Areas of such solitude in the pans are only reachable by 4x4 motorbikes with thick tyres and little weight. The brittle salt crust conceals thick, grey, semi-solid mud that will swallow up heavier vehicles even when appearances are deceptively firm: cars have disappeared overnight, soon to be corroded into oblivion by the saline slime. Speeding along on the bikes, steering carefully in each other's tracks so as to minimise our impact on this untouched land, our hair and clothes were thick with dust. Yet, far from being gruelling, our breakneck journey across the bizarre lunar landscape made our spirits soar.
The first surprise was this: though not a drop of surface water is available for hundreds of miles around, we were on the bed of what was once one of Africa's superlakes, comparable to Lake Victoria. Several million years ago it was fed by three rivers, including the mighty Zambezi and the Okovango that now feeds Botswana's celebrated Delta. But structural changes in the Earth's crust cut them off one by one. The Zambezi changed course to carve out Victoria Falls; the Okovango silted up to form the Delta. As each river was cut off, the lake shrank, leaving three distinct, now grassy shorelines containing 10,000 square kilometres of hot, sparkling salt pan.
As our small safari group struggled to digest the physical vastness and beauty of this space, and its improbable history ("the Zambezi really ran here?"), our indefatigable guide Ralph surprised us further. After a ten-minute walk with a sharp eye, he returned with arms full of perfect stone-age tools: arrowheads, hand cutters, parers, slicers. It was hard to comprehend that what he picked up had not been held by human hands for 50,000 years. We returned them safely to their original places.
Then our small column of chunky 4x4s headed for "dry land": to Ralph's camp, or more correctly Jack's Camp as he has called it, after his father Jack Bousfield. Jack is renowned in Botswana for putting the Makgadikgadi on the map. When he arrived from Tanzania in the 60s, he was told that the forbidding pans were for mad people. "Right then, they're for me," he replied, and dedicated the rest of his life to exploring the mystical salty wilderness.
Jack's Camp is the only permanent camp in the Kalahari. It lies cunningly hidden in one of the grassy "islands" on the edge of the pan. Comprising a series of khaki tents connected by walkways through the undergrowth, this is the closest you can get to raw bush while on a luxury safari. Each guest tent is hidden from all the others and commands its own breathtaking view of the grassy "shoreline" and pan. All have their own private "bathrooms", mopani (ironwood) enclosures with showers made of waterproof canvas sacks. These are filled with fire-heated water and hoisted by rope over a branch. At the bottom, a metal rose protrudes with a small lever which frees the water - the ultimate portable shower. It's a delicious relief from the salt and dust.
The camp is on a site where Jack discovered a perfect bushman bed made of sticks in the broad branches of a camelthorn tree. It is straddled by a narrow palm belt that rises abruptly and stretches far across the desert, planted by the droppings of migrating elephant herds in days past. Their dry fronds clatter when a welcome breeze stirs and their spiky silhouettes make exquisite sunsets breathtaking.
Jack's Camp is specially constructed to be invisible. When away from the island on a game drive, it is impossible to see. Vultures and falcons winged by; buck dodged jackal, and a tall secretary bird scooped up a large snake before thrashing the ground with it until it hung limp and dead. On the horizon, black balls bobbed, levitating in the heat haze. Closer inspection revealed them to be 10 male ostrich. They broke into a run as we approached, but are not to be underestimated: one kick can slit a man from throat to groin. Ostrich have big toenails.
Rather than indulging in directionless ambles with the hope of glimpsing animals, Ralph's game drives all tend to have specific destinations. The most spectacular of these was a giant "upside-down tree", a vast triffid on the edge of the pan which acted as a sort of "lighthouse", guiding 19th-century travellers returning across the desert from the inhospitable interior. A baobab tree known as Seven Sisters, it is visible 30 miles away.
Leafless for most of the year, this tree looks truly alien. "The bushmen trace the baobab's extraordinary appearance to the time of creation," explained Ralph. "When the first spirit was giving trees to the people, he gave everyone something to plant. But he only had one tree left when the hyena arrived. The hyena was the force of evil and he taunted the spirit, saying 'It's no surprise I behave badly when you treat me so differently from other creatures.' So the first spirit gave him the last plant, the baobab tree, which he shoved in the ground upside-down out of spite."
This would indeed explain the extraordinary bulbous tap-root appearance of the baobab, which Livingstone too dismissed as "a carrot planted upside- down". Thought to be 5,000 years old, the baobab's massive trunk splits into seven a few feet from the ground, and contains thousands of litres of water which sustain it. Ralph made us walk along the roots as far as we could before they plunged into the earth. We were about 500 yards away before the great tuber, itself as thick as a tree trunk, disappeared from view. Looking back at the tree, our Land Cruiser looked like a Matchbox toy.
