There's a theory that the big problem with Switzerland is that it doesn't have any big problems. Take away war, strife, indolence and poverty from a country, and what's left is cheese; without blood red in the palette, the big picture is painted in pastels. Orson Welles summed it up in The Third Man: "For 30 years under the Borgias, Italy had warfare, terror, murder and bloodshed, but they produced Michelangelo, Leonardo da Vinci and the Renaissance. In Switzerland, they had brotherly love and 500 years of democracy and peace, and what did that produce? The cuckoo clock." Bavarians will know the Swiss didn't even manage that.
It's true the edges of Switzerland can feel a bit bevelled sometimes, like when you see a front-page headline that translates as "Someone Almost Kidnapped", or when a young, pink-haired punk gets on a trolley bus, pays, and takes a moment to carefully straighten a crooked community service announcement. Harmonious doesn't mean monotone, though - there are four languages, 26 different cantons, and a loose central government that largely lets everyone do their own thing. Switzerland combines the ethno-linguistic divisions of the Balkans, the city-state jostling of Italy and the libertarian leanings of Texas into a recipe for disaster that somehow works better than just about any other country on earth.
The cantons don't have much in common by way of law or even custom, and Swiss national pride is a muted affair. But they do take pride in their shared railways. "Clean, efficient, high-speed rail" can mean industrialised farms blurring past at 220km an hour, but in Switzerland the journey is more like the rail of another era - the interiors might not be a suitable setting for a murder mystery, but the pace and the scenery (vast lakes, permanently snowy peaks) are old-school.
The trains do fulfil the postcard idea of the place - "Swiss" is a word that sits naturally in front of efficiency, cleanliness and punctuality. I've boarded these trains for a trip unencumbered by dirt and delays. But I'm also here to discover that "Swiss" sits alongside "James Bond's mother" and "legal to own a flamethrower", to immerse myself in an unexpected and varied place that's like a well-chosen, slightly eccentric and very distinct mix-tape of Western European culture.
In the shy capital city of Bern, these trains roll past a huddle of gunmetal stone buildings and a medieval clock tower, the Zytglogge. The clock is synchronised to the clocks at the station, and the trains are synchronised to the clock, a feat that didn't require a Mussolini to accomplish it. Just to show you can have a pearl without grit, a young clerk had a good look at that clock every day on his way to work, and our understanding of time hasn't been the same since.
Albert Einstein is an unlikely candidate for the title of the city's most famous resident - the Bernese count themselves alongside the Irish and the Poles as being proverbially slow. ("Why shouldn't you tell a joke to someone in Bern on a Friday?" "Because they might laugh in church.") They're frequently compared to the ancient symbol of their city, the bear, and, despite the ribbing, seem to take a kind of pride in being slow and deliberate. They're also perennially thirsty, which means they make friends easily. Not far from the city's famous bear pit, I drink a few steins of beer with a young Bernese businessman on the balcony of the Altes Tramdepot restaurant. Remo ("In Italian, it means 'I row'") sits facing the Aar River and tells us about his city.
Bern used to be three cities on this bowed peninsula, and the town still draws its character from the river - a long, wide loop of cool water at the foot of a deep valley. "Bern is not as arrogant as the other cantons," Remo says. "Bernese are easygoing people, friendly, open, spontaneous." They literally go with the flow: in summer, bold swimmers walk miles up the banks of the Aar with rubber rafts, then jump into the waters from a low bridge or embankment, letting the current carry them down river before grabbing one of the handles protruding from the bank to drag themselves out. "You must start trying to get out three or four handles from the end," says Remo. "Otherwise, miss the last handle, and you go over the weir." No one can remember this happening.
I ask Remo what Switzerland's problems are generally, and what Bern's problems are in particular. He thinks for a long time, then comes up with this: "Swiss people - they're not in a good mood in the mornings. They will just sit, reading their free newspapers. That's a real problem." Number one on Remo's list of national problems is morningitis.
