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"Sixty-one bears," a man announces in the parking lot of the Hotel Arctic in Iqaluit. He is coming off two weeks of sailing western Greenland and the Canadian Arctic aboard Lindblad Expedition's National Geographic Explorer. I am among the passengers about to embark on the same ship for the same voyage, only in reverse.

When someone from my expedition expresses amazement, the man shakes his head. "The record is 65."

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The bear in question is the polar, one of Earth's iconic species. And it is the reason, I soon learn, that many of the well-heeled travellers on board paid $16,000 or more to travel to Baffin Island.

A male polar bear can stand as high as 2.4 metres (eight feet) and weigh as much as 815 kilograms (1,800 pounds). A natural southpaw, it can sever a human spinal cord with a single swipe of that huge limb. At last count the Nanook, as the animal is known to the Inuit, number only in the several thousand on Baffin. That's mostly where we'll be looking for them, both on land and along the pack ice still covering some of the coastline in late summer.

"I want to see the bears where they live free," one man explains.

Like nearly all the 128 passengers, he also expects to photograph them, proving that he got close enough to capture images of a ferocious animal in a fearsome landscape. Such National Geographic-worthy images, once obtainable only by trained professionals willing to sleep on an ice floe for a month, can now be purchased, in effect, for the price of high-end digital equipment and guided access. Among a certain crowd, a quality polar bear photo is the environmentally-correct version of the trophy head over the fireplace. It proves you're a real hunter. And guarantees bragging rights at the next catered dinner party.

C.T. Ticknor, one of the 14 naturalists and photo instructors on the ship, is there to oblige. But she wants passengers to get more out of the experience – to connect with the natural world and then to forever see and think about the planet differently. "We call this an expedition and not a trip because we want you to start off with one idea of seeing polar bears, and end up with another."

Our banner bear day happens almost too soon into the voyage. Thirty-six hours out of Iqaluit, we spot two animals. They are onshore; we are on the decks of the ship. We have also enjoyed our first hike, in Noble Inlet in the southern end of Frobisher Bay. Brought to shore on Zodiacs, passengers wandered the spongy tundra in the company of crew members with binoculars, flare guns and rifles – just in case. No bears in Noble Inlet, fortunately.

On the second morning we awaken to an announcement of a bear spotted on an ice pack several kilometres to the north. The Explorer is going to sneak up on it. The radar is turned off – the animals register the frequency – and a small flag at the prow is taken down. Silence and caution are demanded by those along the railings and bulwarks; a burst of laughter, even a lens clanging off the floor, could scare the animal into the water.

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The sight is eerie and lovely – a male polar bear on a tiny ice floe. Raising its nose to the wind to catch our scent, the creature watches us with mild curiosity. We, in turn, stare at him, 200 metres off the bow.

Or rather: Most passengers gaze upon the natural wonder through viewfinders. Lucky for us the click-click of digital cameras doesn't register like radar.

Eventually we part ways with the bear and head north again. A tall, friendly man who has been snapping photos asks a fellow enthusiast if he was content with the sighting. The passenger shrugs. It was close, he implies, but not close enough.

The tall man is Sven Lindblad, president and founder of Lindblad Expeditions. His father, Lars-Eric, is often credited with creating ecotourism, and the family pioneered the practice of taking non-scientists to formerly inaccessible corners of the planet.

Since 2005, Lindblad has partnered with the National Geographic society to combine upscale travel with research opportunities. "We need the sense of being connected with something totally wild," Lindblad tells me. "Seeing the bear on the ice, fat and healthy, triggers deep emotions. It makes you feel better about the world."

He welcomes the pressure to deliver intimate, but not too intimate, bear encounters to his passengers. But he, too, insists the expedition is about much more. "Individuals are powerfully charged by these experiences, and are powerfully positioned to do things of magnitude." His ships, he says, are platforms for discussions about the environment. They are also discreet fundraising opportunities for the Lindblad-National Geographic Fund for the Ocean, which supports conservation projects.

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That same afternoon, we definitely get close enough to stir deep feelings. "If you go into the ice, you will see polar bear," the ship's captain, Oliver Kruess, has assured us. Steering the refurbished 375-foot Norwegian car ferry as though it is a kayak, Kruess nestles us deep into pack ice near Cap Searle. Far ahead are at least three animals.

Soon enough, they are closer, and then closer still, to the ship. Two huge males end up beside the prow, though one wanders off after an unfriendly bite to the backside. A third approaches from the stern, and soon two healthy, full-sized polar bears are posing, some might say performing, for the Explorer.

A silent frenzy ensues. Photographers, professional and amateur alike, lean over the gunwales with arm's-length lenses, or drop onto their knees and bellies to sneak a shot through the drain holes when the bears settle awkwardly beneath us. The digital gunfire lasts 20 minutes.

Though the naturalists joke that the smell of reindeer kebabs – the afternoon snack being barbecued on the rear deck – must be the lure, they are clearly astonished by such a prolonged, relaxed visitation from the kings of the Arctic. Conversation at the debrief and dinner is full of excitement and awe.

Later on the voyage we see a female and her cubs, along with playful orcas and a massive bowhead whale. We even spot small groups of the elusive narwhal (minus the tusk) in Icy Arm, one of the fjords that empties into the spectacular Buchan Gulf.

But no experience matches that earlier encounter with the two male polar bears. Our final count for the expedition is 61, a tie with our predecessor. Hard to imagine even the most fickle Arctic traveller begrudging that outcome.

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IF YOU GO

Lindblad Expeditions is not repeating its Canadian Arctic-Greenland expedition in 2014. The New York-based outfit is, however, revisiting one of its more legendary expeditions: the Northwest Passage, last traversed by the company in 1984, when Lars-Eric Lindblad brought the first passenger ship through the fateful route. "It was a challenge back then," Sven Lindblad says. "Nowadays, getting through isn't nearly as difficult."

Part of the 1984 challenge involved making maps of the shallow James Ross Strait, and negotiating almost uncharted waters. For 2014, Lindblad is promising to use that original "mud map."

Two departures will be on offer. The first starts in Reykjavik and finishes 25 days later in Kugluktuk, NWT. The second begins in Kugluktuk and ends 24 days later in St. John's. Prices start at $24,990 a person, and include chartered flights. expeditions.com

The writer travelled courtesy of Lindblad Expeditions. It did not review or approve the article.