One of the baobab trunks harbours a large hole. "This was Botswana's first ever post-box," said Ralph. "Missionaries and travellers left letters in here, so people passing up from or returning to the Cape could collect them and deliver them on arrival". It's a neat idea, but a sender would be lucky to get next year delivery, let alone next day. The thick knobbly bark is red and scarred with hundreds of carved names spanning time, including that of pioneering missionary Robert Moffatt and the now faded cross which Livingstone made his calling card all over Africa.
As we left for camp, the sun turned into a claret orb, lighting the bark of the tree with screaming amber. In the dark, our spot- light picked out bouncing spring hares, a saucer-eyed bush-baby, small buck and an enchanting shuffling aardvark. But most exciting was when the light and engine were switched off.
Ralph made us lie in the sand and listen to the squawks of the bush which were somehow part of the utter silence. We watched a sky so full of white stars and movement that it bore no comparison to the orange, neon-soaked cloud blanket that is much of England's night sky. The Makgadikgadi air is so clear that, as well as shooting stars, satellites are visible traversing the sky. Ralph taught us to pick out the Southern Cross, the huge claws of Scorpio, and some of the bushmen constellations. Struggling to ingest the beauty, I had to force myself out of mesmerising tranquillity and back into the vehicle. Round the fire after dinner, the stars had all moved position completely. You could see that the bushmen could navigate easily from them, but of course I still had no idea how.
The astounding nature of Makgadikgadi attracts some fairly unexpected visitors. Many of Botswana's tourists are safari connoisseurs: they have experienced more commercial "classic" safaris in East Africa and now seek a more genuine, wilder experience. Jack's Camp provides this, though in no less comfort than they are used to. It has its fair share of guests on the "safari circuit", as well as honeymooners seeking the incomparable romanticism of wild Africa when it is unblemished. But Jack's also attracts people who are a blast of fresh air after a few days' polite interaction with safari couples.
Under a huge flat-shaped thorn tree, we dined at night by flame-light next to the Bedpan (so called because of its proximity to the site of Jack's bushman bed), conversing with a team of scientists from the Museum of Natural History in New York. Makgadikgadi is one of the select ecosystems they plan to include in their new biodiversity hall, and they drew on Ralph's immense, intimate knowledge of the region.
Ralph is a trained zoologist who grew up in the bush, and there is nobody else alive who knows so much about every aspect of pans. Nobody else can recall with such animation facts and ideas on geology, palaeontology, ornithology, meteorology, archaeology. And he is quick, spotting and identifying every spiralling bird and thorn-hidden mammal, whilst driving or speaking or pouring drinks. The charismatic writer Michael Main passed through camp, with his ever-present terrier Gypsey. He fixated us with tales from over three years of travels all over Southern Africa, researching every aspect of the Zambezi and Kalahari for two riveting books.
Most bizarre of all was the party of models plus entourage, come to pose in the wildest places for a coffee-table art book. With Kalahari mud and animals skulls as props, they disappeared each day to shoot, returning at night to discuss such thrills as the adrenaline rush of a two-hour make-up session to create the wilderness look. "Don't think fashion, think wild!" enthused the make-up artist. The girls nodded seriously in the firelight. Their face-paints and hairspray were more than incongruous, but they were at Jack's for the same reason as the rest of us: to find a wilderness which man has not yet brought into his domain.
The final morning brought the chance to walk with a bushman. The pervading spirituality of their existence understandably caught the heart of Laurens van der Post in the 60s, but our bushman guide, Cobra, stuck to more practical things, leading us on a walk through grass and pan. Where there seemed nothing to our ignorant city eyes, he pointed out spiders and beetles, two-toed ostrich prints, wide lion pads and zebra tracks. He spotted the droppings and lairs of many creatures, sticking his torso alarmingly far into the resident pythons' nest, before pronouncing, "He will not come out. He is in there eating buck. Will not come for 10 days." The group was divided between disappointment and relief. Tiny scattered oblong scorpion holes were more yielding, giving us a rare daylight sighting of a pale three-inch inhabitant, tail curled. Cobra guided patiently, with silent amusement at our stranger's admiration for what was to him so familiar. He could see a whole micro-Kalahari we would simply have missed.
There would have been many more tracks in the rainy season, when the pan fills up, providing a vital water source for vast herds on one of the few remaining migration routes in Africa. Then, Makgadikgadi fills with tens of thousands of head of wildebeest, zebra and their accompanying predators: lion, cheetah, and scavenging hyena and wild dogs. The bleached- white grasslands sprout green, and countless bright flamingo feathers cover the pan and fill the sky with fluid streaks of pink. Jack's Camp is then in a different world.
Tour operators Abercrombie and Kent (0171-730 9600) offer stays at Jack's Camp as part of a wider tailor-made itinerary, flying in from Johannesburg or Victoria Falls to Maun, the nearest airport. Staying there costs from around pounds 160 per person per night, including all food, drink and activities. Explore Worldwide (01252 319448) also run tours to the Makgadikgadi salt pans, as part of their Botswana safari tour, from pounds 1610 per person.