We have all been there, caught in a moment of distractedness, nervously aware that we are missing a detail that is part of a bigger picture. Perhaps it is a conversation at work, an overheard comment hinting at developments to which we are not party; maybe it is a nagging feeling that we are not in possession of the full facts in a given situation - that something greater is going on beyond our reach. But we carry on regardless, hoping that clarity will emerge in due course. Sometimes it does. Very often, it doesn't.

It is impossible to second-guess the mindset of 17th century explorers 377 years after the event. But it it also easy to wonder whether, amid the salt spray and breaking waves of December 5 1642, Abel Tasman looked up from the deck of his ship as it rocked back and forth in a furious ocean, and swallowed down a similar sensation. Whether he re-scanned the grey horizon, re-examined his compass, and chewed again at that lingering thought in his mind that somehow, somewhere, he was missing a trick.

He would have been justified in doing so, for he found himself at a pivotal moment in history - one that might not only have altered the global map, but could have seen this Dutch seafarer anointed as one of the planet's greatest explorers, a navigator to stand alongside Columbus as a re-drawer of atlases and a re-shaper of worlds. As it was, the wind blew harder, and Tasman acceded to its wishes, abandoning his plans to continue north - going east instead. In doing so, he fell short of a giant prize, becoming - with certain historical caveats - "the man who discovered Tasmania, but missed Australia".

It is probably worth offering a little recap here. General opinion - certainly general opinion based on the British school curriculum - has it that Australia was "discovered" by Captain James Cook, who slipped into Botany Bay - and a place in eternity - on April 20 1770. But while it is true that Cook was the first European to lay eyes on the east coast of the Australian landmass - and was certainly the explorer who finished the jigsaw of the Southern Hemisphere - what is now the vast country of sunshine and surf had been espied by westerners long before HMS Endeavour dropped anchor at 33°S.

The Dutch, long busy in warmer waters, knew of the huge island in the bottom corner of the Indian Ocean. They had even given it a name - New Holland. They just hadn't appreciated how big a place was at their fingertips, nor how close it was to their grasp.

Abel Tasman is a key part of the Australian story

By the early 17th century, Amsterdam had established a firm foothold at the lower tip of south-east Asia. A trading post had been set up at Banten, on the west coast of Java, as early as 1603 - while Batavia, the settlement now better known as the Indonesian capital Jakarta, found its groove on the map in 1619. It would grow to become the headquarters of the Dutch East India Company, a powerful trade hub from which ships would scurry back and forth across the Indian Ocean.

On occasion, Dutch boats would also go south. In November 1605, the navigator Willem Janszoon sailed his vessel the Duyfken east from Banten. He had been instructed to explore the shoreline of New Guinea (modern-day Indonesia and Papua New Guinea) - but he inadvertently passed the Torres Strait, landing at the mouth of the Pennefather River on the west side of the Cape York peninsula (in what is now Queensland) on February 26 1606. However, he believed that he had merely stumbled on a southerly extension of New Guinea, an island of which the Dutch were already knowledgeable. And, fearful of the indigenous Australians, who killed 10 of his men in the course of the voyage, he returned to Banten unaware that he had set foot on a continent of which the maps had no record.

Nor did the penny drop 12 years later in July 1618 when Janszoon charted some of the North West Cape in what is now Western Australia, thinking it part of a small island. And it failed to fall even in 1627, when the sea captain Francois Thijssen and the mariner Pieter Nuyts forged east from the Cape of Good Hope (in South Africa), sighted the south-west corner of Australia, Cape Leeuwin - and mapped some 1300 miles of the south coast, making it all the way to what is now Ceduna in South Australia. The Dutch were on the cusp of a game-changing realisation, but the truth eluded them.

The Torres Strait, as seen from Thursday Island

Tasman's voyage, 15 years later, was part of the same fumbling in the dark. He was seeking the "Terra Australis" - the mythical sweep of dry ground, stretching across the lower half of the globe, which, some geographers believed, had to exist in the Southern Hemisphere as a counterbalance to the Northern. He would not, of course, do this - but he would find a good deal else, without ever fully understanding what he had achieved.

His party set out aboard two ships (the Heemskerck and the Zeehaen) on August 14 1642, and went west to Mauritius - which was seen a viable start-point for the voyage proper; a safe harbour, also in Dutch hands, where the vessels could stock up with provisions. Then, on October 8, the party departed to the south-east, eventually picking up the Roaring Forties - the powerful west-to-east wind currents found in the Southern Hemisphere between the latitudes of 40°S and 50°S - to speed themselves on their way. And speed they did - so much so that they moved into previously unseen waters, then passed all the way along the bottom of the Australian mainland without ever once glimpsing the bays and coves that Thijssen and Nuyts had mapped.

