In southwest Israel, at the border of Egypt and the Gaza Strip, there is a small crossing station not far from a kibbutz named Kerem Shalom. A guard tower looms over the flat, scrubby buffer zone. Gaza never extends more than seven miles wide, and the guards in the tower can see the Mediterranean Sea, to the north. The main street in Gaza, Salah El-Deen Road, runs along the entire twenty-five-mile span of the territory, and on a clear night the guards can watch a car make the slow journey from the ruins of the Yasir Arafat International Airport, near the Egyptian border, toward the lights of Gaza City, on the Strip’s northeastern side. Observation balloons hover just outside Gaza, and pilotless drones freely cross its airspace. Israeli patrols tightly enforce a three-mile limit in the Mediterranean and fire on boats that approach the line. Between the sea and the security fence that surrounds the hundred and forty square miles of Gaza live a million and a half Palestinians.

Every opportunity for peace in the Middle East has been led to slaughter, and at this isolated desert crossing, on June 25, 2006, another moment of promise culminated in bloodshed. The year had begun with tumult. That January, Hamas, which the U.S. government considers a terrorist group, won Palestine’s parliamentary elections, defeating the more moderate Fatah Party. Both parties sent armed partisans into the streets, and Gaza verged on civil war. Then, on June 9th, a tentative truce between Hamas and Israel ended after an explosion on a beach near Gaza City, apparently caused by an Israeli artillery shell, killed seven members of a Palestinian family, who were picnicking. (The Israelis deny responsibility.) Hamas fired fifteen rockets into Israel the next day. The Israelis then launched air strikes into Gaza for several days, killing eight militants and fourteen civilians, including five children.

Amid this strife, Mahmoud Abbas—the head of Fatah, and the President of the Palestinian Authority, the governing body established by the Oslo peace accords of 1993—put forward a bold idea. The people of Palestine, he declared, should be given the chance to vote on a referendum for a two-state solution to its conflict with Israel. Perhaps it was a cynical political maneuver, as the leaders of Hamas believed. The fundamental platform of Hamas was its refusal to accept Israel’s right to exist, yet polls showed that Palestinians overwhelmingly supported the concept of two states. A referendum would be not only a rebuke to Hamas; it also would be a signal to Israel—and to the rest of the world—that Palestinians were determined to make peace. Abbas set the referendum for July.

Just before dawn on June 25th, eight Palestinian commandos crawled out of a tunnel into a grove of trees in Kerem Shalom. A new moon was in the sky, making it the darkest night of the month. With mortar fire and anti-tank missiles providing cover, the commandos, some of them disguised in Israeli military uniforms, split into three teams. One team attacked an empty armored personnel carrier, which had been parked at the crossing as a decoy. Another team hit the observation tower. The two Israelis in the tower were injured, but not before they killed two of the attackers.

The third team shot a rocket-propelled grenade into a Merkava tank that was parked on a berm facing the security fence. The explosion shook the tank; then its rear hatch opened and three soldiers tried to flee. Two of them were shot and killed, but a third, lightly wounded, was captured. The attackers raced back into Gaza with their prize: a lanky teen-ager named Gilad Shalit.

Within days, the Israel Defense Forces, or I.D.F., had bombed the only power station in Gaza, cutting off electricity to tens of thousands of people. The borders were shut down as Israeli troops searched residential areas for Shalit, rounding up males older than sixteen. On June 29th, Israeli officials arrested sixty-four senior Palestinian officials, including a third of the Palestinian cabinet and twenty members of parliament. At least four hundred Gazans were killed over the next several months, including eighty-eight children. The Israelis lost six soldiers and four civilians. Israeli authorities promised not to leave the Strip until they recovered Shalit, but by November he still had not been found, and both sides declared a ceasefire. Nothing had been resolved. Another explosion was sure to come. Certainly, no one was talking about peace initiatives any longer, and that may well have been the goal of those who captured Shalit.

From the Israeli perspective, at least, the Gaza problem was supposed to have been solved in August, 2005, when Ariel Sharon, then the Prime Minister, closed down the Jewish settlements on the Strip and withdrew Israeli forces. The international community and the Israeli left wing applauded the move. But, almost immediately, mortar and rocket attacks from the Strip multiplied. Five months later, Hamas won its parliament victory. Ari Shavit, a prominent columnist for the Israeli newspaper Haaretz, told me recently in Jerusalem, “We dismantled the settlements, and then we sat back and said, ‘Let’s have a new beginning.’ What we got was rockets and Gilad Shalit. People became very angry, and Shalit becomes an icon of that frustration.”

