Climbing with him was the New Zealand guide Mark Whetu, but Rheinberger made slow progress and his companion advised abandoning their attempt. Rheinberger, however, was determined to continue and the two men reached the summit at dusk. With no chance of reversing the long North Ridge in the dark, the two dug a snow hole 20 metres below the summit, the highest night out ever endured.
Next day, they continued down, both suffering terribly. Rheinberger's condition quickly deteriorated and Whetu was forced to descend alone to organise more oxygen supplies. In the event, Whetu was too exhausted to do anything except be helped down to base camp. Rheinberger collapsed close to where Whetu left him, still hundreds of metres from safety. He never got up again.
For the 50 or more climbers who reached the summit of Everest from the Tibetan side this year, Rheinberger's death was a chilling reminder of the price that mountains can sometimes exact. It may have had the most resonance for the British mountaineer Alison Hargreaves. In May, she became the first woman - and only the second person ever - to climb Everest alone and without supplementary oxygen. On her lone path in the final push to the summit, she passed the desiccated bodies of two who had failed to return. She did not let it turn her back. Now she is on the slopes of the world's second-highest mountain, K2, and intends to climb its 8,611 metres (28,244 feet) without oxygen. But while Everest has had hundreds of successful ascents and comparatively few fatalities, K2 has had just 113 confirmed ascents since the first in 1954, and 37 deaths.
Hargreaves does not dwell on such morbid thoughts. "The trick of safe, high-altitude ascents is speed," she says. "It's got to be, since the longer you are above a certain altitude, your body is dying and if you can't go quickly, then you can forget it." In other words, Rheinberger was too slow.
Above about 8,000 metres the body ceases to function properly. Climbers who attempt the world's highest peaks are constantly aware that they are running out of time and have to balance ambition with the need for caution. Hargreaves understands that better than most. Last year, attempting to climb without bottled oxygen to the summit of Everest from the south, sheturned back at 8,400 metres with only 450 metres left to climb. "A friend had told me before I left to be careful, and asked how I would feel picking up the chidren without fingers," she recalls.
She admits that climbing mountains like Everest is a selfish activity - "I've got an ego as big as Mount Everest," she says - but is quick to defend any suggestion that she is inconsiderate to her two children, Tom, aged six, and Kate, aged four. "I find that reaction odd because climbing is my job, it's what I do. I don't wake up every morning and think, 'Oh God! I've got to go and climb Everest.' Everybody takes risks, and for some people the risks are higher. I have weighed the risks and I believe they are worth taking."
The style of Hargreaves's successful ascent of Everest last year reflects her uncompromising tone. Eschewing the assistance of high-altitude Sherpas and bottled oxygen, she carried all her own equipment from her advance base camp at 6,400 metres to her high camp at 8,300 metres on the North Ridge. She left behind her sleeping bag at her penultimate camp at 7,700 metres, figuring that it was too heavy to carry along with her tent. Few climbers of either sex have achieved this level of independence.
Nearing the summit after a fast ascent, she found herself in tears because, she said, she knew she was going to make it. After radioing base camp with news of her success, she stood among the prayer flags and remembrances of other climbers and watched the clouds boiling up. She then left a few silk flowers as a remembrance to those - like Mike Rheinberger and the two she had passed - who had lost their lives on the mountain.
It would have been tempting to stop there and rest, but Hargreaves knew that to do so would only worsen her situation. Despite feeling sleepy - a combination of physical exertion and the lack of oxygen - she forced herself to continue down to below 8,000 metres.
Reaching the summit is often less important than how you got there. When John Hunt's expedition climbed Everest for the first time in 1953, the object was to reach the summit any way they could. Since then, the desire for top climbers has been to reach the summits of the highest peaks either by harder routes or without bottled oxygen.
The courage and determination of men such as Doug Scott, who was on the first ascent of Everest's difficult south-west face, and Reinhold Messner, the first to climb the mountain without bottled oxygen, captured the imagination of the general public throughout the Seventies and Eighties and focused attention on their successors. In the Fifties and Sixties, climbing was still a fringe activity and high-altitude mountaineering the preserve of a few dozen activists. Now hundreds of climbers visit the Himalayas each year and hundreds of thousands climb cliffs and mountains throughout the world.
This growth of interest has spawned a whole industry, with a specialist press detailing the achievements of the dedicated elite and scores of companies competing to sell expensive equipment. Like any other sport, climbing needs its heroes to shift product and so the heroes veer towards mountains that people know - the Eiger and the Matterhorn, Everest and K2.Hargreaves's mental and physical toughness, and the style in which she climbed Everest, have impressed mountaineers all over the world.