The little settlement of Strahan at Macquarie Harbour Credit: Bernhard Richter/Ben185

When Tasman finally made land, on November 24 1642, he did so just north of what is now Macquarie Harbour, on the west coast of Tasmania. He was expecting to run into the Soloman Islands, in the relative calmness of the South Pacific. Instead, he was confronted by an outpost that no European had ever witnessed.

Was it an island? Was it part of a greater whole? Was it attached to New Guinea? He christened it "Van Diemen's Land" in honour of Antonio van Diemen, the Governor-General of the Dutch East Indies, and set about trying to answer those questions. The Heemskerck and the Zeehaen inched south along the west coast of Tasmania, rounded its south end, then tried to make headway north-east in difficult conditions. Tasman did not manage to dock at South Bruny Island, where he was blown back out to sea by a storm - and he would struggle to drop anchor off the Forestier Peninsula, Marion Bay and North Bay as his vessels battled the elements. So he would redouble his efforts and continue north - and, on December 5, would make it all the way to Eddystone Point, at Tasmania's north-east corner.

By this point, he was just 200 miles from the lower edge of what is now Victoria - a sighting of which - coupled with the earlier labours of Thijssen and Nuyts - might just have sparked a lightbulb moment. Instead, the Roaring Forties kicked in again, rushing east through the Bass Strait - clear demonstration to a seaman as able as Tasman that there was no land directly to the west, and that Tasmania was an island rather than the "Southern Continent" he had been tasked with finding. So he let the wheel spin in his hands, and allowed the wind to take him east, away from his "discovery" - until, on December 13, the group became the first Europeans to lay eyes on the South Island of New Zealand.

He would come closer still on a second voyage in 1644, picking up where Janszoon had left off 38 years earlier in tracking some of Australia's north coast - specifically the Gulf of Carpentaria (the enclosed sea which lies above what is now Queensland and the Northern Territory) - over seven hard months. But like Janszoon before him, he did not identify the Torres Strait, nor that it was a dividing line between continents. Instead, believing that he was still looking at New Guinea - and that the hot, sandy soil of upper Australia was a poor basis for colonial settlement anyway - he returned to Batavia with reports that left his paymasters at the Dutch East India Company unimpressed. The puzzle would go unsolved until James Cook sailed into the picture 13 decades later, and what had been under several explorers' noses became an opportunity that Britain swiftly seized.

Would the history of the world have been different had Tasman persevered north in those gloomy hours of December 1642? Almost certainly not for aboriginal Australia - which could have faced a different set of colonial overlords a century-and-a-half sooner, but the same set of infectious diseases to which they had no immunity. But Britain may have taken a different path. The Australian colonies set up in the late 18th century were perfectly timed replacements for the America which had just been lost.

Would the ultimate legacy of a Dutch Australia have been a far smaller British Empire, on which the sun most definitely set? Would there have been a different calibration of global powers when the World Wars began? Would Holland have been transformed?

There can be nothing but conjecture in answering any of those questions. What is for certain, however, is that Tasmania - which was renamed in tribute to its Dutch "discoverer" in 1856 - is a fine destination for a getaway; a calmer, cooler, greener, more rustic version of Australia, where rare birds sing sweetly in the trees and the fabled - although sadly endangered - Tasmanian devil scratches in the undergrowth.

Eddystone Point, where Tasman turned east for New Zealand

And if you so choose, it is not so difficult to retrace Tasman's journey - though he would surely be the first to agree that it is easier to do so by land. Macquarie Harbour remains a great natural bay, opening its arms placidly as it gazes into the sunset. The Bruny Islands and the Forestier Peninsula are untrammelled and lovely, both within day-trip's reach of the capital Hobart. And if you meander all the way up to Eddystone Point, you can admire the lighthouse placed here in 1884, feel the force of the wind which howled into Tasman's sails in 1642 - and ask yourself whether you would have done any differently.

How to see it

Several tour operators offer holidays which focus purely on Tasmania - and options vary considerably. The Inspiring Travel Company (01244 435 868; inspiringtravelcompany.co.uk) offers "Tasmania's Cultural Treasures", an 11-day self-drive which ticks off major historic sites (such as the colonial penal colony at Port Arthur) - from £3,899 per person, with flights. Discover The World (01737 886 156; discover-the-world.com) sells a 13-night "Tasmanian Discovery" road trip which looks at wildlife and scenery in the likes of Cradle Mountain-Lake St. Clair National Park - from £1,392 a head; flights extra. And Austravel (01293 832 114; austravel.com) supplies "The Bruny Island Long Weekend" - a three-day luxury tour (easily built into a longer break) which wanders the mini archipelago that gave Tasman such an unfriendly welcome 377 years ago. From £1,149 per person; international flights extra.