Taking the train from Bern, I board one marvel of Swiss engineering to see another: Neuchâtel canton is still the epicentre of the Swiss watchmaking industry. In the Musée d'Art et d'Histoire in the town of Neuchâtel there are three dolls which have the cutesy, slightly sinister look of Franklin Mint collectibles. These are the Automates Jaquet-Droz, some of the oldest robots - and the first computers - in the world, built by a watchmaking genius some 230 years ago. They have names - the Draughtsman, the Writer, and the Musician - and in a darkened room their well-oiled operator puts on a show once reserved for the royalty of Europe.
Once wound up, the draughtsman's pencil picks out a detailed sketch of a dog, complete with light and shade. The musician tinkles her way across a real pianola, her chest rising and falling as she plays; and the writer can produce almost any short sentence, dipping his quill and following even, flowing script with his glassy eyes. They're impressive and uncannily chilling at the same time. When the Automates were first demonstrated for the Spanish court, the king ordered them pulled apart, trying to find the evil spirits inside. Watching these weird beings at work, you can see where he was coming from.
These bizarre and fascinating creations are among the things - including 140 garish street fountains and a lake where elephants wash themselves when the circus is in town - that give Neuchâtel a sense of the surreal. Here the language and the food are French, and the grey buildings of Bern have given way to the distinctive yellow stone of Hauterive. The French writer Alexandre Dumas senior thought it made the place look like a "toy town carved out of butter", recalling a cruel time when toys were made of butter.
Our next stop takes us away from the train lines, and to a place that has a different kind of chilling effect. While the sharpness is coming off the frost elsewhere, La Brévine, just north of the Val-de-Travers and better known as Swiss Siberia, is still hoary with swells of snow and ice. This string of dark farms in a valley is the coldest inhabited place in the country, a place where cheese-makers, farmers and the odd visiting cross-country skier brave temperatures as low as minus 35 degrees. The hospitality is warm, though, and a couple of old farmers, Mr and Mrs Schmidt, fresh-looking but permanently ruddy with the cold, stop us poking around the edges of a frozen lake and invite us into their farmhouse.
The Val-de-Travers is famous for two things: cold and absinthe. After some not-so-subtle prodding, Mr Schmidt produces a jumbo bottle of the poison, and Mrs Schmidt goes to the kitchen for the spoons, coming back with a full set of regalia and performing the full water pour and louche on the kitchen table. It's weird to take absinthe with a couple of robust old farmers instead of emaciated arty types coughing into hankies, but the Schmidts have to keep warm somehow.
Emboldened (aka tipsy), I ask whether there is any moonshine in the area, and Mrs Schmidt looks scandalised. "Eau de vie?" she says. But it doesn't take Mr Schmidt long to produce a heavy bottle with an ancient label marked "Gentian Pure". "This is a traditional brew made from the roots of herbs and flowers that grow on the hillsides nearby," says Mr Schmidt. "This bottle is over 50 years old. I'd like to offer you some, my special guests from Australia." Gentian Pure tastes exactly like dirt. Offering thanks with a barely operational tongue, I head out past a petrified fox, wondering how he was pickled.
La Brévine isn't the only place that hasn't shaken off its snow in the Swiss spring, and when I rejoin the train line, it's to board one of the most famous trains in Switzerland. The Glacier Express runs from the resort of St Moritz, through Chur, past the rail hub of Brig, and through to Zermatt. I take it from Chur, where it tilts almost over the swelling waters of the Rhine, passes through sloped farms and tiny hilltop church spires, travels along thin arched bridges, and finally, ratcheted up by a pinion system, makes its way high into the pass of the Oberalp. Here, 2000 metres above sea level, it earns its reputation as the slowest express train in the world, easing up the slopes at less than 40km an hour. The tiny dark skiers easing down the slopes must be going faster.
