On the Münsterhof cobbles, drizzle pooled around a stone commemorating British statesman Winston Churchill’s call for a “United States of Europe”. Placid Zurich may be famous for banks and shopping, but its conservatism is often a mask, adopted reflexively. Tales of revolution flow beneath the surface.

I’d arrived at the Münsterhof on a walk through the Old Town, which straddles the River Limmat as it flows north out of glacier-fed Lake Zurich. Behind the Bahnhofstrasse boulevard – the closest Zurich gets to ostentation, with its halogen-lit outlets for Vuitton and Cartier – I’d climbed from the artist workshops of the riverside Schipfe quarter to stand where the Romans stood. On the Lindenhof hill, their Turicum customs post once exacted levies from passing traffic. Now, oldtimers play giant chess while loafers daydream beneath foliage.

The Münsterhof is a short clickety-clack away, over the patterned cobbles of Chimney Sweep Alley, Swan Alley and Stork Alley, leaning against the gradient. Having absorbed one kind of vision – Churchillian – I ducked into the adjacent Fraumünster for another. This 13th-century church sports exquisite stained glass by Marc Chagall, installed in 1970 in five, soaring, Romanesque choir windows. A blood-red image of Elijah in the chariot of fire, an angel trumpeting eternity and only the faintest impression of a crucifix: the juxtaposition of modern art and medieval architecture hints at Zurich’s heterodoxy. This is, at heart, a revolutionary city.

Half a millennium ago, Zurich’s twin-towered Grossmünster (Great Minster), on the opposite bank of the Limmat, was briefly the epicentre of the Protestant Reformation, a tight-lipped theological hurricane that swept the world. From 1518, in twelve years at the pulpit, Huldrych Zwingli – a contemporary of Luther’s – railed against ecclesiastical corruption, preaching individual liberty and the sole authority of the word of God. Zwingli trounced a papal representative sent from Rome in public disputation, and as the city embraced Protestantism, he celebrated Mass for the last time in 1525. His church remains bare inside, its beauty all in lofty austerity – and revolutionary associations.

And then there’s 1916. A few hundred metres along the narrow Niederdorfstrasse, I caused a pram-pushing mother to tut by stopping short outside the low corner windows of the Cabaret Voltaire, where that year a group of artists defied bourgeois sensibility to form the “anti-art” movement Dada, wild forebear of Surrealism. Round the corner shoppers and besuited bankers were passing by the house at Spiegelgasse 14, marked with a plaque noting that Lenin lived there until he departed to lead the Russian Revolution. Five minutes away, amid the plotting and the iconoclasm, James Joyce was holed up in the ground-floor flat at Seefeldstrasse 54, writing Ulysses.

Other cities offer up their choice tidbits on a platter for visitors’ consumption. Zurich, though, doesn’t preen. It’s the city’s capacity to surprise – where what is left unsaid resonates more than what is said – which helps me love it.

And, of course, everything works. The Swiss design aesthetic, apparent in everything from architecture to fashion to the national train timetable, could be summarised as elegance through efficiency. Moving around the city you feel as if there is invisible machinery at work to make things right: not merely that somebody thought about that railing or that roadsign, but that somebody thought about it specifically in relation to me.

The design of the public realm – not just public space, but all the million things that make life function – is so unobtrusively brilliant that even noticing it requires effort. In more boisterous countries bad design forces itself onto you, invading the space between your ears by making life just that little bit harder. In Switzerland, where you can rely on everything to work, your thoughts are your own. Some outsiders, apparently preferring a life of grumbles, have concluded the country is bland. They lack imagination. Switzerland sets you free.

Take the clocks. Zurich railway station has dozens of them, their broad, numberless white faces supported on horizontal stanchions above the platforms, each featuring a red second hand tipped with a large red circle – odd for a country obsessed by accuracy. But look. As the second hand sweeps round to twelve o’clock, it stops. Everything stops. For a second, nothing happens. Then the black minute hand lurches forward, the second hand begins its sweep again, whistles blow, train doors click shut and another minute is dispatched to history.

Since I first saw that, years ago, that image of the temporarily jammed yet eternally accurate clock nagged away at me. How can Swiss railways rely on clocks which stop for one second every minute?

Birgit Bircher solved the mystery for me. Brand manager at Mondaine, a Zurich firm who have sole rights to produce a watch replicating the design of those station clocks, she explained that the idea arose in 1944. At that time Swiss Federal Railways tasked engineer Hans Hilfiker to design a clock to be used across the network that would be both highly visible and pinpoint accurate. First, Hilfiker did away with numbers. But his genius came in conceiving each clock as a slave, controlled from a central master by an electrical pulse produced at the top of every minute. This pulse pushes the minute hand of every clock on the network onto the next mark at precisely the same moment.

But in a country where trains depart on the dot, a problem remained. Since the minute hand could not move until the pulse came, how would people rushing for their train know whether they had 5 or 55 seconds before the scheduled departure time? (Such are Swiss concerns.) With the lack of a mechanism inside each clock, no tick was possible. Hilfiker, therefore, introduced a sweeping second hand, powered by mains electricity. For maximum visibility, he designed it in red and tipped it with a circle, to mimic the handheld “lollipop” signs used by station-masters to signal to train drivers.

Then, Bircher told me, came a yet more abstruse refinement. Fluctuations in the mains current meant that Hilfiker’s second hand could not be relied upon to complete a full circle in exactly sixty seconds. So he tweaked his design to make every second hand run very slightly fast: it didn’t matter when each one reached the twelve o’clock position, since they all had to wait there for the centrally issued pulse.

And this, she finally explained, is why the second hand stops at the top of the dial. Even today, Swiss station clocks mark one minute with, on average, 58.5 seconds, creating a tiny, breathless pause before that pulse shunts every minute hand onward simultaneously.

Hilfiker’s 68-year-old design is a triumph: in one glance it imparts information more quickly and precisely than a digital clock ever could. It is mesmeric to watch.

With the giant four-faced clock above Zurich’s station concourse momentarily frozen, I headed out to meet art curator Boris Magrini. This summer Zurich is hosting an eclectic city-wide exhibition of public art by the likes of Ai Weiwei and Richard Tuttle. Most pieces are dotted around Zurich West, a quarter of towers and post-industrial warehouses flanking the railway lines behind the main station.

As we walked beside a brick viaduct – every arch now occupied by independent galleries and design stores – we discussed why Zurich’s image of prim reserve persists. I wondered if it was because visitors mistake cleanliness for docility. Boris raised the issue of the city’s liberal mayor, the first woman to hold the post.

“Zurich?” he laughed. “It’s not that conservative.”