In Sderot, sighs of relief. Children venture out. Inhabitants who have exiled themselves to other towns return home.

And the reaction? An outburst of jubilation? Dancing in the streets? Applause for the Prime Minister and the Minister of Defense, who at long last have come to their senses?

Not at all. The expression on the nation's face is a grimace of disgust. What kind of thing is that? Where is our victorious army?

The people of Sderot are really angry. OK, so there are no Qassams, but this was supposed to happen only after the army had entered Gaza and wiped it out.

Haaretz headed its front page with the mendacious headline: "Israel pays with deeds - and gets promises".

"It's fragile," Ehud Olmert soothes us, it can come to an end any minute. And the other Ehud, Barak, who pushed for the cease-fire, has an excuse: we have to go through the motions before starting the Big Operation in Gaza. For the sake of Israeli and international public opinion.

And nobody says: Thank God, the killing has stopped!

WHY? WHAT causes this almost unanimous reaction of disappointment? Why is there a general feeling of humiliation, almost of defeat?

It's because the national ego is hurt. How wonderful it would have been to see the Israeli army in Gaza destroying Hamas, together with the entire city. But, instead of the crushing victory, we have something that smacks of a rout. And that in spite of the assertions of those now rooting for re-occupying the Gaza Strip: that at any minute, with just a little more starvation and closure, the population would have broken and rebelled against Hamas.

From the military point of view, a year of war in the Gaza Strip has ended in a draw. IDF-Hamas 1:1. But the IDF and Hamas are not two football teams of equal standing. Hamas is an armed political-religious movement, what is termed in current Western parlance "a terrorist organization". When such an organization achieves a draw with one of the mightiest armies in the world, it can justifiably claim victory.

The aim of Olmert's war was to topple the Hamas government in the Gaza Strip and to destroy the organization itself. This has not been attained. On the contrary, according to all reports, Hamas is stronger than ever, and its hold on the Strip is solid. Even in Israel that is not questioned.

For a year, the Israeli government has maintained a total blockade of the Strip - on land, at sea and in the air. It has enjoyed the unqualified support of Europe, which assisted in starving a population of one and a half million men and women, children and old people. The US was, of course, a full partner in this glorious enterprise. Hosni Mubarak's Egypt, dependent on the US, collaborated, if unwillingly.

All this was not enough to beat poor and crowded Gaza, a narrow strip of land 35 km (22 miles) long and 10 km (6 miles) wide, into submission. Not only did the rockets not stop, but their range increased. Their victims in Israel were few, a child could count them, but their impact on morale was immense.

The Israeli army was helpless against this primitive weapon, which costs next to nothing. The army killed wholesale and in retail, on land and from the air, with missiles, shells and infantry weapons. To no avail.

Hamas has survived, but it, too, did not achieve its aim. It had no answer to the blockade. Only the pressure of international public opinion (as well as the Israeli peace forces) prevented total starvation, but in the Strip there was a shortage of everything. Unemployment was rampant, fuel disappeared, many inhabitants suffered from undernourishment, bordering on starvation.

That is the nature of a draw: neither of the two sides is able to force a decision and impose its will on its opponent.

A CEASEFIRE only comes about when both sides need it. (True, Carl von Clausewitz, the Prussian military philosopher, has said that in war it is impossible for a situation to be beneficial to both sides at the same time, that something that is good for one side is necessarily bad for the other. But in real war there are exceptions.)

Indeed, the Israeli army needed the ceasefire no less than Hamas. That became clear from the comments of the "military correspondents", almost all of whom are thinly disguised army spokesmen. Of course, not one of the cabinet members would have agreed to a ceasefire if the army brass had objected.

Usually, the army bosses press for one more action, one more operation, one more war. Have they suddenly turned into doves? Not really. But they knew that they had to choose between two "bad" options: a ceasefire or the "Great Operation" - the re-conquest of the entire Gaza Strip.

The commanders did not like the first option, and that is an understatement. It means admitting failure. But the second option they liked even less - much, much less.

