Later, Israel strengthened its numbers -- and viability -- by encouraging massive Jewish immigration from neighboring countries in the Middle East in the 1950s, and in the 1990s again by flinging its doors wide open to hundreds of thousands of Jews and their relatives from the former Soviet Union. To this day, anyone who can prove that their grandmother or grandfather was Jewish is welcomed into Zion -- a sign of Israel's desperate need to stay ahead in the race against Arab fertility and a sore point with Orthodox Jews, who insist Jewishness can only be transmitted by a Jewish mother or acquired through conversion.

Goldscheider thinks that talk of a demographic threat to Israel is irresponsible hysteria. He points out that the proportion of Arabs in sovereign Israel has remained relatively constant at about 20 percent since the 1970s, despite their greater natural increase rates, thanks to Jewish immigration.

When immigration flagged in the late 1950s, David Ben-Gurion, Israel's first prime minister, began to talk about "internal immigration," urging people to have more babies. "The thinking was, 'We'll outbreed them,'" said Goldscheider. (A "Ben-Gurion" prize was introduced to reward the mother of the year but, ironically, the winners were always Muslim Arabs, and the prize was eventually scrapped.)

Numbers are also key to understanding Israel's positions on peace with Palestinians today. Realization of the "right of return," for example, by potentially 3.7 million Palestinians registered as refugees with the United Nations would signal the abrupt end of Israel as a Jewish-dominated state. In addition to being impractical (most of the houses Palestinians deserted in 1948 were destroyed or taken over by Jews), it is seen by both left-wing and right-wing Israelis as an unacceptable demand, simply code for the destruction of Israel.

On the other hand, divesting Israel of the territories it gained in the 1967 Six Day War, where roughly 3 million Palestinians live, is seen as a priority by part of the Israeli public. The need to get rid of territory on which Arabs live so that Israel could remain a Jewish-dominated, democratic state was one of the underlying issues driving left-wing Israelis like Shimon Peres and Yossi Beilin to draft and sign the Oslo Accords in 1993. "The point was: Give back territory to save Israel from demography," said Sari Nusseibeh, one of the chief Palestinian negotiators at the time and a moderate intellectual who was recently made Yasser Arafat's diplomatic representative in East Jerusalem.

But for Israeli right-wingers, territory has always been more important than democracy in the competing list of Israeli ambitions. (Nahum Barnea, a veteran Israeli columnist, sums up the differences between the two major Israeli political factions pithily: "Likud is geographic, while Labor is demographic.")

"People on the right usually evade the issue [of Arab numerical superiority], say the statistics are wrong or entertain Zeevi-like fantasies and want to kick Arabs out," said political philosopher Margalit, referring to Rechavam Zeevi, the far-right minister who was assassinated this fall. Influenced by demographic projections like Soffer's, Zeevi proposed to expel or "transfer" Palestinians from the West Bank and Gaza to neighboring Arab states. Other right-wingers, repelled by the ethnic cleansing connotations of the transfer solution, believe in hanging onto Greater Israel by increasing Jewish settlements in the territories and granting non-Jews limited rights. This is where the idea of autonomy within an Israeli framework came from, or in today's terms, the idea of an emasculated "Palestinian state" whose borders, roads and economic life would be controlled by Israel. It is the scenario preferred by current Israeli Prime Minister Ariel Sharon and, basically, a continuation of the status quo.

"It doesn't matter how many people you rule over. France colonized countries larger than itself. You just send more soldiers to control the colonized populations," said Goldschieder. "Whether you occupy 3, 4 or 5 million Arabs is a security issue, not a political problem, as long as they don't have political rights," concurred Margalit.

But for Soffer and many other Israelis, if Israeli Jews start lording it over a population significantly larger than their own, the situation will smack of apartheid: "This is a South Africa situation with a minority of whites controlling others," he said, apparently more worried by the negative parallels international public opinion might draw than mindful of the moral argument against abusing people's rights, regardless of their numbers. "Voting rights is not the only thing that matters. We will be flooded by others. We already have a hard time being both Jewish and democratic. I cannot say that we have solved this problem yet."

Israeli Arabs and Palestinians are already subject to various forms of apartheid -- on the roads, at checkpoints and in the job market. But Soffer fears that pent-up frustration against state discrimination and growing Palestinian nationalism among Israel's Arab minority will express itself in the future in a large unified voting bloc that will undermine Israel's political stability. On war-and-peace issues, some of the 11 Israeli-Arab representatives in the Knesset already have begun showing more solidarity with their Palestinian brothers than loyalty toward the Jewish state. (Azmi Bishara, an Arab member of the Knesset, is currently on trial for calling this year for the continuation of the armed intifada against Israel at a meeting attended by members of Hezbollah, the Lebanese Islamic guerrilla group and one of Israel's sworn enemies.) In another few years, as the representation of Israeli Arabs grows, "they will be able to decide whether the state of Israel should be a Jewish-Zionist state or whether it should turn into a state of all its citizens," warned Soffer in his study.

Soffer also predicts that the demographic boom will turn the security situation into an even bigger nightmare than it is now. Increased numbers of Palestinians living in abject poverty in the West Bank and Gaza will feed radical movements and multiply Palestinian attempts to sneak into Israel to work or commit violent acts, he warns. If Gaza's population doubles in 20 years as it is expected to, while its already overburdened infrastructure continues to collapse, "then one has to expect a decline in the standards of living and despondency. Such an embittered population is dangerous and it is reasonable to assume it will turn to extremist measures, from terror to holy war," wrote Soffer in his latest study. (Palestinian population growth is already a problem for the Palestinian Authority, whose limited resources, corruption and inefficiency prevent it from addressing society's growing needs, thereby opening a breach for Islamic charities run by radical groups like Hamas.)

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