"Oxygen is not an issue for me," she declares. "If you take oxygen, you haven't climbed the mountain, you've reduced its height."
Those who romantically believe that mountaineers have a hotline to Gaia may be shocked by the discovery, but the small, international world of high-altitude mountaineering is as riddled with petty jealousies and one-upmanship as any other sphere of life.
There is little money, even for the best mountaineers, in comparison with mainstream sports, but that does not mean that reputations are any less guarded. In recent years, with more climbers than ever going to the highest mountains, differentiating between what is impressive and what is not has become harder, with public relations companies hyping some achievements while others, often more noteworthy, are ignored.
Hargreaves's disinterest in the British climbing village and her strong opinions have led some to believe she is more ambitious than most. The truth is that she is a straightforward, determined woman who understands what she has to do to realise her dreams and is prepared to use media interest to get there. The question remains, however, of what she will do when - and if - she does finally get there.
"When I set off for Everest last autumn," she says, "I was desperately afraid that if I got to the top, I wouldn't know what to do next. I felt I'd have a big black hole afterwards and I was frightened."
It is ironic that a lack of direction should scare Hargreaves more than the risk of avalanche or the danger of frostbite, but her problem has been solved, at least in the short term, by her departure for K2 in Pakistan earlier this month. If she climbs it, she will secure her reputation as one of the world's finest mountaineers. No one has climbed the world's two highest mountains within a matter of months as she is intending - most climbers would settle for one of them. And if she succeeds on K2, then she will go straight to Kangchenjunga, the world's third-highest peak on the Sikkim-Nepal border.
But there are uncomfortable reminders waiting for her on these mountains, just as there were on Everest. High on K2, buried in snow, is the body of Julie Tullis, the first and only British woman to climb the peak, who died in a storm in 1986; later came Polish climber Wanda Rutkiewicz, who disappeared on the peak in 1992. Rutkiewicz was the greatest woman mountaineer who ever lived. Hargreaves will have to step carefully to reach that peak.
The art of survival
The British climbers who first attempted Everest in the Twenties and Thirties wore thick woollen vests and drawers, flannel shirts and gabardine windsuits. On their heads they wore fur-lined motorcycling helmets and on their feet nailed leather boots with as many as four pairs of socks. For K2 Alison Hargreaves will have 70 years of development to draw on. Next to her skin she will wear polyester fleece layers of increasing thicknesses. These layers draw sweat away from the body, keeping her body warmer when she is at rest and not generating heat. Over these layers goes a down suit and the whole lot is topped by a breathable nylon windsuit made from a fabric such as Gore-Tex which allows water vapour out but will not let moisture in.
Hargreaves - who is sponsored by British manufacturers Sprayway - says she wore 10 layers of clothing on the day she went to the summit of Everest. Some high-altitude climbers wear boots that have a battery-powered heating element to ward off frostbite, a problem exacerbated by altitude. All hardware - such as ice axes and crampons - is made as light as possible, and those who take oxygen use titanium tanks to reduce weight still further. Tents are made of breathable nylon stretched into dome shapes over light alloy poles, a far cry from the traditional wedge-shaped tents used by Ed Hillary and friends on the first ascent to Everest in 1953. Hillary's tent weighed three times as much as Hargreaves's and was less capable of resisting the fierce winds of altitude.
Climbing Everest has never been cheap, but increases in peak fees and expedition costs in Tibet and Nepal have made high-altitude mountaineering big business. Expedition organisers will now sell you a place on an expedition to Everest; it costs $25,000 for the Tibetan side and as much as $60,000 for the Nepalese route via the more popular South Col. The Nepalese government charges a royalty of $50,000 for Everest, making it impossible for those without private means or sponsorship to make an attempt.
Andy Broom, of OTT Expeditions, which has had two successful expeditions to Everest, says his clients include oilmen, millionaires and businessmen, as well as professional climbers who have managed to raise sponsorship. For British climbers, raising sponsorship has become difficult, with a waning interest in expeditions from the public and the media. The one exception is women climbers: Rebecca Stephens had the heavyweight backing of courier company DHL. Even so, Alison Hargreaves had great difficulty raising sufficient money to climb Everest. Some climbers earn a living as high-altitude guides, working alongside the Sherpas of the Khumbu region of Everest who carry equipment and oxygen for clients. Sherpas earn $5 a day on an expedition, but get an equipment allowance of $1,200 which they often do not need to spend. Sherpas get a bonus of $250 if they reach the summit and an extra $200 if they do not use supplementary oxygen, which costs expeditions $450 a cylinder.Reuse content