For thousands of years, humans have clung to the edge of Greenland's ice cap. Its beauty is awesome - but it isn't easy to live with, says Alex Leith

I ate this shaggy animal's powerful-tasting flesh for lunch, however, and it's churning around my stomach. It's not even as cold as it's meant to be, hovering around zero. As we judder towards the umpteenth crest, Niels says: "This is about the point where people usually say, 'wow'." The sight before me is incredible. My mood changes immediately. I only have one word to say, and it comes out involuntarily.

"Wow!"

We park and gaze at the 400m jagged wall of ice rising into the sky. The edge of the ice cap. It has a bluish tinge. Occasionally, it lets out an almighty crack: it is melting. This is the only sound we can hear, apart from an occasional wraaak from the pair of enormous ravens which fly possessively around the summit. We are stunned into silence. Niels, who sees the ice wall several times a week, is gazing at it as intently as I am. It's not just its shimmering, unearthly beauty that gets you. You can sense the immense power of the thousands of kilometres of ice that stretch behind it. It's scarily beautiful.

Greenland: what a misnoma. The vast majority of this country is crushed under the weight of the ice cap - a covering of compressed snow up to 3km deep and 100,000 years old. Man has managed to scratch an existence for the past 5,000 years, on and off, on the fringes of the island, the only inhabitable part of a land mass otherwise completely ruled by ice. Even the hardy Inuit have found it difficult to settle this territory: the island has only been continuously inhabited for the past 1,200 years or so. Today the population of the whole country, which is as big as Western Europe, is only 55,000. The ice may be beautiful, but it's terribly difficult to live with.

The next day we are flown north in a propeller plane over mountains and frozen lakes which are haughtily unaware of the existence of human beings. We fly west of the ridge of the ice cap, which stretches out to the horizon to our right. The ice has smothered the land, sucked the life out of it. It is a mighty sight, and a frightening one. To our left is the coastline, which the ice has left uncolonised. There is nowhere that humans could possibly settle. I am invited into the cockpit, and it is from there that I first see Ilulissat Icefjord. A wide inlet filled with what looks like a flotilla of little white ships. Icebergs!

Icebergs are called ilulissat in the Greenlandic language, and the city of the same name is the best base in the country from which to examine these amazing phenomena. The glacier 40km down the fjord on which the town is built is the most productive iceberg factory in the Northern hemisphere, "calving" thousands of structures a day, which float majestically out to sea. Ilulissat is a peach of a town, built into a sheltered bay: when I arrive the primary colours of its wooden Lego-like buildings are brought out to their full by a warm sun shining from a bright blue sky. It's much warmer than it should be. At my hotel I am stunned by the view from the window. In the bay hundreds of blue-tinged icebergs float in a calm turquoise sea.

The easiest way to get a closer look at them is to take a two-mile hike to Sermermiut, the original site of the city, where you can still see the remains of Inuit turf houses abandoned in 1850. From afar the icebergs look like a futuristic maritime city, glinting in the sun. The closer I get to the beach, the more mesmerising the nearest one becomes. I'm transfixed by its dazzling shade of electric blue, its vastness, its unique asymmetry. I'm brought down to earth by a whistle from Neeva, my Inuit guide, who beckons me back. "Don't go too close," she says. "If it tips over, you will certainly die."

Ice punctuates all the best moments of my trip. One night I watch the Northern Lights do their swirling dance in the sky, drinking a glass of Greenlandic vodka. The vodka is made using melted glacial ice instead of water. Another day I go husky-dog sledging. I lie in the back of a large sledge pulled by 16 dogs directed by a driver who sits in front of me, and occasionally jumps out and runs behind, so the thing can go faster. At one point I am left alone on the sledge as we hit a vast patch of ice, and the contraption swings dangerously out of control, hurtling between rocks, before being slowed up by a patch of bare earth where the pack ice has melted. The driver catches up and jumps on, twisting around and flashing me a grin. I grin back.

Another day I get a boat to the small village of Oqaatsut, about an hour's chug north of Ilulissat. The boat, skippered by an old Danish salt with a white beard and a cloth cap, meanders between icebergs, allowing me to examine their form, and look through the clear water at their looming mass below. As we approach our destination, I wonder how we're going to dock: the 100 yards or so of sea between the boat and village is frozen solid. The boat simply ploughs straight into the ice.

A young Inuit crew member climbs out and jumps on the surface to test its strength. When he is sure it's thick enough he sets up a ladder and we climb out and walk to shore. We're told to watch for fishing holes. Fall through the ice and you die. I climb out first. I'm nervous, of course. I've never walked on the sea before. You're not meant to walk on the sea.

Alex Leith travelled with the Greenland Tourism and Business Council (00 299 342820; greenland.com). Arctic Experience (01737 214 214; discovertheworld.co.uk) offers six night itineraries in Greenland including three nights in Ilulissat from £1,643 per person, based on two sharing. The price includes return flights, transfers and b&b.

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