So often, in human affairs, change happens while we're not looking. But now and then, there's a moment or a day when one knows that history is being made, that a new chapter is opening.

In Israel as the Palestinians voted, you had the feeling that the last piece of the first puzzle was dropping into place, and that with the end of this beginning, the process has indeed been rendered irreversible.

The forecasts had been ominous: Either Arab extremists or Jewish extremists would disrupt the elections, and the fear of violence, together with the call by some Palestinian factions for a boycott of the elections, would keep masses of Palestinians from voting.

But with very few exceptions, the elections were a smash hit. There was almost no violence, and participation (75 percent overall, better than 90 percent in Gaza) exceeded most pre-election estimates. Talking with prospective voters in Nablus and in Gaza just before election day and spending time at three precincts in Ramallah and at two voting places in Jerusalem on election day itself, I felt as I did in Budapest several years ago as the Soviet empire was beginning to collapse. I was in Hungary on the day that the government authorities announced that the Russian language would no longer be a required course in the public schools.

Among the Palestinians, with all the problems left to be worked through, with all the ambiguities that remain to be resolved, there was this week a palpable sense of relief in the air. One man, when asked how long he'd had to wait in order to cast his vote, replied, "All my life" — probably not realizing that he was quoting so many new South African voters.

Some observers came away disgruntled, while some were downright furious. The police presence in Jerusalem, they said, was so massive that it amounted to intimidation. And, indeed, there were huge numbers of police of every variety — some wearing Darth Vader riot masks, other quietly tapping ominous batons against their legs, some on horseback.

And, yes, some of the police seemed to think their job was to show the voters who was really in charge, elections or no. But by any reasonable standard, the good news vastly outweighed the bad. From what I could see — and no observer could see more than a tiny fraction of the whole — police courtesy was the rule, police rudeness the exception.

And outside Jerusalem, where the Palestinian police and not the Israelis were in charge and where the police presence was in fact minimal, the mood bordered on the festive.

Jerusalem, of course, remains a problem, and that problem was fully reflected in the election day arrangements. A relatively small percentage of the nearly 5,000 voters who were to cast their ballots at one of the city's five post offices actually did so. If the international press — present in Jerusalem in numbers that at times seemed to compete with the numbers of police — based its judgment of the elections on what it saw in Jerusalem, that judgment could well prove critical.

As those of us among the international observers with experience in Israel understood, it was wiser for the police to err on the side of too much security than on the side of too little. Sooner or later, it will be Palestinian police who are responsible for the security of Palestinian voters on Palestinian election days, even in Jerusalem. When that day comes, Jerusalem's Palestinians will join with their compatriots around the country in the pride of freely exercising their right to vote.

After all these years of conflict, after all the years of the occupation, after all the years of violence, it takes some doing to perceive the Palestinians as voters in a democratic election. Truth to tell, it takes some doing for many of us to perceive them as people. We see them instead as teenagers throwing stones and running, or as wailing demonstrators at funerals of miserable murders, or worse, as those murderers.

Some of them no doubt still carry hidden knives, some plan suicide bombings. But many are on the way to becoming neighbors. It is too soon for either side to trust the other; trust will grow only with the passage of uneventful time. But it will never grow unless we make room for it, unless we fertilize its fragile shoots with hope, unless we are prepared to revisit and revise old perceptions and comprehend new realities and, above all, new possibilities.

In a cab on the day after the election, I asked the driver, a Palestinian, about how the voting had gone for him. "No problem," he said. And we spoke, in Hebrew, about the future. "Some day," he remarked, "people will look back and wonder what took us so long to stop the fighting." "Inshallah," I replied in Arabic– may it be God's will. And he, as we pulled up to my stop, turned to me and said in Hebrew, "Im yirtzeh hashem" — may it be God's will.