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Is the Egyptian military religious or secular?
Mostly secular. Hosni Mubarak was an officer in the Air Force and has built the military in his own image. Mubarak viewed himself as a bulwark against the Muslim Brotherhood and would not have installed officers whom he suspected of having Islamist sympathies. Most Egypt observers view the Egyptian military as a secular force in Egypt.
That said, the Egyptian military is largely a conscript force, so there are undoubtedly Islamist soldiers scattered among the 470,000 * people in its ranks. The man who assassinated President Anwar Sadat * in 1981 was both a member of the Muslim Brotherhood and a first lieutenant in the army. In the 1990s, Ali Mohammed, a former major in the Egyptian army, helped plan the bombings of the U.S. embassies in Tanzania and Kenya. (Read Andrew McCarthy's skeptical take on the secularism of the Egyptian military.)
What does all this mean for the Israelis?
They're worried. Egypt was the first country in the Middle East to recognize Israel. Mubarak made some efforts to stem the flow of weapons into Palestine and helped maintain the embargo on the Hamas-ruled Gaza Strip. Just a few days ago, Israeli politicians privately expressed doubt that the long-serving dictator could be overthrown by popular protests. But when President Obama urged Mubarak to step aside, pundits across Israel howled, and President Shimon Peres lamented the likely end of Mubarak's reign.
It's too soon to say how Israel will react to the resignation, as Prime Minister Benjamin Netanyahu has forbidden his ministers from making public comments. Netanyahu himself has expressed concern that Mubarak's departure could create an opening for Islamists to seize power.
Israel has survived seismic shifts before, though. Aluf Benn of Haaretz notes that Israel forged its peace with Egypt around the time that its former ally, the Shah of Iran, was deposed. It's likely the instability in Egypt will motivate Netanyahu to strengthen ties with Jordan or even Syria, which might be looking to improve relations with the U.S.
Did U.S. intelligence drop the ball on this?
Some people think so. According to Marc Ambinder of National Journal and The Atlantic, most CIA analysts stationed in Egypt spend more time monitoring arms shipments, the Muslim Brotherhood, and young Islamic radicals than worrying about the stability of the 30-year-old Mubarak regime. In addition, cooperation between American and Egyptian intelligence has declined after it became publicly known that the U.S. was relying on the Egyptians to torture terror suspects.
(Thanks to Twitter user @ McMoPat for this question.)
If Mohamed ElBaradei took over the country, what would he do?
He's a blank slate right now. ElBaradei has spent his entire career as an international diplomat with no involvement in Egyptian politics, so he hasn't had to take many substantive positions (aside from opposing Mubarak's prolonged rule). He has played his hand expertly so far, according to Steven Cook of the Council on Foreign Relations. Mubarak has hobbled opposition figures through the years by harassing them with charges of corruption and libel. Because ElBaradei was outside the country and had no involvement in Egyptian affairs, the president wasn't able to use those tactics against him in the same way.
ElBaradei's inscrutability has enabled hopeful protesters to unite behind him. On the other hand, it has also encouraged skeptics to accuse him of harboring nefarious plans. Anne Bayefsky of the Hudson Institute, for example, thinks ElBaradei will work to make Egypt a nuclear power.
(Thanks to Facebook user Greg Lindsey for this question.)
Got a question about what's happening in Egypt? Ask the Explainer.
Correction, Feb. 11, 2011: The original article incorrectly stated that President Nasser was assassinated in 1981. In fact, it was his successor, Anwar Sadat. (Return to the corrected sentence.)