JERUSALEM - The best advice I've heard after four weeks in the Middle East came from a wise Jordanian: You can't solve the Israeli-Palestinian problem unless you deal with demography and geography.

When Israel's Prime Minister Ariel Sharon and Jordan's King Abdullah visit the White House this week, and the administration debates how deep to plunge into Mideast madness, President Bush should ponder this pair.

"The major concern of Israel is demography," says Adnan Abu Odeh, long a key adviser to the late King Hussein. He refers to Israel's constant concern that its Jewish majority - which guarantees that Jews will always have refuge from persecution - will be overtaken by a majority of Palestinian Arabs.

Israeli doves have always argued that Israel must give up the occupied territories because otherwise it would gain a permanent population of 3 million Palestinian Arabs, with high birth rates. But the doves were undermined when Yasir Arafat demanded that Palestinian refugees have the right to return to Israel proper. That raised the specter that Israel's Jews would become a minority in their own state.

"The major concern of Palestinians," Abu Odeh continued, "is geography." Most Palestinians lost faith in the Oslo peace process because the building of Israeli settlements convinced them Israel would never leave the West Bank and Gaza. Arafat blew a stellar chance to test this thesis when he stonewalled Ehud Barak's offer to give back 96 percent of the West Bank and switched to a strategy of fighting and talking. Arafat's mistakes got Sharon elected.

But Sharon's incursions won't stop terrorism if Palestinians are now convinced they won't get back West Bank land.

There are many formulas being tossed around by Americans and moderate Arabs for starting a new political process to replace the defunct Oslo peace talks. But none of them confront the crucial issues of demography and geography.

Sharon has talked in the past of possibly returning around 40 percent of the West Bank. Today, he speaks of keeping buffer zones - and every settlement. According to Zalman Shoval, a former Israeli ambassador to Washington and Sharon adviser, the Israeli leader will talk in Washington about a Marshall Plan to rebuild the very Palestinian institutions destroyed by the Israeli incursion. Presumably the West and Japan will be asked to foot the bill.

On the issue of geography, however, Sharon will be vague. He will focus on a long-term interim period, not on return of territory. At best he holds out a distant possibility that Palestinians may someday control pieces of contiguous West Bank land - and get to call it a state.

Shoval admits that if Israel keeps control of West Bank Palestinians, it faces a demographic problem. Israel would lose its democratic character if Palestinians are kept under permanent occupation; if they are incorporated into Israel, the country ceases to be a Jewish state.

"Almost anyone in his right mind understands there will have to be some kind of separation [of Palestinians from Israelis]," says Shoval.

As an example, he referred to a debate between dovish Knesset member Yossi Sarid and minister of tourism Rehamim Zeevi (who was assassinated by Palestinians in October 2001).

"They both want to get rid of the Arabs," Shoval noted. Sarid wanted a Palestinian state, however; Zeevi wanted to expel - the euphemism was transfer - Arabs out of the West Bank.

Sharon's strategy has the clarity of neither, leaving Israel in control of 3 million Palestinians. On the other hand, Arafat hasn't confronted the need to deal with demography, nor has he clarified his geographical goals.

By stoking Palestinian emotions on the "right of return," he convinced many Israelis that his real goal was to take over Israel proper.

"Yasir Arafat wants two Palestinian states, one in the territories, one in Israel," says Shoval. The rash of recent suicide bomb attacks inside pre-1967 Israel only fueled such fears.

Now that he's out from under the Israeli siege, Arafat is waiting for the United States or Europe to come to his rescue. But no international conference, such as the United States is proposing, can succeed unless it goes right to core issues.

There's no hope of persuading Israelis that Sharon is wrong unless Arafat is willing to compromise on the right of return (or Arab states make him do so.) There's no hope of convincing Palestinians to stop violence unless they believe they will get roughly back to 1967 lines - and that in the meantime there will be a settlement freeze.

Unless Washington comes up with a formula that addresses Israeli demography and Palestinian geography, any new political process won't get far.