Never plan a trip mathematically. I know this – but when I consulted the guidebook Top 10 Iceland ahead of a winter trip to the island's Arctic fringe, it would have been cheering to have seen more than just a single highlight in the entire north of the country. And that one top sight wasn't even Dettifoss. This may sound like an oral hygiene product, but it turns out to be the most powerful waterfall in Europe – a howling torrent that roars over a jagged lip of rock, plummets 150ft and fuels a perpetual rainbow before continuing its journey, carving a dramatic canyon through the fresh rock of this young island.
The dry statistic for the quantity of wet stuff dragged over the brink by gravity is one million litres every two seconds; perhaps more helpful is that this represents the entire alcohol consumption of the Icelanders in a year. Which may touch another arithmetical raw nerve: in common with other Nordic nations, beer and wine is taxed mercilessly, and the local spirit that may occasionally be proffered in your direction by one of the friendly folk of north Iceland is appropriately nicknamed "Black Death". It should, accordingly, be politely declined.
Fortunately, the wonders of north Iceland are so intense that they require no liquid reinforcement to enjoy – starting with Dettifoss itself, which resembles Niagara only in its brutal power. No neon, no crowds, no quietly turning down the falls at night to conserve water. In summer, you can hike north along this laceration in the planet; in winter, you are free to rejoice in its dramatic desolation.
In one sense, I had been relieved to learn that there is, apparently, only one "must-see" in the northern half of a country the size of Ireland, because I imagined that the average 24 hours on the brink of the Arctic at this time of year would be a study in darkness, with only a brief interlude of ghostly daylight. In fact, this is a location in which, in early March, you can watch the day stretch before your very eyes. At the start of my six-day trip, the first approximation to usable light appeared shortly before 9am, and ended by around 6.30pm; in less than a week, a 12-hour day seemed the norm. It is as though you have landed on the bright side of the Moon.
My favourite Icelandic word is now ljostillfun, which translates scientifically as "photosynthesis" – but literally as "light creates life". The books I had brought went unread, because the rough edge of the planet proved more enthralling than prose. A journey here is like one big geography field trip, a succession of craters and canyons and cliffs resembling crumpled parchment. In the fjords that serrate the coastline, the steely waters serenely reflect the snow draped on the muscular mountainsides, and the islands scattered like a sculptor's offcuts.
The ocean also provides a living for the hardy folk who dispute the assumption that 65 degrees north is a latitude unfit for human habitation. A sequence of fascinating exhibitions shows the fragility of life on the edge. At Husavik, the Whaling Centre (occupying a former slaughterhouse) explains how Icelanders took a leading role in exploiting the world's largest mammal. It stands adjacent to the jetty that is now the centre of the country's whale-watching industry; the creatures are worth more alive than dead.
Far more plentiful were the herrings that, for a time from 1903, made Siglufjordur the richest place in Iceland. The sheltered harbour hosted hundreds of trawlers in the "herring rush", capturing the protein that kept the rest of northern Europe healthy. The herring shoals have suffered the same fate as the cod that enriched Iceland until overfishing ruined the industry. But the modern twist here is fashion: fish skins are cured in the same manner as sheepskins, and have been transformed into fabric that is lighter and tougher than leather. The skins are exported to Milan and Paris, allowing the stylish to look slinky in salmon.
The fortunes of the far north are even more fickle than fashion. A harsh winter characterised by northerly winds could deny essential access to the sea, starving communities in the process. The best place to understand the endless cycles of hope and despair that have characterised the millennium of human settlement in Iceland is at the Icelandic Emigration Centre in Hofsos. A handsome old mansion – almost torched by the townspeople after it became derelict – has been revived as a testament to the tens of thousands of Icelanders who sought new lives in North America.
Hofsos is also a good place to learn that the 21st century has not been entirely cruel to Iceland. Just before the financial crash, a pair of bankers' wives signed a cheque for a new swimming pool there – a spectacular, cliffside outdoor pool, naturally heated to resemble a warm bath, with the bonus of an infinity aspect aimed at the North Pole.
New road tunnels make life easier for locals and visitors. Between Siglufjordur and Olafsfjordur, the previously treacherous journey across a mountain pass has been superseded by a quick drive that takes only about as long as a foreigner does to pronounce the names of the towns it connects. And there is an aesthetic bonus: halfway through, the tunnel takes a break for breath, and this short outdoor segment comes at the head of a fjord previously off-limits except to the hardiest hikers or trawlermen.
North Iceland is full of extreme experiences, but thankfully also simple comforts. I stayed in a succession of friendly hotels and guesthouses, mostly charging under £100 for a double room with breakfast – and usually featuring unlimited quantities of smoked salmon and home-made bread.
The diminutive capital of north Iceland is Akureyri, prettily located beside a fjord and hemmed in by mountains (which makes the airport an exciting "Category C" experience for pilots and passengers). The biggest number of beds, though, is around Iceland's mother lake, Myvatn, which shimmers at 1,000ft in the heart of its own national park – and is the one northerly location to make it in to Top 10 Iceland.
Other countries may boast continental divides, but Iceland can brag of an intercontinental divide, as the North American and European tectonic plates noisily tear themselves apart. The Mid-Atlantic Ridge, as this fault is known, runs through the country and beneath the lake. Yet at this time of year, when the ice is so thick that locals play on it in their 4x4s, it is the sky that screams for attention. I wondered why the Sel-Hotel Myvatn had a funny little conservatory attached, until – shortly after dark, a dozen nights ago – the cry went up that the Northern Lights had been switched on, presumably by God. The leaden skies that sometimes make Iceland look like a nation in mourning had cleared, revealing a gust of solar wind beautifully entangled in Earth's magnetic field. Not quite a natural Las Vegas of colour, as sometimes happens, but a pearly veil that appeared to flutter before melting into the night.
The mathematics of the cosmos predict the Aurora Borealis. But its naked beauty is incalculable.
Icelandair (0844 811 1190; icelandair.co.uk) flies from Heathrow, Manchester and Glasgow to Keflavik airport, the main gateway for the island; a typical fare for a week today from Heathrow is £228 return. Iceland Express (0118 321 8384; icelandexpress.com) flies from Gatwick to Keflavik, for a typical fare of £226 return.
From Keflavik airport, Flybus runs frequently to the capital, Reykjavik for a fare of ISK1,950 single/3,500 return (£11/£19.50). The bus terminal is across from the domestic airport, from where flights to Akureyri, the "northern capital", cost around €61 each way on Air Iceland (00 354 570 3030; airisland.is).
Akureyri: Skjaldarvik Guesthouse (00 354 552 5200; skjaldarvik.is); B&B starts at €62.
Myvatn Lake: Sel-Hotel Myvatn (00 354 464 4164; myvatn.is); B&B starts at €86.
Husavik: Guesthouse Arbol (00 354 464 2220; arbol.is ); B&B starts at ISK12,600 (£70).
Varmahlid: Hotel Varmahlid (00 354 453 8170; hotelvarmahlid.is); B&B starts at ISK12,300 (£66).
More information (but not too much)
Top 10 Iceland, DK Eyewitness, £7.99.