By Jeremy Bowen
BBC Middle East editor
Israeli warplanes have targeted buildings across Gaza
Israel has laid out an ambitious war aim. It says it wants to create a new security environment, to protect Israelis who live within range of rocket fire from Gaza.
It wants, according to one official, "to neutralise the Hamas militia men" so they can no longer fire into Israel.
In the last day, the way Israel believes it can do that has become a little clearer.
The air strikes have tried to kill as many Hamas fighters as possible and to destroy the infrastructure of power and governance that Hamas has been trying to build since it took over in Gaza.
The first wave of attacks went very well from Israel's point of view.
During the Palestinian armed uprising after 2000, Israeli bombers attacked Palestinian security bases many times.
Often their attacks were expected, and they flattened empty buildings.
But at no time did they attempt an air offensive on the scale that they began on Saturday.
The ground for it was prepared by clever psychological warfare.
Prime Minister Ehud Olmert issued warnings to the Arabic press that there would be bloodshed if Hamas did not stop rocket fire.
But at the same time, Israeli spokespeople told journalists that the war plan had not been authorised by the cabinet.
But it had been. So when the first wave of Israeli warplanes came in over Gaza they were able to attack bases and compounds that had not been evacuated.
That was one reason why so many people were killed so quickly.
The fact that Israeli army reservists have been called up - and the movement of tanks - suggests that the air strikes will be followed by ground incursions. How big, and for how long, is not clear.
An Israeli intelligence briefing this morning argued that many Palestinians in Gaza were fed up with Hamas.
Israel seems to believe it can work on the divisions that already exist between Palestinians until it is possible to detach Hamas from all but its core support, and force it to accept its terms.
But Israel might not get it all its own way. Hamas is unlikely to surrender. It has an ideology of resistance and martyrdom.
Palestinians under fire may forget some of the divisions which have crippled them in the last three years, and come together against a common enemy.
Images from a third day of Israeli attacks on targets in the Gaza Strip
Israeli generals always assume that they have a limited time to achieve their goals.
They will have expected the critical statements that were issued by the UN Secretary General and others within hours of the first raids.
The United States is already providing its usual diplomatic cover for Israel at the UN.
But a new American President is sworn in next month. As President, Barack Obama will give Israel firm support.
But he will not want to take office in the middle of a raging crisis in the Middle East.
Israel has already killed civilians, as well as children. International pressure on it to stop the attacks will increase with the numbers of deaths.