Not far from Chur, there's an even more remote place called Vals, a tiny alpine village that was once faced with bankruptcy and an empty hotel. Rather than pack it in, the locals pooled their natural and financial resources and enticed the reclusive Swiss architect Peter Zumthor to use the mountain and the natural springs to create a spa. The modern masterpiece he created is called Therme Vals, and it draws cars and coaches up the mountain roads to this remote place for most of the year. From 60,000 slabs of locally quarried Valser quartzite, Zumthor built a cathedral to water: a cavernous series of pools and steam rooms bathed in cool natural light, capped off by a turf roof that gives the whole edifice an ancient feel, as though it was carved out of the mountain itself.
Outside, a pool of naturally warm spring water extends into the open air, where steam mixes with frosted breath, and swimmers can take in the clouded mountains on the horizon. It's an isolated, stark, beautiful place at the foot of a mountain, where the almost sheer farms (some can be accessed only by sled) make you wonder what type of people must have settled here. On the ridge against the skyline, someone pushes something, inching it along the precipitous ridge. It's a pram.
Vals is one of the few areas of the country where Switzerland's fourth official language, Romansh, is still spoken. Only around 35,000 speakers are left, and because there are at least five different dialects, many struggle to understand even each other. Bilingualism and TV are slowly killing the language, but pockets of the distinct Romansh culture survive. At a local café, we're treated to a specialty called capuns. It's a mixture of bacon, cheese, three different kinds of chopped sausage, milk, eggs and herbs, wrapped in silverbeet, cooked in milk and bouillon, garnished with cheese and bacon, all served in a glossy soup that could be broth but turns out to be melted butter. Romansh culture might be imperilled, but not as imperilled as the Romansh are by their own cuisine.
Far from the earthy, larded world of the Romansh is the urbane façade of Montreux, on the shores of Lake Geneva. There are no signs of fish in the lake. "It's actually too clean to support life," a local tells me, a verdict that at first glance could apply to the town itself, a spectacular but staid congregation of old buildings and new boutiques hunched over a lakeside boulevard, overseen by the Belle Epoque balconies of the Grand Hôtel Suisse-Majestic.
But this quiet place has long played a role as a kind of capital of bohemia, taking in artists, writers, musicians and layabouts for centuries. It might owe as much to the tax breaks as to the scenery, but these grand buildings have served as an unlikely backdrop for the turns of the culture and counterculture, full of serendipitous meetings and strange collaborations, with everyone from Dostoevsky to Shania Twain in occasional residence. Their presence is still felt in the annual jazz festival.
The weird history starts before we've even left the station: it was here that Albert Hofmann, the Swiss chemist who invented LSD, bumped into Timothy Leary, his unwanted hippy evangelist, and gave him a stern talking to. When the old casino was burnt down in 1971 by an excitable Frank Zappa fan, Deep Purple were eyewitnesses - the water in "Smoke on the Water" is here. Charlie Chaplin spent his dotage at nearby Vevey, and is commemorated by a statue on the shore of the lake. It's since been upstaged by a monument to Freddie Mercury, who also saw out his days here; he stands facing the waters in a one-fisted salute. "If you want peace for your soul, go to Montreux," Mercury told his friends, and he chose a view across the lake for the cover of Queen's Made in Heaven album. With subtle afternoon sun casting down on the far shore, it doesn't look so different today.
A few minutes down the coast is another waterscape immortalised by a visitor. Whether or not the "Byron" in the stones of Chillon Castle was scratched there by Lord Byron himself, there's no doubt the place made a deep impression on him. You can hear the lap of the water from the dungeon where the monk and politician François Bonivard spent six years chained to a pillar - a story which inspired Byron's epic poem The Prisoner of Chillon. Byron himself became a tourist attraction in the town of Lausanne, where English tourists would stay in the Angleterre hotel, training their binoculars on his house, trying to glimpse him doing something scandalous.
On the train out of Lausanne, casually awed by the scenery again, I think back not just on the things I have seen in Switzerland, but the things I haven't. It takes some time here to notice what you're not seeing: dirt, homelessness, penury, rage, anyone - man or woman - who doesn't look a little bit like Roger Federer. But the tranquillity doesn't feel bloodless, especially not once you've found the warm register of Swiss eccentricity and variety; sometimes it is stilted and strange, but for those who take the time to find it, it is as welcoming as it is humble.