The Great Operation, which a large part of the public yearned for, which almost all the media demanded at the top of their voices, is very problematical. Hamas has had a lot of time to prepare for it. No army likes to fight in a built-up area, among a crowded population. Every alley is a potential trap, every man - and every woman - a potential suicide bomber. Even if the army succeeded in entering and occupying the strip with only "tolerable" casualties, that would just be the beginning of the troubles. Every day soldiers would be killed. The mutual bloodletting would be endless. See: the Iraq war.

Public opinion is fickle. Every dead soldier whose smiling picture is shown on television increases the pressure to get out. Sooner or later the army would be compelled to leave - and the situation would revert to what it was before, only worse.

The army chiefs know this. Olmert and Barak also know this. The lesson of the Second Lebanon War has not been forgotten. There is no mood for war.

THE CEASEFIRE has far-reaching political implications. It changes the Palestinian - and perhaps the regional - map.

One can protest from here to eternity, one can shout from the rooftops that "we don't negotiate with Hamas" and that "we have no agreement with Hamas" - every child understands that we indeed do, and indeed have.

This is an agreement between the Government of Israel and the Gaza authorities. It means a de facto recognition of the Hamas government there. In Gaza, too, every child understands that the Israeli government was compelled to agree because it was unable to break Hamas by force.

In the eyes of the Palestinians, the situation is clear: Mahmoud Abbas in Ramallah has not got anything from the Israelis, Hamas has.

Abbas tries by peaceful means. He is the darling of the Americans and the Israelis. But since the great performance in Annapolis, not only has he not achieved any meaningful concessions at all and not freed a single prisoner, but additional prisoners are being taken every night, the settlements are being enlarged and the Israeli government announces grandiose new building projects in East Jerusalem and the entire West Bank. And the Israeli government would not dream of agreeing to a ceasefire there.

While at the same time Hamas, besieged by the whole world, losing fighters every day, has attained a significant military and political achievement: goods will flow into the Strip, cars will again bounce along the potholed roads, the Rafah crossing, which cuts off the Strip from the world, will be opened. In the coming prisoner exchange, hundreds of Palestinian prisoners will be released in return for the captured Israeli soldier, Gilad Shalit.

The conclusion? Everybody can ask themselves: if I were a Palestinian, what conclusion would I draw?

The ceasefire affects the balance of power within the Palestinian people. Hamas has proved that it can maintain an orderly government. Now it is proving that it can control the radical organizations, too.

The wisest thing Mahmoud Abbas can do now is to form a Unity Government, based on both Hamas and Fatah.

WILL THE ceasefire hold? The correspondents report that nobody expects it to.

When Olmert says that it is fragile, he knows what he is talking about.

There is no written agreement. No orderly mechanism for settling disputes. No arbitrator to decide, in case of need, which side is responsible for a violation.

If somebody in Israel wants to break the ceasefire, nothing will be easier: a squad leader opens fire on a group of Palestinians near the border fence, because he suspects that they are about to plant an explosive device. A spy helicopter pilot believes that he is being shot at and launches a missile. The army intelligence chief claims that large quantities of arms are being smuggled into the Strip.

It can be done in other ways, too. The army will kill half a dozen Islamic Jihad militants in the West Bank. In response, the organization will fire a salvo of Qassams at Sderot. The army will announce that this is a violation of the agreement and answer with an incursion into the Gaza Strip. It will even be right formally, since the ceasefire does not cover the West Bank.

Every agreement holds only as long as both sides believe that it serves their interests. If one of them thinks otherwise, it will break it (and assert that the other side broke it first). In this case, the first to break it will most likely be the Israeli side.

A CEASEFIRE is not peace (salaam), and not even an armistice or truce (hudnah). It is no more than an agreement between combatants to stop shooting for some time.

In the nature of things, each side will use the ceasefire to prepare for the next round of fighting - to breathe deeply, to rest, to train, to plan, to obtain more advanced weapons.

But the ceasefire can become more than that. It can lead to Palestinian unity, to Israeli re-thinking, to a practical advance towards a peaceful solution. At the very least, every day of the ceasefire saves human lives.

And in the meantime the Hebrew and the international dictionaries have acquired another Arabic word: Tahdiyeh, calm.