This week, Alpher discusses whether Operation Protective Edge against Hamas in Gaza is winding down; what the two sides' conditions for a ceasefire are; why Israel doesn't want to remove Hamas from power; what are the alternative strategies that Israel could invoke; whether Hamas' strategic aim is to kill Israelis; and some perspective, looking back and looking forward on Operations Cast Lead in 2009-10, Pillar of Defense in 2012, and now Protective Edge.

Q. Is Operation Protective Edge against Hamas in Gaza winding down?

A. It has entered the stage--by now a "traditional" phase in Israel's wars against terrorist neighbors--in which various regional and international actors try to arrange a ceasefire. Meanwhile it continues with full intensity. By Monday noon, 172 Palestinians had been killed (about one-third of them civilians) and nearly 4,000 wounded (Palestinian and UN figures), and well over 1,000 rockets had been fired at most of Israel.

Q. What are the two sides' conditions for a ceasefire?

A. Israel wants an end to rocket fire and guarantees of some sort that Hamas will no longer be able to procure or produce rockets. Hamas wants Israel and Egypt to open their borders with Gaza and demands that Israel release Palestinian prisoners freed in the Shalit deal several years ago who were rearrested by Israel during the hunt for the three kidnapped yeshiva students.

The two sides' declared conditions are far apart, but that's how negotiations start. Notably, Israel does not wish to see Hamas rule ended in Gaza. And Israel's demand to somehow remove rockets and rocket-making from Gaza, which is ostensibly modeled after the successful international effort of the past year to remove chemical weapons from Syria, is almost certainly a non-starter. In Syria, Bashar Assad knew that in getting rid of his chemical arsenal he was giving himself a free hand to suppress the opposition using every other violent method; in Gaza, the rockets are used against an external rather than internal enemy and they remain, in Gazan eyes, the only deterrent Hamas has to use against Israel.

As for Hamas' demands, note that it is attacking Israel but making demands on Egypt as well--an interesting sign of the times. Its demand regarding re-release of prisoners will only make sense if, against all odds, Israel concludes that the kidnapping-murder of the three yeshiva students was not a Hamas operation.

An additional difficulty regarding a ceasefire is the identity, motivation and capabilities of the mediator. The US and Europe have called for mediation, yet cannot themselves mediate directly because they shun contact with Hamas, a terrorist organization. So they can only work from the sidelines; besides, US Secretary of State John Kerry is also busy trying to save the P5+1 nuclear talks with Iran. This reservation also applies to Quartet envoy Tony Blair, another volunteer prohibited from talking to Hamas. Turkey, Qatar and Egypt can directly contact both Israel and Hamas, but Turkey and Qatar are broadly unacceptable to Israel and to the moderate Arab world.

That leaves Egypt whose leader, President al-Sissi, is grateful to Israel for speaking up for him in Washington and appears broadly content to allow Israel to continue to punish Hamas, which he identifies with his arch-enemy the Muslim Brotherhood. Besides, Egypt reportedly has a condition of its own: the introduction of armed units loyal to moderate Palestinian leader Mahmoud Abbas to police Gaza's border crossings and man its police force instead of Hamas. Earlier this month, as the tit-for-tat armed exchanges between Hamas and the IDF were building up to Protective Edge, Hamas' military leadership rejected precisely these conditions.

Then too, Abbas himself could play a mediatory role. This could enhance his prestige, which is in need of a boost. On the other hand, this would likely reinforce the staying power of his unity government with Hamas, which Netanyahu opposes. An additional irony is that if Hamas is a party to the current Palestinian government, where is Abbas' responsibility for Hamas' behavior? Moreover, Abbas' inclination to blame only Israel for this war and ignore Hamas' deliberate targeting of Israeli civilians hardly qualifies him as a mediator; after all, he is the Palestinian leader who usually condemns Palestinian violence toward Israelis.

Finally, Norway has also reportedly offered to mediate. This is intriguing: the Norwegian government is friendly to Israel but also, as a non-EU member, maintains contact with Hamas.