We were sitting in Restobar, a noisy café in downtown Jerusalem. Nearby, Shalit’s parents and supporters maintain a tent; from this makeshift office, they lobby for Israel to release hundreds of Palestinian prisoners and detainees in exchange for Shalit’s freedom. Shalit had just graduated from high school when he began his compulsory military service. His father, Noam, has described him as “a shy boy with a nervous smile and a studious disposition,” who loved basketball and excelled in physics. Two weeks after Shalit was captured, Hezbollah abducted two other Israeli soldiers, sparking thirty-four days of war in South Lebanon. In that instance, the captured soldiers were already dead; after the war, their remains were returned to Israel, in exchange for five Lebanese prisoners and the remains of hundreds of fighters. But Shalit is presumed to be alive, and his plight has driven Israel slightly mad. There are demonstrations, bumper stickers, and petition drives demanding his freedom. On Web sites and in newspapers, counters chronicle how long Shalit has been in captivity. “Israel is obsessed with Gilad Shalit in a way that no other nation in history has been obsessed with a prisoner of war,” Shavit said.

Gaza is a place that Israel wishes it could ignore: the territory has long had the highest concentration of poverty, extremism, and hopelessness in the region. Gaza makes a mess of the idealized two-state solution because it is separated from the West Bank, the much larger Palestinian territory, not just physically but also culturally and politically. In 2005, the RAND Corporation proposed integrating a future Palestinian state with a high-speed rail and highway system that would connect the West Bank and Gaza. Former President Jimmy Carter told me that, in 2005, he and Ariel Sharon had agreed to promote a land swap between the Israelis and the Palestinians that would provide a corridor between the two halves of Palestine.

Such potential solutions have been poisoned by the frustration that both Israelis and West Bankers feel toward Gaza. The political distance between the two Palestinian entities has caused many Israelis to start talking of a three-state solution, rather than two. “Hamas in Gaza is a fact of life until further notice,” Yossi Alpher, a political consultant and a former Mossad officer, observed. “All our ideas about dealing with them have failed.” Shavit and other Israeli intellectuals have proposed that the Egyptians deed a portion of the Sinai to Gaza, to make the Strip more viable—“a semi-Dubai,” as Shavit terms it. The Egyptians have expressed no interest. “Egypt’s strategy for Gaza is to make sure it’s Israel’s problem,” Alpher said.

Hamas, which was founded in Gaza during the intifada of 1987, has come to embody the fears that many Israelis hold about the Palestinians. Its charter declares, “There is no solution to the Palestinian problem except by jihad.” The document, which is in many respects absurd and reflects the intellectual isolation and conspiracy-fed atmosphere in Gaza at the time, cites the “Protocols of the Elders of Zion,” the anti-Semitic forgery, and links Zionism to the Freemasons, the Lions Club, and “other spying groups” that aim “to violate consciences, to defeat virtues, and to annihilate Islam.” Part of the paradox of this conflict is that many Palestinians who firmly embrace the two-state solution have voted for Hamas.

In Restobar, Shavit pointed to a spot a few feet away. “In March, 2002, there was a beautiful twenty-five-year-old girl dead on the floor, right there,” he said. A suicide bomber had targeted the café, which was then called Moment. That month, eighty-three Israeli civilians were killed by Palestinians. Jerusalem was in a panic. Shavit was living nearby at the time, and on the night of March 9th he heard the bomb explode.

Running to the café, he saw mutilated bodies scattered on the sidewalk. People had been blown across the street. The dead girl was lying near the doorway. Inside, at the bar, three young men were sitting upright on the stools, but they were all dead. “It was as if they were still drinking their beers,” Shavit recalled. Eleven Israelis died, and more than fifty were injured. Hamas proclaimed it a “brave attack” intended to “avenge the Israeli massacres against our people.”

The Hamas attacks derailed the peace process initiated by the Oslo accords and hardened many Israelis against the Palestinian cause. Photographs of Gazans celebrating the Moment bombing confirmed the dehumanized state of affairs. Gaza became “Hamastan” in the Israeli newspapers. In 2007, after Hamas solidified its control of Gaza, the Israeli government declared Gaza a “hostile entity,” and began enforcing a blockade on a population that was already impoverished, isolated, and traumatized by years of occupation.

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Hamas was not weakened by the blockade. Instead, the collective punishment strengthened its argument that Israel wanted to eliminate the Palestinians. The only thing that Gaza has that Israel wants is Gilad Shalit, but Hamas says that it will not free him until Israel releases fourteen hundred individuals, four hundred and fifty of whom have been convicted of terrorist killings, including the men who planned the Moment bombing.

