre of the country running from Uhm El-Fahm, the second largest Israeli Arab town, with a militant Islamic leadership, situated near Megiddo in the north, to Tira and Kafr Qassam near Petach Tikvah.
More than 300,000 Arabs live in this area. In the 1948 war, it was never conquered by Israel; nor did the Arab middle-class living there flee. But at the Rhodes armistice talks in 1949, it was ceded without their consent by Jordan because Israel insisted on widening its narrow waist. The Rhodes agreement stated that the Armistice was temporary and determined purely by military considerations. But, today, with sophisticated military technology and a demilitarised Palestinian state on offer, the width of Israel's waist should no longer be a security issue. Finally, there are a few Bedouin towns in the Northern Negev close to the Green Line which could also be swapped.
The combined effect of these swaps would be to reduce the Arab minority from 21 per cent to about 12 per cent, a more manageable number, concentrated in the western and central Galilee, on which Israel could focus greater efforts to integrate.
But there is one serious obstacle. According to the opinion polls, a large majority of Arabs in the Triangle and northern Negev do not want to join a Palestinian state. Israel, it might be thought, should rejoice at such polls, rush to hold a plebiscite and publicise its results globally. They would vindicate what the Zionist movement has been saying for the past 100 years, namely that, for the silent majority of Palestinian Arabs, nationalist or pan-Islamic ambitions are less important than the higher living standards and political freedoms offered by Jewish migration to Palestine.
But, good PR aside, there are good reasons for refusing to give a veto to the Arabs living in the areas to be ceded. First, a plebiscite could not bind future generations of Israeli Arabs who, if a Palestinian state achieved a modicum of political freedom and economic prosperity, might well demand secession. And a "no" vote in a plebiscite today would be swelled by militant Islamists who want the two-state solution to fail as they see greater potential for undermining Israel from within.
Second, the Triangle Arabs are the most sophisticated of the Israeli Arabs with a much more intimate understanding of Israel, the workings of modern capitalism and a liberal democracy than their cousins across the Green Line. They would form a stabilising force in a newly formed Palestinian state and be a bridge for trade and peace with Israel, a matter in which Israel, too, has a legitimate interest. The Palestinian state needs both the Triangle and the East Jerusalem Arabs - and they in turn should accept their duty to help build the nation they say they are part of.
Third, there is no obligation in international law on a state to continue to exercise sovereignty over a territory once it no longer wishes to do so. A nation (or nation state) is a daily plebiscite, as French philosopher Ernest Renan said. And, as some Conservative MPs have noted, if Scotland can withdraw from its union with England, England can withdraw from its union with Scotland.
The same applies to Israel, which, having inherited the Ottoman patterns of ethno-religious settlement, has become in effect a union between Jewish towns and villages - and disaffected Arab ones.
Some contend that ceding a territory could not justify, under international law, stripping the Arabs in it of their Israeli citizenship. That is wrong. One automatically leads to the other, as UN General Assembly Resolution 55/153 of 2001 makes clear, unless the withdrawing state gives the residents of the ceded area an option to retain citizenship. But it has no obligation to do so. In any case, such Arabs need not be stripped of their Israeli citizenship. They would merely be unable to bequeath it to their children, while their voting rights would become exercisable in Palestinian, not Israeli, elections.
Alternatively, Israel's long-mooted plans for a new constitution, which the Israeli Arabs themselves have been demanding, could be implemented by stripping everyone, Jew and Arab, of his old citizenship in exchange for a new one in either Reconstituted Israel - or Arab Palestine.
Moreover, any Israeli Arabs particularly fearful about joining the Palestinian state could move home elsewhere within Israel before the cut-off date. The indications are, however, that few would do so - and their numbers would be further reduced if Israel offered a generous "dowry" to every Arab family living in the areas to be ceded.
A maximally "efficient" border in separating Jew and Arab would be long and convoluted. Jewish "fingers" would stretch deep into the West Bank while two or three bridges or tunnels across the Trans-Israel Highway would connect the Palestinian state to its western Arab enclaves. If terrorist incursions resumed, the separation barrier might require extension along the new border at a $2 million per kilometre cost.
But the expense of guarding such sinuous borders would be tiny compared with the costs of no Palestinian state at all within agreed borders. Political maps do not have to follow the modernist architectural aesthetic of straight clean lines.
Some argue it would be racist to re-partition Palestine into two ethnic states with borders artfully drawn to ensure that as few Arabs as possible are in the Jewish state - and vice versa. But that was precisely the principle behind the complex UN partition plan for Palestine in 1947, and behind many other partitions before and since. Even today, the cultural, linguistic, religious and political gap between Arabs and Jews remains much wider than that between, say, Irish Catholics and Protestants, Czechs and Slovaks, Walloons and Flemish, Serbs and Croats, Hindus and Muslims or Greeks and Turks. The bi-national state, even if desirable in principle, will have to await the next century.
Certainly those doveish Israelis who, like the novelist AB Yehoshua in London recently, warn of the dangers of a bi-national state, should swallow their distaste for Lieberman and the pragmatic centre-right and support them on this fundamental issue.