When it's seen from almost a kilometre up, you realise nature doesn't like geometry. It abhors geometry. Hundreds of dry kilometres of dead rivers and lumpen moonscapes of sprawling rock; loopy tangles of brush in the desert; and wavy banks of sand, punctuated with the occasional tree looking frankly startled to find itself still alive: these hot, awful distances roll below in tangles of abstraction.
Then you peer a little closer, gazing down at the immensity of Darfur, a part of Sudan slightly larger than France, and suddenly see tiny geometry. Squares, triangles, perfect circles on the ground: all speak of astonishing mankind, and its presence, for so many centuries, in this unconscionable environment.
As we civilised beings fly overhead, men are busy down below trying to kill each other. Insects are trying to bite babies. Women are seeking water to keep their children alive, and men are trying to stop them, and when the water is found it will make men kill each other once more, and it will breed the insects that kill the babies.
And it's tempting, as we chew up the kilometres in our United Nations helicopter - the government airline, Air Sudan, has recently been celebrating its cavalier approach to aircraft maintenance with its 13th crash in 12 months, resulting in a triumphant 120 deaths - to stay at this airy remove, with our cool khaki and our boiled sweets, and simply think big thoughts about the geometry below.
The faint, faint circles of thorns and sand denote a village given up on decades ago. The stronger, darker squares of mud walls, pocked at the centre with a tiny hut, show villages that still live - and there will be smudges of green nearby, showing that somewhere under the sand, even if the women and the plants have to dig and scuttle for it, there will some days be water; and then the dark squares broken at the edges, without a hut in the middle, show the villages ravaged, burnt and ruined.
It's all down there, written in the geometry: history and life, and man's curious compulsion to insert his own brutality into a land already reeling from nature.
We can see it from up here. Do we have to go down, into the flies and guns and heat; into the tears and lies and smells and death?
The chop of the rotor slows, shifts into a minor key, and the ground rises to meet us.
A man with a weedy beard is shouting, while many beautiful women are trying to tell me something. Their voices are lilting and mellifluous voices, their faces perfectly oval in headscarves of colour: startling fresh lime, and rich cochineal, and bubblegum pink, Disney pink. Their high cheekbones flash blue-black. They are talking about rape: about having to have the babies of rape, and about bringing them to this camp.
"I want to tell you about me," shouts the man. The translator translates, and the man grows less agitated because someone is finally listening, however reluctantly.
"I had to dig up my family," he begins. We all stop, and quieten, and finally listen to Sharif Yahaya, from a small village near the town of Tawila.
"Janjaweed had come and killed them, many near me, and we buried them, and we all went away. And came back. Days later. Maybe at the wrong time.
"Janjaweed were there and told us to dig up all the graves. I don't know why, I think just to make it worse. We had to dig people up who had been dead, and then look at the bodies, and then put them back in the earth. Just to make it worse. Just to show that they could make it worse."
This is Darfur, today, where everyone has a story, each one worse than the last. Let's recap, briefly, for those other fools like me confused by the war.
Sudan, the 10th-largest country in the world, has been host for the past quarter-century to Africa's longest civil war, with the Islamicised north, centred on the power base in the capital, Khartoum, asserting itself over the mostly black, African, Christian or animist south. So far, so simple, but it doesn't really tell the story of Darfur.
For centuries, there was a rough coexistence, here towards the west of the country, between black farmers and the travelling, nomadic, historically more Arab peoples, who would drive their cattle from north to south and back, as the rains and pastures came and dried. There was wary coexistence. Trade. Friendships.
But early in 2003, it all started to go wrong. The black natives in Darfur had had enough. The serviceable land they had shared with the nomads was becoming scarcer. Desert has been encroaching on the arable land for years, and it is now racing and engulfing many kilometres every year, exacerbated by global warming. Khartoum, Arab-run Khartoum, would always take the side of "its" nomads.
With arms from the south - arms provided to most of this part of Africa, for decades, by the West - the Sudan Liberation Army (SLA) began to attack government and army outposts, determined to have a greater say in its own affairs.