On June 25, 2007, several days after Hamas took over in Gaza, the captors of Gilad Shalit released an audio recording to prove that he was still alive. “It has been a year since I was captured and my health is deteriorating,” he said. “I am in need of prolonged hospitalization.” He urged the Israeli government to accept Hamas’s demands for his release: “Just as I have a mother and father, the thousands of Palestinian prisoners also have mothers and fathers—and their children must be returned to them.”

Gaza is a sea of children. The average woman there has 5.1 children, one of the highest birth rates in the world. More than half the population is eighteen or younger. “We love to reproduce,” Khalil al-Hayya, a senior Hamas official, told me on a searingly hot July day, as hundreds of young boys in green caps shouted slogans at a Hamas summer camp. Hayya, a former professor of Islamic law, has six children; a seventh was killed by an Israeli bomb.

There is very little for children to do in Gaza. The Israeli blockade includes a ban on toys, so the only playthings available have been smuggled, at a premium, through tunnels from Egypt. Islamists have shut down all the movie theatres. Music is rare, except at weddings. Many of Gaza’s sports facilities have been destroyed by Israeli bombings, including the headquarters for the Palestinian Olympic team. Only one television station broadcasts from Gaza, Al Aqsa—a Hamas-backed channel that gained notice last year for a children’s show featuring a Mickey Mouse-like figure who was stabbed to death by an Israeli interrogator. The mouse was replaced by a talking bee, who died after being unable to cross into Egypt for medical treatment. The rabbit who followed the bee passed away in January, after being struck by shrapnel from an Israeli attack.

The main diversion for children is the beach, and on Fridays, after noon prayers, the shore is massed with families. Unlike the topaz waters off Tel Aviv, here the sea is murky, a consequence of twenty million gallons of raw and partially treated sewage that is dumped offshore every day. The main water-treatment plant is broken, and because of the blockade the spare parts that would fix it are unavailable. Fishermen with nets wade into the surf as kids romp in the stinking waves.

Israeli authorities maintain a list of about three dozen items that they permit into Gaza, but the list is closely kept and subject to change. Almost no construction materials—such as cement, glass, steel, or plastic pipe—have been allowed in, on the ground that such items could be used for building rockets or bunkers. While Hamas rocket builders and bomb-makers can smuggle everything they need through the secret tunnels, international aid organizations have to account for every brick or sack of flour. Operation Cast Lead—a three-week-long Israeli attack on Gaza, which began in December, 2008—has left Gaza in ruins. “Half a year after the conflict, we don’t have a single bag of cement and not a pane of glass,” John Ging, the director of the United Nations Relief and Works Agency for Palestinian refugees, told me in July. (Later that month, Israeli authorities announced that they would allow the U.N.R.W.A. a limited amount of steel and cement. Ging says that that has yet to happen.) Humanitarian supplies that suddenly have been struck from Israel’s list of approved items pile up in large storage warehouses outside the Kerem Shalom crossing, and international aid worth billions of dollars awaits delivery. “For the last two school years, Israeli officials have withheld paper for textbooks because, hypothetically, the paper might be hijacked by Hamas to print seditious materials,” Ging complained. (Paper was finally delivered this fall.) When John Kerry, the chairman of the Senate Foreign Relations Committee, visited Gaza in February of this year, he asked why pasta wasn’t allowed in. Soon, macaroni was passing through the checkpoints, but jam was taken off the list. According to Haaretz, the I.D.F. has calculated that a hundred and six truckloads of humanitarian relief are needed every day to sustain life for a million and a half people. But the number of trucks coming into Gaza has fallen as low as thirty-seven. Israeli government officials have told international aid officials that the aim is “no prosperity, no development, no humanitarian crisis.”

Visitors enter Gaza at its northeastern end, through the Erez Crossing—a high-security, barnlike building that is rarely congested, because scarcely any Palestinians are allowed to exit, and so few foreigners care to visit. In 2004, the first female suicide bomber for Hamas, Reem Riyashi, a twenty-two-year-old mother of two children, blew herself up there, killing four Israelis. Since then, the Israeli staff has largely been replaced by security cameras and remote-controlled gates.

In Gaza, the rocky hills of Jerusalem have been ironed into a sandy plain sparsely adorned with oleander and cactus, as in South Texas. The area near Erez used to be the region’s industrial zone. Until Operation Cast Lead, there were several concrete plants, a flour mill, and an ice-cream factory, but they have all been bombed or bulldozed, and the mixing trucks for the concrete have been knocked over. Houses and mosques and shops lie in rubble; entire neighborhoods have been demolished. Israeli forces concentrated much of their fire, and their wrath, on northeast Gaza. From Erez, one can easily see Sderot, the Israeli town that has suffered the most rocket attacks.