Whatever else that might be said about the Arab revolutions, it’s obvious that they pose a problem for Israel. But how bad, and what should the Israeli government do to hedge its risks? I heard some interesting — but not very encouraging — ideas on this subject from top government officials last week.

To sum up: Most officials think that relations with the Arabs are gradually going to get worse, perhaps for decades, before democracy really takes root and the Arab public, perhaps, will be ready to accept the Jewish state. The challenge for Israel is how to avoid inflaming Arab public opinion, a newly important factor, while protecting the country.

The trouble ahead is symbolized by the election of Mohamed Morsi, a Muslim Brotherhood leader, as president of Egypt. His inauguration prompted a wary message of congratulation from Prime Minister Benjamin Netanyahu, expressing hope that ­Israeli-Egyptian relations will be cooperative and based on mutual interest. The statement masked deep Israeli anxieties.

Netanyahu fears an erosion of the relationship with Egypt over time and wants to slow that process, if possible, while preparing for potential trouble. Netanyahu is said to view these precautions as the equivalent of putting up shutters before a storm.

The most obvious test will be Gaza, where the militant Hamas leadership is closely allied with the Muslim Brotherhood. Netanyahu has tried to de-escalate crises that have arisen, but if rocket attacks increase, they may draw a harsh Israeli military reaction — which could worsen relations with Cairo.

Efraim Halevy, the former Mossad chief, says Israel should face reality and begin talking with Hamas. But others stress the growing threat in Gaza: Israel has intelligence that militants there have tried to buy shoulder-fired anti-aircraft missiles from Libya, and the Israeli air force now operates on the assumption that such missiles are present in Gaza, in addition to the array of other rockets.

The Sinai Peninsula is another flash point. This vast desert is becoming a lawless area where al-Qaeda and other terrorist groups are trying to find a haven. Intelligence officials here believe the extremists’ strategy is to provoke an Israeli retaliation and thereby encourage an unraveling of the Israel-Egypt peace treaty. I didn’t hear any clear formula for how Israel can respond to attacks without falling into this trap.

The chill in Israel’s relationship with Turkey adds to the dangers of instability in Egypt, Libya and Syria. Netanyahu has responded by seeking new allies, including:

? A “Balkan arc” anchored by newly closer relations with Greece, Cyprus, Bulgaria, Romania and Albania. Some of those countries allow the Israeli air force to train in their airspace, providing an alternative to the now-unfriendly skies over Turkey.

? An implicit, if unspoken, alliance with Saudi Arabia and other gulf states against Iran and against Muslim Brotherhood extremism. In this silent courtship, the Israelis are offering an alternative to an America that’s no longer seen as a reliable protector of the conservative gulf regimes.

? New links with governments in sub-Saharan Africa, such as Kenya, Uganda and the Ivory Coast, which are worried that the rise of militant Islam in North Africa will spread south.

Israeli leaders know these new friendships, however useful, won’t alter the basic threat posed by an Arab awakening that, in most countries, has empowered militant Islamic groups. Within the government, there’s a range of views about just how bad the future will be, but nobody uses the congenial phrase “the Arab Spring” that has been common in the West.

Among the optimists, relatively speaking, is said to be Defense Minister Ehud Barak. He thinks Egypt and other neighbors will move toward a version of the “Turkish model” of Islamic democracy, which may be cool toward Israel but will also be pragmatic. Barak thinks Israel can’t simply wait for the storm to pass. The process of change is irreversible and may eventually be benign as the Arab societies mature.

A darker view is taken by some of the officials who know the Arab world best. They think that for at least the next several years, as Morsi and other Muslim Brotherhood leaders try to consolidate power, they may appear cooperative. But at the core of the Brotherhood’s ideology is rejection of Israel, and any compromises with Israel will be tactical moves, rather than real peace.

Israel’s existence, never easy, has gotten more complicated and unpredictable. “We are still inside this huge historical shift,” says one senior official, “and we don’t know where it’s going to take us.”