We set off and offered to help join the search for the insurgent. As we hurtled along in the growling vehicle, I could watch our progress on screen. The dusty street passed beneath us at speed, then we paused at a wide cesspool, a common sight in Baghdad. The Stryker's camera, ever watchful for roadside bombs, zoomed in on a stick-like object rising above the water's surface, then jerked to a man who seemed to be foraging nearby. On closer inspection the man was ageing, dishevelled and lame, walking by the kerb with a shambling gait.

The Stryker reversed to seek another route. Then another image appeared on the monitor. Before another cesspool was a pile of rubbish strewn in the middle of the street - again, nothing unusual. A woman in a long, black robe approached it, turned a household bin upside down and poured its contents on to the pile. Then she took a second bin and repeated the action. The US soldier sitting at the monitor shook his head in despair.

So did I. Somehow there was something more shocking to me, in Baghdad at least, about this act of throwing litter than the throwing of a grenade. The middle-aged woman had performed it without a hint of the social embarrassment that might nag a litterlout in Britain. More than that, there was something habitual about her action that suggested her mind was otherwise occupied, as if pouring household garbage into the middle of the road was now casual routine, now second nature.

And so al-Hadar, formerly one of the Baghdad's most prosperous areas, has become - quite literally - a waste land. The spacious houses with gardens, walls and front drives are still there, but the streets are strewn with sewage, rubbish and rubble. Stepping outside, it is often the smell that hits you first. You might also suddenly be taken aback, in this modern city, by the sight of a flock of goats or sheep, or a woman riding a donkey trap.

Among the most poignant discoveries are the empty buildings. I looked around an old gym which until recently had been used by insurgent gunmen as a vantage point. All the equipment had gone, but there were still posters of western musclemen on the walls, now watching over debris and stillness. I visited a school that is trying to reopen, the rows of empty desks and chairs speaking volumes, the chalk writing of a teacher still on a blackboard but no one to read it.

Earlier this week I attended a memorial service for 2nd Lieutenant Peter Burks, a member of the regiment killed last week when a roadside bomb hit his Stryker vehicle. He was 26 and left behind a fiancee. It would be a mistake to think that, because soldiers face death every day, they feel grief and loss any less acutely than other people. In a large white room, rows of uniformed soldiers waited for the service to begin with sorrow etched on their young faces, the silence punctuated only by sniffs of choked emotion.

At the front of the room was the symbolic helmet balanced on the end of an upright rifle, and a framed picture of Lt Burks under the words "In memoriam". Everyone stood as the Star Spangled Banner was played through loudspeakers. Lt Burks's squadron commander, Lieutenant-Colonel Antonio Aguto, had to pause, his voice breaking as he paid tribute. "We can take comfort from the fact he did not die in vain," he said. "He died a soldier's death on the streets he swore to protect."

Chaplain Bryan Smith said Lt Burks had been a strong Christian. "Even though I feel his absence, I know where he is: heaven ... it took God six days to create the earth; he has been working on heaven for 2,000 years."

There was a moment of silence, when all heads bowed, then a sergeant, Kevin Muhlenbeck, shouted the name of a regiment member as if on the parade ground. "Sir!" came back the reply. He shouted another name. "Sir!" came the reply. "Burks!" No reply. "Peter Haskell Burks!" No reply. Avoice outside gave an order to fire, and three times gunfire cracked in the night air.

More than 3,850 US troops have died during the Iraq war. From afar that can look like a statistic. Up close, it looks like a room full of sadness and a search for consolation.