A decade ago, Fabrice Schnöller was an engineer working on systems for tracking sharks. Then, in 2007, he went on a sailing trip to the island of Mauritius, where something happened that would change the course of his life.

As his boat approached the coast, giant towers of steam began exploding out of the water. One by one the columns closed in, until they surrounded the whole boat. Curious as to the source of this strange ocean phenomenon, Schnöller grabbed his snorkling equipment and a camera, and jumped in.

Diving down beneath the ship, Schnöller's ears were bombarded by what sounded like underwater explosions, growing louder the deeper he went. At first he feared the boat had suffered a mechanical failure. But as he circled around, he began to sense that he was not alone.

Glancing downwards, Schnöller froze. Out of the darkness, a series of giant dark monolithic shapes were heading directly towards him. It was a pod of sperm whales accelerating towards the surface.

As they approached, the sounds grew louder and louder until they penetrated his flesh like an X-ray. Schnöller felt the warm vibrations passing through his skeleton from every angle.

With sperm whales you really feel a connection, which is totally different to other animals

The whales surrounded him, staring with large, unblinking eyes. At more than 60 feet in length and weighing approximately 125,000 pounds, they dwarfed him. But rather than swallowing the helpless Schnöller in one giant gulp, the whales appeared to be deeply intrigued.

After scanning him, the rhythm structure of their sounds began to change. Schnöller later realised that these were the patterns that we believe sperm whales use to communicate and send information. The whales appeared to be speaking to him.

They stayed for two hours, circling, staring and showering him with bursts of sound, before vanishing once more into the deep. Schnöller was entranced.

"In France we say that you see the soul of a person through their eyes," he says. "With sperm whales you really feel a connection, which is totally different to other animals. When you dive with a big fish like a shark there's nothing at all, but when a sperm whale looks directly at you, you can feel he's thinking and analysing you, and you don't know who's weighing up who."

Sperm whales are the loudest animals on the planet

The whales were curious about Schnöller. "I could see instantly that all of them were very interested in my camera," he says. "One of them would take it in its mouth, and I'd have to go bring it back. That kind of extreme curiosity is something you would typically expect from only humans. But what I wanted to find out was whether their behaviour was simply curiosity, or was there something more?"

Were the whales really trying to communicate with Schnöller? To find out, in 2009 he began a new project called DareWin to understand sperm whale communication at a deeper level than ever before.

There are only 20 or so scientists in the whole world studying sperm whales, which are notoriously shy and elusive, so progress is slow. Schnöller aims to speed things up by collecting the largest-ever database of sperm whale vocalisations and behavioural videos.

His ultimate goal is to first decode the information contained within whale clicks, and then construct a new click that he could send to the whales. But this would require going where none of his peers had gone before: freediving and mingling with the whales.

Sperm whale vocalisations have long fascinated scientists for one reason in particular. They are almost inconceivably loud.

They dive up to 10,000ft under the ocean surface, hunting for fish and giant squid

While normal human speech takes place between 60 and 65 decibels (dB), sperm whale clicks, described as such because we hear them as "tak-tak-tak", can reach as high as 235dB. In contrast, a loud rock concert is around 115dB and the sound of a jet engine is roughly 140dB. Quite simply, sperm whales are the loudest animals on the planet.

Such is the power of their clicks that whales can comfortably transmit information to others from hundreds of miles away, and even across vast oceans. A sound of 180dB is enough to cause drastic cell death in your ears, but the most powerful sperm whale clicks will not merely deafen you: they can vibrate the fragile human body to pieces.

The whales have evolved these astonishingly powerful vocalisations to cope with their extraordinary lifestyle.

Sperm whales range across the open ocean, but they typically gather at deep canyons, to socialise, mate and huntfood sources no other predator can reach. They dive up to 10,000ft under the ocean surface, hunting for fish and giant squid.

Some scientists believe the whales also use them to pass information between each other

A sperm whale detects its prey by sending echolocation clicks from the front of its nose and listening for the echo, which reverberates in a fatty sac beneath its mouth. This enables it to pinpoint a single squid from thousands of feet away.

"Sperm whales spend most of their lives in the darkness because they hunt in a part of the ocean where light does not reach," says Fred Buyle, an underwater photographer and cameraman with DareWin. "They use these clicks as a visual tool to see and analyse what's around them. They perceive the world through sound."

But as well as using clicks as a form of sonar, some scientists believe the whales also use them to pass information between each other.

Sperm whales sometimes produce special clicks called "coda clicks". When slowed down and viewed on a computer, these clicks reveal almost infinitely detailed layers. Each click contains a series of smaller clicks interlaced within, and a series of even smaller clicks within those, and so on.