Retaliation was swift. The government sent in gunships. And armed the nomads. "Janjaweed" translates as "men with guns on the backs of beasts", and they did exactly what it said on the tin: raided the black villages, at dusk, on horseback and on camels and in trucks, and slaughtered and raped, and sneaked back into the brush at nightfall.
More than 60 000 died - shot and macheted by the Janjaweed, or bombed from above by the government.
Thousands of villages were razed, and after a while there wasn't even the excuse that they were sheltering rebels: this was simple ethnic cleansing. The world belatedly sat up, and towards the end of last year, the Khartoum government had to listen. The slaughter slowed. A north-south peace deal was signed. Articles of negotiation were begun, and promises made to give no more support to the Janjaweed. Peace, it seemed, was breaking out. The world stopped watching and the story seemed to go away.
It didn't, of course. There are, today, a sliver less than two million homeless Darfurians still living from hand to mouth in camps. There are a further million living in the towns that host the camps, who have been directly affected by the slaughter, growing hungry because so many farmers have lost their livelihoods.
Of these terrible figures, more than 50% are children. More than 1,5-million of those with their futures stolen are under 18; 600 000 of them are under five.
This is the forgotten reality of Darfur today. The world has turned away to the next crisis. But, look. Look at the aftermath of war. Look back at those figures. Three million people, ruined. More than half-a-million of them babies. Or come and look at the camps.
They are not awful places. Life goes on. Babies are saved. They are taking in babies, still, at the Abu Shouk camp near El Fasher, in north Darfur, and slowly giving them diluted milk, according to how much their bodies can take at the time.
The aid workers going quietly about their business in a dark, flyblown medical tent towards the edge of the camp think they can save Selma, who looks up with tiny dull eyes from the lap of her mother, Fatima Abdullah. Selma is 20 days old and they've got her up to 1,8kg. When she was brought in she weighed precisely 1kg. They can feed her, and maybe even save her from hypoglycaemia, malaria, polio and that great local baby-killer, diarrhoea.
There are latrines. Foul holes beneath makeshift tents, perhaps, but latrines. There is sporadic education: in health and hygiene. There are inoculations. Youngsters go to school, and sing. There is at least one meal a day. Rigs drill for water.
There are signs of human nature asserting itself. Most of the makeshift huts, tarpaulin over wood, now have their own walls: the women spend weeks digging mud and baking it with water and donkey excrement into bricks, making their own perimeter; the same instinct that puts up white picket fences around pretty Surrey cottages. Not awful places, these camps: but terrifying and impossibly huge. To drive the perimeter at a fair lick can take an hour. To helicopter over it, more than three minutes.
Two million people. Six hundred thousand babies.
And the answer, of course, would be for them to go home, start tilling the sand again, plant their sorghum and millet, and try to pick up their lives rather than scramble with two million others for limited aid.
But they cannot go back, because they are still so scared. Major General George Okowu is commander of the African Union peacekeeping force in Darfur, which is by most accounts doing an effective job at tremendously basic levels: they will walk out, for instance, with the women from the camps when they embark in the mornings on their 20km round trip to look for firewood; so the women are no longer being raped when they reach the stumpy forest.
Okowu laughs loudly when asked how many people, in this part of the world, outside the camps, are armed: "All of them!"
The government may be officially dissociating itself from the Janjaweed, but out here the fears are seared in. Some children jump at the sound of horses. All flinch at the sound of helicopters. Villages are, at least on the evidence I saw in six days, no longer being razed, but the aftermath of any war in this part of the world is hungry men with guns.
"The government say many things, but we do not yet believe them. They are still arming Janjaweed, no matter what they say. So, we still have to fight. Sadly, we still have to fight."
Sultan Suleiman, once a respected government official, speaks for the rebels in the SLA camp at Musbat, an hour's flight north of El Fasher. It is centred on solid brick huts built by the British occupiers in the 1950s; 12 white men once administered all Darfur from here. Now boy soldiers laze outside in the searing heat.
