In 1909, 60 white single-storey houses rose from a bumpy sand dune a mile from the ancient port of Jaffa. The middle-class Jews who had purchased the 55-acre plot hoped to achieve a way of life that belonged to the Jews themselves. This had proved impossible under the shadow of their Arab landlords in Jaffa. So was born the world’s first Jewish city in 2000 years. “There is only one Jewish city,” wrote the novelist Joseph Kessel a couple of decades later, “and that is Tel Aviv.”

Taking its name from a not very good novel by the Zionist visionary, Theodor Herzl, Tel Aviv has been called many things. The Hill in Spring, The White City, The Riviera of the Near East, Tell-a-Bluff, Medinat Tel Aviv (“the state of Tel Aviv”). A city without a past in a country with too much history, today it is content to be known by the rest of Israel as “the Bubble”.

In Tel Aviv, everything goes on as if nothing is happening at the front. Its conversations are not to do with “the dark fundamentals of truth and cruelty”, but, as the travel-writer Jan Morris overheard, “only the cost of cucumbers or why little Moshe can’t spell.” A manic young waiter tells me during his cigarette break, “Tel Aviv feels like a bubble. It has everything, but the concrete can choke you. There’s no rest, no calm. The conflict is always there, but because there’s no rest we don’t have to think about it.” His reluctance to dwell on what might be occurring in Jerusalem – visible on a distant hill – or in Gaza 50 miles south, helps explain Tel Aviv’s dislocating 24-hour energy. On a tree-shaded bench in Rothschild Boulevard, I fall into conversation with a “communications investor” reading a Murakami novel and recently emigrated from Boston. He cheerfully passes on what someone told him on his arrival 14 months before: “It’s a happy place because people realize they might one day be dead.”

Not that this is a dangerous city – actually, with its fortress border and double-ring of missile protection, it’s probably among the safest in the world. But in its frenetic, insecure and touching way, Tel Aviv is keen to remind you of its kinship to all those other cities from which its inhabitants have streamed.

“It’s the result of a passionate night between New York and Miami,” was a slogan I heard – this to explain the city’s vibrant combination of business and pleasure. Personally, it appears more like the pushy offspring of a one-night stand between Canary Wharf and Tangiers, with its dilapidated alleys, crumbling Bauhaus balconies and ever-sprouting concrete skyline – one morning, I counted 60 cranes pecking away at half-erected tower-blocks.

As with Tangiers, most people in Tel Aviv are not what they were before. For one thing, they are free. Walking along its crowded beach on the Sabbath, the day that best brings out the character of the place, I have to pinch myself. This is where Jews really could be themselves for the first time.

If a single image encapsulates Tel Aviv, it is feet. Bare. In flip-flops. In orange trainers. In green high-heels. In office slip-ons. But no longer the feet of the Wandering Jew, in flight and pursued since the time of Abraham. As the English traveller Dorothy Kahn observed back in 1935, once you have caught the music in the freedom of these feet – jogging, playing beach tennis, pedalling along with dog in tow, dancing on a tabletop at Ninochka’s bar – the effect is irrevocable. “Never will you not be able to like Tel Aviv.”

The city demands to be explored on foot, being flat and easy to navigate. It was laid out in a simple grid by a Scottish town planner called Geddes in the 1920s. But be warned. There’s nothing here for holy pilgrims, no sites of antiquity; nor does it boast of anything iconic. Instead, it celebrates the secular, and offers up, in place of the Almighty, a fairly heavenly combination of the senses – food, wine, people, culture, nightlife. “There isn’t one specific thing which makes it different,” decides a Tel Avivan woman brought up in Peru. “What makes it different is its vibe. Tel Aviv has a special vibe.”

You catch it in the air on Rothschild Boulevard, in the slightly burned smell of good hummus. In the expressions of young men on their laptops outside Café Landwer, hoping to create start-up companies in cyber-security or bio-medicine (not least so they can afford the city’s astronomical rents). In the faces of the young women strolling by, straight-backed and fit (a by-product of their military training which continues to require many Tel Avivans to do two days a month reserve duty). In the messages on their T-shirts: “Vive le Rêve”, “J’aime les mauvais garçons”, “Life is a bitch, but she can love you if you let her”.

A prize-winning Tel Avivan documentary-maker remarks of his city’s women: “They look like Brazilians, can argue like the French, and complain like nice Jewish girls.” Currently working on a film about Tel Avivan prostitutes, he has noticed a surprising but telling trend. “In dominatrix parlours, young women want to be slaves. Why? Because women here feel dominant, comfortable – and very sexy.”

Sit in a café and strike up a conversation and you find that everyone speaks English, has a story to tell. It’s a place where the questions are frequently better than the answers – which invariably take the shape of still more questions. Aged 86, Amos Oz is Israel’s leading writer and, for many here, its conscience. “As a child, I asked my father why do you always answer a question with a question. My father said: ‘Why not?’”

We sit sipping coffee in his twelfth-floor apartment that looks down over Tel Aviv – “the last stronghold of a sane Israel,” he has called it – to the sea. For Oz, what we’re gazing at is “a very Mediterranean city”, not Barcelona, but similar: creative, warm-hearted, temperamental, noisy, materialistic. “Tel Aviv belongs in a Fellini movie, not in a Bergman movie,” he says. “In day-time, this city is self-confident, energetic, optimistic, sometimes even aggressive. At night, it turns into the refugee camp, full of hysteria and insecurity and terrible traumas. There are more troubled dreams per square kilometre than any town I know.”

I ask: “If the Founding Fathers came back, what would they make of it?”

