AMMAN, Jordan _ These are tough times for cynics. America’s goosebump-inducing elections had people cheering across much of the globe. Cynics, however, die hard in the Middle East.

Here in Jordan, skepticism reigned, with jaded Jordanians saying they expect little change from the soon-to-be occupant of the White House. And yet, even those who assume great depths of understanding by declaring “nothing will change” had to take notice on that historic day. Now is when the entire world is paying attention.

This, as Barack Obama might say, is his time. And this is his moment.

When he visited Jordan last July, Obama vowed to start working for peace in the Middle East, “from the minute I am sworn into office.” He also recognized that an American president cannot simply snap his fingers and expect to magically untie such a tight, many-stranded knot. Still, parts of that thread could start loosening up if the president-elect uses this moment, when the world is entranced by his historic election, to make a few crucial points to some key audiences.

Consider the dilemma of two peoples fighting over one small piece of land. For years, many (not all) on both sides of the Israeli-Palestinian conflict argued the other side had no legitimate claim on the territory. Although some voices always called for compromise, others always maintained that only We, (Palestinians or Israelis) have a valid demand on that narrow strip on the edge of the Mediterranean sea. Then, amid tears and bloodshed, moderates on both sides agreed to divide the land.

In order for moderates to prevail, both Arabs and Jews must accept the reality that their adversary’s claim has real merit.

In Israel, the vast majority of the population now accepts that view. While Jewish Israelis understand the strong historic links of the Jewish people to territories lying on the West Bank, most now also agree that Palestinians, too, have a right to the land.

A small number of very religious people believe the land was given by God, and to them that settles the question. That position, however, is in the minority. The government and most of the people have already agreed that Israel will relinquish land in exchange for peace and security. The tough part, however, is securing the peace portion of the transaction.

Even moderate Israelis have no interest in letting go of territory if it will become the operating headquarters for those seeking Israel’s destruction. If Israelis were convinced that Palestinians will not turn their new state into a base for attacks on Israel, they would probably stand up to the settlers, whose methods and ideology put them far from the Israeli mainstream.

For now, most Israelis dislike the deeds and ideas of the far right, but they have little enthusiasm for fighting them. A recent poll showed that more than two-thirds of Israelis support the creation of a Palestinian state, but an even greater number fear that their families will be harmed by Arabs. The fears are based on realities, such as the 35 rockets fired into Israel as America counted the votes.

The situation makes life tough for Palestinians, leading them to become even more suspicious of Israelis.

Israelis hear the words of Palestinians speaking of peace in English and know that their speeches often sound different in Arabic. They know that when Arab leaders speak to their own people their message is much less conciliatory.

Many deny the history of a Jewish presence in this part of the world for thousands of years, claiming Jews only recently thought of this as their home. Millions of Palestinians and other Arabs still believe Jews have no business in the Middle East.

Here in Jordan, for example, one can see maps of Palestine everywhere, dangling from the rear-view mirror of a taxi; hanging on a shop wall, on T-shirts, hats, tourist souvenirs. Everywhere. There is one small problem with these maps of Palestine: They include every millimeter of the state of Israel. Israel has already been wiped off the map, to paraphrase another Middle Eastern leader. To the millions who refuse to believe the Jews belong in the Middle East, the map of Israel, all of it, is the map of Palestine.

Which brings us back to Obama. Today, he has the world’s ear. If he wants to advance the chances for peace, Obama must speak to all who claim the others have no right to live here. Let them hear from the man who triumphed using his extraordinary capacity to persuade and inspire. Let them hear from him that the two peoples really do have a right to live in the Middle East. Make it even harder on the cynics. This is the time. And when it comes to peace, this is the place.