Q. Why doesn't Israel want to remove Hamas from power? Wouldn't this end the repetitive cycle of bloodletting?

A. There is a political camp in Israel on the far right, represented in the security cabinet by Foreign Minister Lieberman and Economy Minister Bennet, that talks about reoccupying Gaza and removing Hamas. It exercises little influence over policy because it is unable to justify the huge cost in Israeli and Palestinian dead and wounded that would be entailed in conquering the Strip, not to mention the cost of reoccupying more than 1.5 million people and providing for their needs for an indefinite period of time.

The "conquer Gaza" camp also ignores the fact that, post-reoccupation, the opposition to renewed Israeli rule in Gaza would be a more extreme organization than Hamas, thereby making it difficult to withdraw. The PLO's Abbas would never agree to be reinstalled in power by Israeli bayonets. The international community would attack the Israeli occupation. True, rocket fire against Israel would cease; but, sad to say, Israel would pay an even higher price than that entailed in a week or two of conflict every year or two.

Here we encounter two more paradoxes. First is the paradox of Israel attacking Hamas military and political targets while simultaneously allowing the daily delivery to Gaza of fuel and food to avoid humanitarian catastrophe. The second is the paradox of Israel signaling to Hamas that it wants it to survive this war and remain in power, thereby offering it a regime insurance policy and indirectly encouraging it to continue fighting.

Q. What are the alternative strategies that Israel could invoke?

A. The current strategy, if one can call it a strategy, is dubbed "mowing the lawn". If Hamas won't recognize Israel or talk to it, insists periodically on attacking it, and is unable fully to control even more extremist Islamist groups in the Strip, then Israel will periodically attrite and decimate all these armed groups until they agree to a ceasefire. But the ceasefire will be constantly violated by sporadic rocket and mortar fire and won't last for more than a year or two, thereby generating the need for Israel to repeat the operation.

Leaving aside the suitability of the mowing the lawn metaphor (lawns, after all, are for pleasure), it really tells us that Israel (including past governments since the 2005 unilateral withdrawal from Gaza) does not have a viable strategy for dealing with Hamas in Gaza. I have long been an advocate of Israel abandoning the Quartet conditions--recognizing Israel, accepting existing agreements, abandoning violence--and offering to talk with Hamas without preconditions and to open the Israel-Gaza crossing points to much-enlarged trade and movement of people, while maintaining the naval blockade. This would recognize Hamas as an enemy with whom the conflict has to be managed directly, without mediation. But I realize that Hamas would almost certainly not agree to talk with us and that, under current conditions, an Israeli offer of this nature would alienate both Abbas in Ramallah and al-Sissi in Cairo. Similar ideas are once again being discussed in Israel, including easing the naval blockade and allowing specific European countries that can closely monitor their ships' cargo to sail to Gaza.

Additional contingent strategies currently under consideration include occupying only select parts of Gaza, such as the northern end of the Strip which is lightly populated but serves as a launching site for a large proportion of rockets fired into Israel. This is where on Sunday the IDF called upon residents to flee in anticipation of an Israeli attack on rocket-launching sites.

In discussing all of these possible strategies, Israel enjoys two notable advantages. One is the presence in Egypt of a regime that loathes Hamas and is prepared to coordinate security policy with Israel. The other is the Iron Dome rocket-interception system, which with its 90 percent success rate now guarantees most Israelis a large measure of security in which to go about their daily lives "under fire". In the long run, it may emerge that Iron Dome constitutes something of a strategic revolution in the prosecution of asymmetric warfare with terrorists.

But this points to another area where, ironically, Israel needs new strategic thinking. When no Israelis are dead after a week of conflict but the Gazan casualty rate continues to rise, including the inevitable civilian casualties entailed in attacking an enemy that is embedded among civilians, the world increasingly sees and empathizes with the Gazan side of the conflict. This in turn generates growing international pressure on Israel, but perversely not on Hamas, to cease fire without achieving its war aims. And while those war aims ostensibly can be achieved if there is more time, in fact neither time nor success is a certainty.

This is where the "inevitable atrocity" paradox enters the picture. If Israel inadvertently and, despite its precautions, kills a large number of Palestinian civilians in one spectacular bombing or, almost inevitably, in the course of a major ground offensive, it will come under heavy international pressure to end its Gaza campaign. On the other side, if Hamas finally succeeds in killing a large number of Israeli civilians, thereby fulfilling its conscious war aim, it might itself "declare victory" and a ceasefire. The more time goes by, the more likely it is that one of these grisly war-ending scenarios will in fact take place.

