The hand-painted calligraphic strokes, drawn in thick, black lines, are works of beauty. Two or three kanji characters – some with as many as 20 directional turns – grace each of the sheets of rice paper arranged in the shop glass. The handmade paper’s flecks of white grain undulate against the midnight-black paint; the sheets’ rough-torn edges highlight the smooth perfection of the brushstrokes.

Haiku? Art? If so, how much would each of these exquisite pieces cost? In fact, the signs read: “Gout”, “Neuralgia”, “Sleep Deprivation”, “Vein Thrombosis”, “Vertigo”, “Canker Sores” and other assorted afflictions for which the little shop offers herbal remedies. (Judging by the contents of the jars, a common prescription is one pickled seahorse before bedtime.)

The signs, and the riddle they contain, are typical Tokyo, though the shop itself is Chinese. Beneath its concrete ugliness and anonymous vastness, Japan’s capital hides beauty and wonder in every crevice. Naturally, for those who will it so, the same holds true in reverse. For them, a better symbol of Tokyo might be Nihonbashi bridge, the historic stone landmark now buried beneath a thundering flyover. Behind every calligraphic swirl lies gout.

But Tokyo is mystery revealed, not mystery trampled underfoot. Though its skyscraper restaurants offer blazing night-time vistas to compare with Manhattan, the way to look at Japan’s capital is not as a whole but in fragments.

My personal image – actually one of thousands – is three blue-uniformed policemen outside Shinjuku Gyoen park in spring, staring, in deadly seriousness, at a single cherry blossom. With a scandalous lack of crime to go round, they were examining the delicate pink leaves with as much intensity as if they had chanced upon a strand of hair on a bloody knife.

I had reduced a city of 30m people, a conservative estimate for greater Tokyo, to the fluttering hearts of three badge-wearing professionals. They had gone one stage further, condensing their surroundings to a few fluttering petals.

Tokyo is not a planned city like Kyoto, the much older capital of grand straight lines and grander temples modelled after China’s Xi’an. Outside the wide, Tarmac boulevards of the centre and the expressways that have been hacked through its concrete jungle, Tokyo is a tangle of side streets, switchback hills, narrow pathways, railway crossings, footbridges, alleyways, graveyards, tiny parks and medieval-style embankments.

Arranged into chome, or closely packed neighbourhoods, Tokyo’s maze of streets and twisting lanes is so complex that, before the age of car navigation systems – ka navi in abbreviation-crazy Japanese – people routinely faxed each other maps to give visitors a sporting chance of reaching their destination. (What they did before the fax machine, I leave to historians.)

In much of Tokyo, one is still more likely to hear the ting-ting of a bicycle bell or the hissing of train brakes than the rude intrusion of a car horn. In few other conglomerations of comparable size (and there really are no conglomerations of comparable size) can one turn down a side street and immediately feel oneself in a village, with its tangle of bicycles and tumble of shops.

Far from a modern concrete jungle – though it is, indisputably, a modern concrete jungle – the whole earthquake-prone city has an impermanent feel, like a circus tent that could be packed up at a moment’s notice. Little wooden buildings, concrete prefabs and clapboard stalls are still surprisingly common. Even the taller buildings, with the exception of blinding glass skyscrapers, look as if constructed of Lego, a mess of bricks and marble and concrete in variegated colours and angles. Tokyo feels more like a living creature than a stable fixture, a place where buildings are put up and pulled down every 20 years and where plants in summer push through every crevice with conquering ambition.

The city was, indeed, a bit of an afterthought. In 1590, when Ieyasu Tokugawa, a powerful warlord, was offered the wilderness around Edo Bay in exchange for his territory near Kyoto, his followers thought he was mad to accept. True enough, the offer was made by a rival warlord to get him away from the centre of real power.

But Tokugawa had other ideas. He set about turning his backwater into an illustrious capital from which he could dominate the country. He constructed an imposing castle behind a moat, now the Imperial Palace, from which, just 10 years later, he would emerge as the ruler of all Japan after the decisive battle of Sekigahara.

Kyoto, where the emperor then lived, was left to dabble in tea ceremony and symbolism. Power shifted to Edo, where lords from throughout Japan were obliged to spend half their time. Each summer, the country’s highways echoed to the pomp of the daimyo lords’ travelling retinues. All roads led away from Edo and all roads led back.

By 1700, upstart Edo had swelled to a million people, already surpassing the venerable cities of Europe, the Middle East and China with their hundreds, even thousands of years of history. By 1868, when the emperor was transferred from Kyoto as symbol of the Meji revolution, the newly renamed Tokyo became the capital of an ambitious world power that would go on to fight Russia, China and, eventually, America.

Even as it mushroomed, Tokyo never achieved permanency. Rampaging fires regularly swept through the wooden city and, in 1923, a huge earthquake buckled the land beneath, killing 143,000 people and destroying large swathes of the city. Two decades later, US firebombs incinerated 100,000 civilians and 16 square kilometres of buildings.

Fortunately, despite each new catastrophe, Tokyo squandered the chance to plan anew. Streets and buildings simply sprang up in their old patches, like seedlings thrusting from the same bed.

To take in the essence of Tokyo, one simply needs to study one of its seedlings. Turn left instead of your usual right, or head down an unknown alleyway at night, Tokyo’s most magical time, when shadows fight with the glow from red paper lanterns and with blazing neon illumination. Open the sliding paper-slatted door of the shop with steam billowing from its entrance. Or walk up the dingy stairwell and tap on the door marked with Chinese characters you can’t quite make out.

I simply got off the train. I left the purring Yamanote Line, which circles central Tokyo – at a station I must have passed dozens of times but whose name had never registered. I could have alighted at Hamamatsucho, or Takadanobaba, or Nishi-Nippori or Uguisudani.

Instead, for no particular reason, I chose Komagome. And there was Tokyo. Within seconds I was furiously scribbling in my notebook. How could so much diversity be shoehorned into so small a space?

I took the east exit, through a Victorian-style tiled archway. It gave out to a pedestrianised street, with a tiny plant-infested lane breaking off to the left along the railway tracks and, on the right, a thicket of basket-fitted bicycles, many unlocked.

I took to writing down the types of shops. Within an improbably short distance – I still can’t understand how they could all squeeze in – were: a soba and udon noodle stall, steam floating from a curtained-off kitchen; a French bakery, plying baguettes and authentic curry buns; a pachinko parlour, rattling with the sound of people exchanging money for demonic silver balls; a ramen shop; a fish stall; a dowdy fashion emporium; a “snack” hostess bar; two coffee shops; a hair salon in a pillar-shaped building; a karaoke bar; a wooden Japanese restaurant with large paper lanterns hung outside; a watch repair shop; a Daily Yamazaki convenience store; two estate agents; a photo shop; another soba restaurant; a Y100 shop, where all items cost 100 yen (expect for those that don’t); a yakitori chicken restaurant; a flower shop filled with orchids; a shoe shop; a Chinese dumpling shop; a tempura takeaway; a book shop, mostly comics; and a sushi restaurant, with little lacquer boxes displaying the lunchtime specials available behind its slatted, secretive wooden doors.

The most extraordinary thing about this little street was its utter ordinariness. Every street in Tokyo is like this. And no street is the same.

It was here I found my gout calligraphy. Yet, no doubt, I missed some other treasure, discernible only to the trained eye of the cherry-blossom-viewing policemen.

David Pilling is the FT’s Tokyo bureau chief

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