“They’d be very ambivalent,” he admits. “On the one hand, it is a fulfilment beyond their wildest expectations. On the other, a disappointment below their darkest fears.”

Even so, despite Jewish racism, chauvinism and violence, Oz still believes that the city where he has chosen to retire remains something of a miracle. “Tel Aviv is a dream come true. One hundred and seven years ago, it was a mere title of a futuristic novel by Herzl. The only way to keep a dream rosy and unsullied is never to live it out. That is true of any dream – about travelling, about having sexual fantasies. Israel is flawed because it is a fulfilled dream. It’s not about the nature of Israel; it’s about the nature of dreams.”

In pride of place on his study wall, Oz shows me a handwritten list compiled by one of the world’s authentic dreamers: a framed page, taken from Franz Kafka’s notebook, of the Hebrew words Kafka was teaching himself. Oz, who was taught by two of Kafka’s former classmates, runs his finger down it, translating: equilibrium, human, duty, equality…

“In 1911, Kafka dreamed of coming to Palestine. He wanted to start a restaurant in Tel Aviv with his last love Dora Diamant. He would be the waiter, she would cook. Imagine giving a tip to Kafka!”

I recalled Oz’s words in the bustling restaurant I sat in beside the main synagogue; also Dorothy Kahn’s observation: “Never before had I seen a waiter serving so many people and all talking Hebrew.” I don’t think I was served by a budding Kafka that night (in the event, Kafka never made it to Palestine), but I did talk in staccato succession to a publisher, a music critic, a jeweller, plus the daughter of Ben-Gurion’s bodyguard. I was impressed by how open and direct they were. As well, by the unanticipated quality of the local food and red wine – although an earlier walk through the Carmel market ought to have alerted me; the baskets of spices, dates, ebullient-coloured tomatoes and cucumbers, a momentary affirmation of a remark by the New Zealand globetrotter, Hector Bolitho: “Tel Aviv is the expression of an ecstasy.”

Tel Avivans may tell you their city has no one thing that is special, it’s all in the general vibe. Yet there is a place you must visit, and it’s called Jaffa.

Jaffa in Hebrew means “beautiful”. It stands at the end of the beach, a magnet with the sun on its walls; alone, modest, and its sandstone that is the colour of corn a chastising contrast to Tel Aviv’s concrete. A promenade leads you, past fisherman gripping mast-high rods, to the oldest port in the world. From here Jonah fled God into a whale’s jaws. This afternoon, the small harbour (c. 4000 years old) is a Cubist riot of Mirror dinghies full of children learning to sail. Richard the Lionheart leapt ashore near here to relieve his garrison, then besieged by Saladin. The English King wore on his feet, we are told, the deck shoes of an ordinary sailor.

In Jaffa’s famous flea-market the pyramids of old shoes for sale have come from the apartments of the dead. I stand for a moment, imagining the lives of their owners, until a thin-faced trader in a yellow headscarf interrupts my reverie. “You always find crazy stuff,” he says. Once in Bnei-Brak, not far from Tel Aviv, he uncovered a rocket-propelled grenade launcher in a box. “I gave it to the police. What am I going to do with it? I don’t have any bad neighbours.” He’s joking, yet in Jaffa his words ring almost true. Inside the Abuelafia bakery, the boys serving doughnuts seem proud to wear their orange T-shirts with the logo: “Jews & Arabs refuse to be enemies”. Trapped in the telegraph wires further up the street, a toy aeroplane rainbowed with the colours of Gay Pride Week, which took place a few days before, dips and flips in the warm sea-wind, and tantalises passers-by with a fragile hope: If only we learned to celebrate our religious and cultural differences as joyfully as our sexual ones, how high we might fly.

The best thing I saw in Jaffa – in fact, the best thing I saw in Tel Aviv – was the Ilana Goor museum, in an old house overlooking the port. I sat on the roof terrace with its exuberant owner/curator/founder, surrounded by an eclectic collection of kitsch, modern and ancient art, plus examples of Goor’s own work. Exciting was the way that each object complemented and sparked off the object next to it, as if she had captured Tel Aviv’s elusive “vibe” and wittily recast it in plaster-of-paris and chickenwire.

Ilana Goor is a 79-year-old, immensely well-connected Jewish sculptress: her statue of a woman holding a child with shoes on, “Never Again”, is on permanent exhibition at Jerusalem’s Yad Vashem holocaust museum. She makes no apology for her dominant role in her own museum. “Every nail in the wall, I’m involved. It’s one eye, one person’s taste. The eyes do not rest, they adjust to something different.” Her collection attracts many visitors to Jaffa.

She grew up among Arabs in the northern town of Tiberias, speaking fluent Arabic. “I said, ‘If ever I come back I’ll only live in a town with Arabs and Israelis.’” Jaffa was the nearest example to her childhood model that she could find in modern Israel, a repository of the long Palestinian presence here. She sighs, “I love them more than my people.” She hires local Arabs to work in the museum, in the foundry, in her house. “And with my big mouth I have a good name. I support the place all out of my own pocket. For twenty years, it’s existed.”

Afterwards, I wandered a short way up the hill to the old French lunatic asylum of Saint Louis which the English architect, John Pawson, is converting into apartments for short-term rentals. Like Jaffa’s Turkish prison, which is being turned into a boutique hotel, it’s a sign of the feverish building activity that is evident in every direction – the Ritz is about to erect a 50-storey hotel off Rothschild Boulevard. It made me think of another story I’d heard, about the traveller who asked: “Is there a loony bin in Tel Aviv?” And the answer: “We’re just going to put a roof over the city.”

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