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Swim with whale sharks in the waters off Mafia Island, Tanzania.

Tatiana wants to know about sharks.

Not whale sharks. She's already been briefed by Skipper Dan and appears to have bought what he was selling: that whale sharks – despite being the biggest fish in the sea – are harmless, toothless galoots; eaters of plankton, not people.

No, Tatiana wants to know about the other sharks, the people-eaters, and because Tatiana is from France and I'm a scuba diver who speaks passable French, it falls to me to set her mind at ease. Only a few species of shark present any threat to humans, I assure her, and none of those species is found in the waters off Mafia Island, Tanzania. This is not entirely true – but I figure that nothing is to be gained by planting seeds of concern in soil so obviously fertile.

We are on an excursion to swim with whale sharks, after all. How Tatiana found herself here, on an African dhow in the Indian Ocean, is a question I choose not to ask. Perhaps she was egged on by the boyfriend hovering by her side. Perhaps she felt an urge to put her fears to the test. Perhaps, like me, she simply could not let pass an opportunity so extraordinary. Although adult whale sharks may grow to more than nine metres and live for more than 100 years, the ones here are juveniles, a modest five metres in length. Not only do they not pose any threat, they are actually known to be playful toward divers.

A total of eight passengers and three crew are on board the 7.5-metre dhow, run by operator Kitu Kiblu. Our leader is Skipper Dan Smith, a young, affable South African with a diploma in digital marketing. When the season closes, he hopes the owners will hire him to set up their website. For now, he is looking for fishermen. And birds. Where there are either, there are likely to be fish. Where there are fish, there is plankton. And where there is plankton, there may be whale sharks.

It's the first week of February, near the end of whale-shark season, so Skipper Dan has done his best to lower our expectations: Sightings over the past two weeks have been few. If we should find one, we are to put on our mask, fins and snorkel and sit at the side of the boat, legs dangling over the gunwale. The helmsman will pull up alongside, then cut the engine so as not to alarm the fish. On Dan's command, we will lower ourselves gently into the water and swim with the shark, taking care not to touch it or startle it. The objective is to make the encounter benign and stress free for the animal.

All this careful instruction is forgotten when Skipper Dan lowers his arm and points to a large dark mass moving slowly, maybe nine metres away. A dorsal fin breaks the surface. All hands, even Tatiana's, are scrambling madly for gear. We gather, waiting for the order to enter the ocean. At a piercing cry of "GO! GO! GO! GO!" we splash over the side with the grace of tumbling bowling pins.

Ten minutes later, we are back on board.

"I saw it feeding," Nancy says. "I screamed in my snorkel."

"I swam alongside it," John says.

I saw nothing but churning water. I look over at Tatiana. She shrugs and shakes her head, seeming almost relieved.

By now, our actions have attracted interest from another boat, which spills its passengers into the water and tries to herd the shark in their direction. It's precisely the type of behaviour that Kitu Kiblu hopes to stop before whale shark tourism takes hold on Mafia Island. We move along. We're in the right area, Skipper Dan says. More should appear. And soon they do.

This time I'm better prepared. My legs are dangling over the side when Skipper Dan barks his command. Visibility is poor in the plankton-rich water, and I don't know which way to turn, but I catch a hint of motion to my left and there it is – the back half of a massive, spotted body, the great tail swishing in the sea. I keep up with it briefly, but soon it is out of sight. When I raise my head to the surface, I see Tatiana in the water, but still by the boat.

We climb back aboard and the dhow circles the area once more. I let Tatiana take her place at the gunwale and wait behind her. The tips of her fins skim the water as the boat steers a parallel course to a swimming shark. The helmsman cuts the motor, and suddenly the shark makes an abrupt turn, swimming directly toward us. Or, more precisely, directly toward Tatiana.

The shark is less than nine metres away, and closing.

"Go!" I cry to Tatiana as others push their way into the water beside her, but she has an iron grip on the side of the boat.

It's less than six metres away. "Go, Tatiana!" I urge, to no avail.

Realizing I may never have a chance like this again, I place my hand firmly on Tatiana's back and shove her into the path of the approaching shark, then slip in behind her.

I cannot believe how close it is. I look it in the eye. I see its enormous mouth, its pectoral fins. It swims by slowly and I take my place alongside. I feel I could reach out and touch it.

The encounter lasts for what seems likes minutes, but is likely only seconds, each one memorable. Back on the dhow, Skipper Dan and the crew are raising the sail for the trip back to shore. I remember Tatiana; I should apologize. But she is by her boyfriend, excitedly describing what she saw. I hear her say, "Maintenant, je suis contente." She is happy.

Maybe she doesn't know how she ended up in the water. Maybe it's best that it remain that way.

IF YOU GO

Tanzania's largest city, Dar es Salaam, is your jumping-off point for Mafia Island. International airlines offering one-stop connecting flights between major Canadian cities and Dar es Salaam include KLM, Swiss, Ethiopian Airlines, Turkish Airlines, Emirates and Qatar Airways. From Dar es Salaam, connect with either Coastal Aviation (coastal.co.tz) or Tropical Air (tropicalair.co.tz) for a 30-minute flight to Mafia Island.

The prime season for spotting whale sharks near Mafia Island runs October to February. Kitu Kiblu, which promotes low-impact encounters, runs half-day tours for $100 (U.S.), which includes breakfast and transportation to and from your lodge. kitukiblu.com

By turning whale sharks into a tourist attraction, operators such as Kitu Kiblu hope to help protect the population. Whale sharks are at risk, in part due to the shark-finning industry. Their fins are particularly vile-tasting, but they are prized as displays by restaurants that serve shark-fin soup.

Where to stay: Chole Mjini is a collection of seven open-air treehouses built into baobab trees. The hotel is located on Chole Island, adjacent to Mafia and easily accessible by dhows and water taxis. Double-occupancy rates start at $220 (U.S.) a person, and include all meals. cholemjini.com

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