The time intervals within these clicks are of the order of milliseconds, yet sperm whales can replicate them exactly. They can also make precise revisions, reorganising the pattern of the clicks within a click and then sending it back to a neighbour, all within a fraction of a second.

We want to try and access the information within these clicks and try to show that these animals have a complex language

This is a level of control that humans lack. Our voices vary constantly in volume and frequency, so that the same word spoken twice will never be exactly the same.

"Human speech is built on units of sound called phonemes," Schnöller says. "When we speak, we put it in a timescale, like 'I', 'talk', 'to', 'you.' It's analogue. Sperm whale communication is digital. They transmit a thin sound with all the information contained inside it and then they can modulate it, a bit like the way the internet works."

The challenge is to decode the clicks. "We want to try and access the information within these clicks and try to show that these animals have a complex language," Schnöller says.

One reason Schnöller and others are convinced that sperm whales possess a complex language is that they have such advanced brains.

Sperm whales have the largest brain of any living animal. At 8,000 cubic centimetres, it is over five times the volume of ours, a comparably minute 1,300 cubic centimetres.

They gather in the first 50 feet below the surface and that's where we try to study them

What's more, their neurological processes are far more cemented in evolutionary history. The human brain has changed markedly over the past million years, and we have only had the big brains we do now for about 200,000 years. In contrast, the current size of the sperm whale brain has changed little from that of its cetacean ancestors, which evolved some 55 million years ago.

In addition, the sperm whale cortex contains neurons called spindle cells. These long, straggly structures are found in humans and only a small handful of other species. They are thought to allow for rapid communication between distant brain regions, as well as allowing us to feel love, process emotions, interact socially and feel empathy for others.

All this suggests that sperm whales are pretty adept thinkers. However, even getting data on their behaviour is long, painstaking and sometimes dangerous work.

For starters, finding sperm whales is not easy. They spend much of their time prowling thousands of feet below the ocean surface in search of food. They are also easily spooked and avoid submarines, underwater robots and humans in scuba gear.

DareWin team members can hold their breath for seven minutes at a time

But they do come to the surface to breathe and socialise.

"They gather in the first 50 feet below the surface and that's where we try to study them, because it's where they seem to 'talk' with each other," Buyle says. "We try to film and record the sounds they make, so we can determine which whales in the group are sending clicks specifically aimed at each other."

This is a tricky business. "You have to try and integrate with a large group of whales," says Buyle. "That's why we free-dive, because it's not invasive or threatening at all. It's silent and it allows us to move better in the water and get the animals curious."

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Being experienced free-divers, and in Buyle's case a former competitor, DareWin team members can hold their breath for seven minutes at a time. They spend nine hours or more underwater each day, recording the animals in three-dimensional video and high-definition audio.

They take great care to let you into the middle of their group while not bumping into you or causing you harm

But how much access they are able to get is largely in the whales' hands.

"Trying to get close to a wild animal doesn't really work, because they just swim away from you," Buyle says. "We always let the whales discover us and decide if they want the encounter, because then we know they want to interact. Sometimes our boat will drop us 400m from the whales and we just wait there, sometimes for an hour, in the middle of nowhere."

Often the whales are not interested. "Sometimes they just pass by 15m away, and they see you, but they just keep on swimming," Buyle laughs. "It's exactly the same as with us, there's times of the day when you're at home and you don't want to be bothered. When they're in feeding mode, they will just dive, come up and dive again for hours at a time. They have a job to do and they're totally focused on that."

Even when the whales do play ball, being in the midst of a pod of animals 500 times your weight and 10 times your size comes with certain dangers.

Happily, being eaten does not seem to be one of the risks.

The energy from the smallest clicks is so strong that you can really feel it tingling through your body

"The funny thing about them is that they eat one and a half tons of fish and squid every day, and their teeth are seven inches long, but as soon as you get in the water with them, you're immediately sure that they're absolutely not interested in us as a potential meal," says Buyle. "Instead they are very conscious of their space in the water. They seem to be able to understand that we are comparatively useless in their environment, and they take great care to let you into the middle of their group while not bumping into you or causing you harm."

"The adults are incredibly conscious of their own size, so they can sometimes come centimetres from you and you don't even feel the water moving," Schnöller says. "But the really young whales don't really know their space, so you have to be careful."

A playful tail flick from a juvenile can be instantly fatal, and anyone swimming side-by-side with them runs the risk of being accidentally smothered.

What's more, their loud calls are an issue.

"The energy from the smallest clicks is so strong that you can really feel it tingling through your body," says Schnöller.

