Hope. For a moment, it seemed as though Defense Minister Ehud Barak had found the formula for fighting an enemy armed with rockets, striking at it hard and bringing quiet to Sderot. We so badly wanted to hope that the replacement of the failed defense leadership from the Second Lebanon War, Barak's record as a watch tinkerer and crafty military planner, and the training and re-equipping of the Israel Defense Forces over the past year would result in something new and different. And then indeed it happened: Saturday's air strike gave Israelis a sweet moment of nostalgia for the heroic tales of earlier generations.

But it was an illusion. The Cast Lead got stuck in the throat, just like all previous operations of its type. The war in Gaza is starting to resemble the past confrontations in Lebanon with the Palestine Liberation Organization and Hezbollah. It's hard to stop after carrying out a hard-hitting reprisal action. Israel believes that a little more pressure will prompt the enemy to surrender, but is hesitant to pay the price that would be exacted by a ground operation, and does not want to be dragged into a reoccupation of Gaza.

The Israel Air Force, which has already hit all its designated targets, is now trying to hit "launching areas" at the very moment Hamas takes out those rockets it stored up and hid during the period of calm and attempts to bring new parts of Israel into the line of fire. The result is ongoing attrition, in anticipation of either international intervention or a "tie-breaker" move that would result in the enemy's collapse. As long as the public believes that Barak still has such a move up his sleeve, it will support the war's continuation. The only question is which will hold out longer - Hamas or Israeli public support.

Olmert. From the prime minister's perspective, as of yesterday, everything was going according to the plan presented to the cabinet at the outset, aside from two surprises: Hamas was hurt worse than expected, and the Israeli home front was hurt less. There's no reason to stop, or to pressure ourselves, before the goals are achieved. Ehud Olmert decided that the war would be run in accordance with a "success strategy" and not an "exit strategy," and that he would handle all the diplomatic contacts. As of yesterday, he was still waiting for a good proposal from the key international players. Until it is forthcoming, the fighting will continue.

Livni. During this war, the foreign minister is playing a wholly different role than in the Second Lebanon War. Back then, Tzipi Livni acted as a moderating force, opposed to escalation, searching for "exit opportunities" and trying to push Olmert in the direction of diplomacy. This time, Livni situated herself in a difficult position for any foreign minister - to the right of the defense minister. This is what happens when an election is on the horizon. She pushed for Israel to go to war against Hamas, and was very pleased with the achievements of the operation's first days, when Israel showed the world that the master of the house had had enough.

Yesterday, Livni traveled to Paris for a few hours - not to hold negotiations for a diplomatic accord, but to explain Israel's position to the French. She is wary of an agreement that would grant legitimacy to Hamas, and would like to see the war conclude with "deterrence": Israel will keep on attacking until Hamas stops shooting. Then we'll know that deterrence has been achieved, and if they resume attacking, we'll strike at them again. In this part of the world, there are no perfect solutions.

Melancholy thought No. 1. The conflict between Israel and the Arabs is beginning to resemble the wars we studied in history class, the Hundred Years' War and the Thirty Years' War and World Wars I and II. In those conflicts, too, the fighting was not continuous; instead there were outbreaks of concerted violence punctuating periods of calm. So it is with us: Each time the operation has a new name, the objectives change, as does the enemy's identity, but the principle remains the same - one side sees an opportunity to change the status quo to its benefit, and initiates another round of violence. Sometimes it works, as it did for Egypt in 1973. Sometimes, you end up back where you started, as in Lebanon in 2006. And sometimes it turns out to be a bloody and painful own goal (as it's called in soccer), as happened to Egypt in 1967, to Israel in 1982 and to the Palestinians in 2000.

The deal. If the war ends in a draw, as expected, and Israel refrains from reoccupying Gaza, Hamas will gain diplomatic recognition. No matter what you call it - international mediation, a combination of Palestinian President Mahmoud Abbas and his people in Gaza or even "calm plus," Hamas will obtain legitimacy. After three years of some success in isolating Hamas among the international community, Israel is currently searching for mediators who have the phone numbers of Khaled Meshal, the organization's political leader in Damascus, and Mahmoud Zahar, a Hamas co-founder. The Foreign Ministry, which took pride in the quick formulation of an "exit strategy" during the last war, did not properly prepare this time. While the air force was gathering intelligence about targets, the diplomats were not preparing drafts for a cease-fire or building an array of potential mediators for an emergency. This was evident in the chaotic response to the French cease-fire proposal.

Bibi. Benjamin Netanyahu appears to be the war's big loser. His rise in the polls was already stalling, and this week he was left outside the decision-making circle and resumed his old post as an English-speaking talking head on television, while his rivals were busy overseeing the military campaign. This is an illusion, of course. If the operation is successful, Netanyahu will say it's because they listened to his advice. If the operation falls short, Bibi will say that he would have done a better job of it. In the CNN studios, unlike the cabinet room and the chief of staff's headquarters, it's hard to make fateful mistakes. This puts Netanyahu in what will ultimately be a near-certain win-win situation. Unless, of course, Barak manages to bring Gilad Shalit home, to completely crush Hamas in one week, or to pull off some other magic trick.

Melancholy thought no. 2. What has changed since the reprisal operations of the 1950s? Then, Moshe Dayan said, "It was in our power to set a high price for our blood, a price too high for the Arab community, the Arab army, or the Arab governments to think it worth paying." Israel is following the same logic today. The main difference is that today the Arab side has a steadily growing deterrent capability of its own - rocket fire on the Israeli home front - that somewhat balances out the IDF's aerial superiority. Israel showed Hamas that it's not afraid to bomb Gaza, but the rules of the game have changed on the other side, too: Before the war, they fired at Sderot and Ashkelon; now they're firing at Ashdod and Be'er Sheva, too.

Preserving Hamas. The Gaza war has been the first test of the strategy formulated by the IDF after the Second Lebanon War, which holds that if the government is one of terror, then its institutions are to be destroyed. The idea was to threaten the destruction of Lebanon if Hezbollah were to attack Israel again. But its first implementation was in Gaza, where institutions such as the education ministry were destroyed, because it is headed by Hamas. Gabi Ashkenazi's IDF spearheaded the view that Gaza is a Hamas state, while the political echelon was hesitant to call it that.

The experts propounding this strategy recommend that it not be taken too far, that Hamas should still be preserved, so that Gaza doesn't fall apart into a rule of militias and gangs who would be impossible to deter and would continue to launch rockets at Israel. Hit Hamas hard, but don't destroy it completely. Israel needs a "diplomatic address" in Gaza as a basis for armed coexistence. As with Hezbollah in Lebanon.

A revolutionary proposal. Here's an idea that could contribute to world peace: Shorten the length of the U.S. presidential election campaign and the transition period between administrations. These twilight times in Washington invite all kinds of trouble on other continents. The war in Georgia, the terror attack in Mumbai, the Gaza war - all have occurred against the backdrop of a fading Bush administration and the anticipation of its departure. Like fights among kindergartners when the regular teacher is away and the substitute is having a hard time imposing discipline. Maybe the Americans could give up some of the convenience of an orderly change of governments and take a little more responsibility as the guardians of world order?