"Nobody wants peace more than me," says Suleiman. "More than all of us here. But there must be law. We would love law, accept law. If there are going to be trials, for war crimes -- I will stand and be counted. I will go on trial. As long as it is real law, from outside, not from this government.
"There must be security, for our people. You have been told Janjaweed are no more. They are. Until we are satisfied, until we trust, we cannot put down our guns."
Ali Abdul Karim Ismail has been fighting for the SLA for four years. He is 23. Can he see one day when he would he put away his gun? Farm? He smiles.
"Not today. I have lost too much. I would not know where to go. I have grown up protecting my people, and I will not stop doing that until I know no more Janjaweed."
And then? He thinks. "Yes, then. People say we have seen too much killing. I have killed. But the difference is that I am a soldier. And soldiers know the difference between what is war and what is peace. We can live with peace. We would like to live with peace."
Two days later, we are in another SLA camp. Finna is in the mountains in south Darfur. The helicopter lands on a field filled with rocks. A patch nearby is being back-breakingly cleared by women. It is impossible to reach this place by road; food is not getting through, but the United Nations Children's Fund (Unicef) has so far managed to immunise about 14 000 people in these hills against increasingly rampant disease. This is as remote as it gets, and yet Janjaweed reached it, on horseback, to rape women fetching water. The last attack was three days ago. The community is being slowly forced up the mountains.
But news has reached this hot back of beyond: Abutalib Abdallah Mohamad, a dapper young local leader, astonishes us with his opening address.
"We would like to extend our sympathy, of our village, of the SLA, with London. You are suffering, too, from terrorists. We are with you, and thinking of you. Perhaps you, too, can some time think of us."
Darfur is not one grey round of misery. Africa is used to death, and used to forgetting. Life goes on, in large part, because of the children. Wide-eyed and eager and giggly in the camps. And, here in Finna, dancing and singing for the visitors, exhausting themselves with glee, chasing after the helicopter as we lift off from truly one of the last unfound places on God's Earth.
Always, there is glee and colour, so close to misery. Close to the grassy plateau where children giggled, four young men sit in a mud hut full of grenades; all shot while trying to protect their women from an attack. The youngest has a bullet lodged in his thigh. He cannot be taken to hospital, and no transport can make it here.
Always, the glee beside the misery. We had, with us, a delightfully sharp celebrity companion, and I had watched her slide one morning, with shrieks of helpless happiness, down the neck of a furiously unhappy camel in the first SLA camp.
Boy soldiers had to put down their guns, they were laughing so much. An hour later, I found myself trying not to watch as she furiously rearranged her headscarf and her emotions, her face turned from any camera, eyes welling at the sight of four-year-olds whose existence was reduced to fighting flies beneath a square of hot blue plastic. An actress determined not to be seen crying? How Sophie Okonedo ever won an Oscar nomination I'll never know.
There is a chance of a future. You can see it in the eyes of the youngsters, even in the thoughtful comments of raped women.
It depends on families going home. They do not know what is left of their villages, many days' walk away. They need security: they need to be convinced, that someone is not taking Khartoum's word on "peace". They need to know they will not be macheted, or raped, or have to dig a brother from a grave. Then they can go home, and grow food again. This year's harvest in Darfur will be less than 40% of normal, and even in a normal year many people die.
It depends on a return to a vague semblance of normality so these children are not carrying Kalashnikovs in 10 years' time.
It depends on funding. Unicef, in particular, has to talk to all sides, to government spokesmen lying through their expensive teeth: and compromise, all to get some food and medicine through.
Unicef's 2005 budget for Darfur was set, at the beginning of the year, when people were still watching, at =A3123-million. About =A350-million has so far been offered. Forty percent, and we are almost in the eighth month of the year, and the world has turned away, its eye caught by famine in Niger.
But surely the world can watch two African countries at once? For this crisis is not over. The slaughter, the constant chattering gunfire of the past two years, may have stilled. The terror is that this was simply the opener; just throat-clearing for a longer-term disaster to come.
Two million people. Six hundred thousand babies.
Actually, it's all rather simple after all. It just depends on us not forgetting.
Guardian Unlimited =A9 Guardian Newspapers Limited 2005