I've been sitting on a rock three metres below the Mediterranean for nearly a minute, wearing nothing but goggles and a pair of trunks. In the sea-blue gallery before me, my wife turns somersaults, the fish oblivious to her presence. She glides towards me, performing the hand signals we've learned over the past few days. First an OK, then a thumbs up, followed by the internationally recognised wanker sign, as she twists away and spirals to the surface surrounded by a necklace of air bubbles.
We were away on what is quite an unusual activity break: Turkey's only free-diving course for beginners. This oxygen-free diving discipline has been around for millennia; Japanese pearl divers routinely stayed underwater for three or four minutes at a time. The technique, however, has undergone a recent surge in popularity as swimmers like us discover the joy of basking, dolphin-like, in a weightless undersea world.
Our tutor, Burak – accredited by the German free-diving federation – runs his diving school right on the Blue Flag beach of Kas. Joining us in his barefoot classroom are Michael and Maria-Theresia from Germany.
Lesson one is theory. We discuss apnea (from the Greek word "without wind", or literally "breathless") free-diving techniques. This method uses specific breathing procedures to aerate the blood and slow down your pulse, helping your body to consume as little oxygen as possible when you shoot below the waves.
As a veteran of 600 scuba dives as well as a meditation teacher, Michael is particularly interested in the skill. He says it will allow him "to be one with the fish" in the way that diving with heavy scuba apparatus doesn't. Burak believes that underwater enthusiasts fit into one of two categories: those interested in scuba, who tend to be more social, and those into free-diving, who are, in Burak's words, individual and "a little strange".
Burak further subdivides the sport into those who do it for fun, and record-breakers. The latter are epitomised in the 1980s movie The Big Blue: divers who cruise to depths of more than 200m with the aid of an electronic "sled", then shoot to the surface clinging to a balloon of compressed air. A similar technique was once used by local Greek sponge divers, who would descend to the seabed with their legs tied to a boulder, before resurfacing laden with wares. Michael also begins to tell us about some free-divers who have experimented with inhaling pure oxygen pre-dive, while wearing specially carved contact lenses instead of masks, allowing them to swan about like the Man from Atlantis. But before he can finish, Burak shoots him a dirty look. It's clear that this particular course is as much about safe, step-by-step breathing techniques as it is about coasting around in tranquillity under the waves.
After lunch, the five of us simply swim out from the classroom for our baptismal free-dive. The water is crystal clear – one of the big attractions of Kas, an overgrown fishing village basking in nearly year-round sunshine. The town is also equidistant from Dalaman and Antalya, with cheap flights to both airports.
We pair off to try out the breathing technique we learnt in class: half-yogic, half-scientific. First are quick "agitation" breaths, then several deep "exchange" breaths. Using a little contortion, we suck oxygen down into the diaphragm, into the mid-section, into the chest, and, by bending forward, into the upper lungs. A few "relaxation" breaths slow the pulse. After one final mega "exchange" breath, we're ready to dive. The average human will take on board five litres of fresh air in this manner, although Michael's merman lungs can hold a mammoth eight litres. He's had them measured.
One by one we descend using flippers. I wanted to use a mermaid-style monofin like the one featured in The Cove, a recent dolphin movie involving some stunning free-diving sequences, but Burak says these only work for experienced swimmers, as novices simply waste valuable oxygen flapping about.
Sadly, it turns out that I need neither. After a few flips below, the pressure in my ears becomes overwhelming. Moreover, I'm too nervous about running out of breath to stop and equalise my eardrums.
But in the hotel pool the next morning the whole technique clicks into place. I'm able to take my time, concentrate on my breathing, then slip to the bottom of the pool, pinching my nose every few seconds to pop my ears. I lie there in quiet meditation for 30 seconds, staring up at the bougainvillea-splashed mirage on the water's surface, before drifting skywards, fired up for the tasks that Burak has set for us on day two.
We join a scuba-laden dive boat and leave Kas harbour. Our destination promises deeper water, plentiful fish and a more intense free-diving experience. In 10 miles of coast we see two sea turtles and just one minor settlement: this is the Med without the cement mixers.
On board, the scuba group is indeed a different crowd, backslapping and sitting on crates of post-dive beers. We, on the other hand, are on deck, where Burak acts as yoga teacher, running through partner-assisted stretches and breathing drills.
It takes a minute to get our kit on and into the water (compared with 15 minutes for our scuba friends). After several practice dives and a 60-second face-down breath-holding exercise (surprisingly easy when you know how), Burak explains our final task: diving down to a line he's laid out 4m below the surface, then following it underwater for 25m – the entire length of an average swimming pool.
Free-diving is all about focus, preparation and patience. As each of us dives down, we know we can do it. We're also assisted by the underwater mammalian reflex, an impulse found in dolphins and seals – and humans too – that directs blood to the heart and brain, allowing a submerged body to survive on far less oxygen. Pulses automatically slow down too. The heart of Cuban free-diving ace Francisco "Pipin" Ferreras slows to an unbelievable six beats per minute during dives.
A gaggle of scuba divers gather to watch us trace Burak's line. In the silent blue we glide past them, slowly and in complete control: streamlined subaqua superheroes compared with the clunky underwater astronauts.
Snorkelling will never be the same again.
• Burak at Mavi Diving (+90 242 836 3141, mavidiving.com) is running three five-day courses this summer and autumn. Private three-day courses cost £85 per person, per day. Kas's Hotel Oreo (+90 242 836 2220, oreohotel.com) has double rooms with sea view for £50 a night. Half-board costs just a few pounds extra