In one incident in 2011, a calf began jostling Schnöller with its nose. He held up his hand to gently move the whale away, and felt a sudden hot pain through his arm. Such was the power of the clicks coming from the calf that his hand was paralysed for several hours.

If you do something playful, then they stay. They love it

But some moments are worth such risks.

"The most incredible experience was when I got in the water and there was a female who had just given birth minutes beforehand," Buyle says. "There was a big pod of more than 30 whales and given that when an animal gives birth, it's at its most fragile, I was backing away. But instead, they integrated me in the midst of their group and the mother pushed the little new-born sperm whale towards me. It seemed like they could understand what I was about and that I wasn't a threat."

"So far the best connection we can establish with them is through play," Schnöller says. "They don't come just to stare at you. If you do nothing, then they leave after five minutes. But if you do something playful, then they stay. They love it."

Schnöller is hopeful that we might one day understand some of the meaning behind sperm whale clicks. However, while we know the basic structure of human language – for instance, that words can be assembled into sentences – we have no idea how the sperm whale clicks are built up.

The solution is to use advanced computer algorithms to examine thousands of clicks, breaking them down and analysing their frequency structure and organisation, and probe for common trends.

At this point, Glotin can look at a click and tell whether the whale is male or female

At the University of Toulon on France's Mediterranean coast, Hervé Glotin is doing just that.

Glotin, the head of an international bioacoustic research consortium called SABIOD, is combing through data collected from sperm whales around the world. He is using machine learning – the same techniques that banks use to predict stock market trends – to see whether each whale has a unique "signature" in their clicks that identifies them, in the same way that every human has a unique voice.

"From what we've seen, we think that each sperm whale has a pitch to their clicks, similar to the timbre of a human voice," Glotin says. "In humans, this timbre is determined [by] our vocal tract, head size and head shape. We can't yet say definitively, but the texture and fine spectral content of the clicks from a particular whale are probably dependent on the head structure and tissue of that animal."

At this point, Glotin can look at a click and tell whether the whale is male or female, and get an idea of the size of the animal.

What's more, in a study published in January 2016, scientists studying clicks made by different pods of sperm whales detected signs of different dialects or even accents. "There is a rhythm structure to the clicks," Glotin says. "Each burst of clicks comes with a particular rhythm, and that rhythm is unique to the pod of whales."

This is all promising. Nevertheless, our understanding of sperm whale clicks remains primitive, largely because the way they perceive and sense the world is completely different.

"Humans have a very poor idea of high-frequency and high-intensity acoustics, because we don't live in these kinds of worlds," Glotin says. "Our acoustic range is 100Hz-20kHz, with a decibel range of 40dB. And that's it. Sperm whales can process acoustic information from 5kHz-50kHz with a decibel range of 200dB. Their world is based around sound."

Sperm whales often communicate with whales so far away that they will never come into physical contact

The whales may even use sound to "touch" each other. "We believe that, as a pod, they caress and touch each other at short distances using acoustics," says Glotin. "They emit very strong and heavy sounds, which vibrate inside the others like a deep caress, and that is how they display affection."

"Their body language is also extremely important," argues Schnöller. Intriguingly, when the whales send coda clicks they are normally facing each other. "We're studying their posture and looking at whether there are situations where there may be a dialogue rather than just a simple question, and if so, what sounds do they use?"

Such behaviour occurs at short distances, but because sound travels so well underwater, a sperm whale's immediate world stretches over several kilometres. We humans normally only talk to people that we can see – at least, until the invention of the telephone – but sperm whales often communicate with whales so far away that they will never come into physical contact.

This can all seem quite alien. If sperm whale communication is so profoundly unlike ours, could we ever get a handle on it?

"We don't know if they ask the same questions, or if they can have the same paradigms that we have," Glotin says.

Still, there are some things that it seems the whales simply have to be discussing. "There is… basic information which they must share with each other, such as the structure of their society, where the food is, what type of food it is, and whether there is any danger to their young," says Glotin.

We believe that, as a pod, they caress and touch each other at short distances using acoustics

Although some of this might be encoded in body language, it at least gives us a place to start.

"From the level of detail within the click, we can try to ascertain whether the whale is looking for a squid with precision, or whether it has a question in mind, such as the size or quality of the squid," says Glotin. "I am sure that within the clicks we will eventually find cues as to whether the whales are hunting or socialising, by looking for the level of stress in the click structure."

Still, deciphering what the clicks represent to other sperm whales – let alone making comprehensible clicks of our own – remains a distant dream.

"Acoustics for them is their eyes," Glotin says. "By playing with frequencies, decibel levels and rhythms, they are drawing complex scenes to their neighbours. And we are not ready, I think, to imagine what can be drawn by those sounds."

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