Q. Is that Hamas' strategic aim: to kill Israelis?

A. That is certainly Hamas' tactical aim. Its strategy in prosecuting this war appears to be the survival of a bankrupt and virtually friendless (except for its Qatar/al-Jazeera friends) Islamist regime by rallying popular support and declaring victory over the Zionists. This would be accomplished either by virtue of an atrocity visited upon Israelis or simply because Hamas' leaders emerge relatively intact from their huge network of bunkers under Gaza city once the war is over. Given Israel's aversion to removing Hamas from power, this seems to the leadership like a win-win scenario: Hamas declaratively "wins" even when it loses.

Hamas' management of the war is rendered extremely complicated by virtue of the movement's fragmentation. Inside the Strip the militant military leadership, which even opposes aspects of the dysfunctional Palestinian unity government, is calling the shots--not the political leadership. It was the military leadership of Hamas that violated a ceasefire mediated by the Egyptians with the political leadership just before Operation Protective Edge was launched a week ago, thereby precipitating the current war. Both leaderships, needless to say, have disappeared underground, leaving the Gaza citizenry to bear the brunt of war.

Then there is the Hamas external leadership in Qatar and, lately, Turkey, whose declarations are not necessarily coordinated with Gaza City. Nor is it clear to what extent any of these leaders can give orders to Islamic Jihad and other extremist jihadis firing rockets from the Strip at Israel. Thus it is entirely possible that one branch of Gazan militants will accept a ceasefire while others will reject it.

Q. Operations Cast Lead in 2009-10, Pillar of Defense in 2012, and now Protective Edge: can you give us some perspective, looking back and looking forward?

A. Some researchers actually count a total of nine Israeli operations against Hamas in Gaza over the past 12 years. All the operations encountered the strategic constraints outlined above. While each operation was triggered by a specific incident, it would be a mistake to link Protective Edge directly to the kidnapping and murder and resultant Israeli roundup of Hamas activists in the southern West Bank. Protective Edge was inevitable: witness the months of rocket-fire provocations and the many Hamas preparations, including highly-sophisticated tunnels intended to facilitate a massacre in an Israeli village bordering the Strip.

In present day terms, Hamas can be seen as the "moderate" end of an Islamist continuum whose other extremity is ISIS with its crucifixions and horrific atrocities. That Israel now seemingly has an interest in Hamas remaining in charge in Gaza is a very sad sign of our times in the Middle East. But make no mistake: Israel and Hamas cannot peacefully coexist over the long term.

Last Thursday, my wife and I went for a morning swim in the neighborhood pool. Suddenly, there were sirens warning that rockets could fall on us within 90 seconds. We rushed for cover, looked outside, and witnessed the spectacular Iron Dome interception. Then back into the pool. For many Israelis, this is a bizarre war in which normalcy is the best way to fight back. Yet Israel cannot forever coexist this way with Hamas in the south and Hezbollah and possibly ISIS on our northern borders, all seeking our total destruction. The advocates of an all-out Israeli campaign to eliminate Hamas in Gaza display a kind of correct absolutist logic, even if their strategic acumen and their grasp of Israel's regional reality are warped.

All the more reason why Israel should jump at the opportunity to reach some sort of two-state solution with Abbas. The current Israeli government not only lacks a viable strategy for Hamas in Gaza; it also lacks one for maintaining Israel as a Jewish and democratic state, meaning reaching some sort of two-state solution. Such a strategy just might enable us to really collaborate with the more moderate Arab states in dealing militarily with the jihadist threat. It will certainly make it easier internationally to conduct wars like this.

That Netanyahu shuns this option and buries us deeper and deeper in a single-state reality with his settlement-building is a reflection of his ideological hang-ups and lack of political courage. This is particularly troubling at a time when we actually see him at his best: exercising the utmost caution and restraint in the Gaza campaign and, refreshingly, speaking to fellow Israelis in moderation, without bombast and incitement.