This must have been what Alice felt like when she climbed through the Looking Glass.

Alleyways narrow and narrow as if to dwindle away, then suddenly open onto a square teeming with people. You set out from, say, the train station to find Piazza St. Marco and end up miles from either, staring up at a statue of the Virgin wearing a halo of twinkling lights.Maybe Venice works an alchemy that tricks you into traveling away from the direction you're aiming, the way your finger defies your brain trying to trace a pattern in a mirror reflection. Or maybe the rainbow-colored lights of the Venetian glass in every other shop window hypnotize you into wandering like a sleepwalker.

Whatever the cause, there's only one thing to do: Succumb.

You will get lost. You'll receive an alleged map at the tourist office. But Venice, built centuries ago around waterways, is a cartographer's nightmare. Native Venetians, a local explained to me, negotiate the city's bridges and trails via a mental map. Anyone else is left to squint at street signs and trace hypothetical routes on a map that's to actual roadways what Picasso's three-eyed Cubist females are to real women.

So don't try to figure out where you are. You're in possibly the most beautiful city in the world; what else do you need to know? Just start walking.

Virtually every corner features a sight of jolting beauty - an ancient Catholic altar carved into a wall and modernized with plastic flowers and Kodaks of the recently deceased. A glass-topped capillary canal reflecting the umber walls of the palazzi on each side of it. A circular courtyard staircase built to resemble the Tower of Pisa.

Much of the time, the object-of-beauty's purpose is unfathomable: An iron dragon mounted on a wall and holding multicolored umbrellas in its teeth. A statue of a horse walking on the water of the Grand Canal. A circle of park benches of which only one is occupied - by a collection of cats sunning themselves.

Walking is not a way of getting places, as it is in other cities. Here, walking is the city: Turning a corner into a view of a clothesline of underwear suspended over a canal. Getting caught amid a group of nuns in wimples and sturdy shoes. Coming up suddenly upon the Rialto Bridge and its view of the Grand Canal, so beautiful in color, architecture and people that it hurts to look. Finally glimpsing the to-the-horizon Adriatic Sea and the gauzy veil over distant islands.

Don't visit any museums in Venice if you can help it. That's what the rest of Italy is for. Florence has its Uffizi; Rome has everything else. Venice is a respite from that, a place you'll probably reach after days of doing the travel-book itinerary in other Italian cities.

Color is rampant. There's the Venetian glass: pink-and-white chandeliers like spun sugar, perfume bottles made of what looks like melted Christmas candy. The fruit market, with its rows of fat grapes and berries out of some Renaissance still life. St. Marcos square, where the Basilica sits, embedded with multi-colored mosaic tiles and whose columns are each made of a different pattern of marble. Even the street vendors' gelati, with flavors such as nougat and pistachio, is a pastel rainbow.

Occasionally, you'll want to get to a specific place at a specific time, in which case you should leave breadcrumbs. My friend and I gave ourselves plenty of time to locate a church where a guitarist would give a Bach concert later that evening. We had asked our hotel concierge for directions, and he drew the route on our "map."

"Fifteen minutes to walk there," he said. "For me, five minutes." (He was a native.)

We found the church almost immediately and bought our tickets. Then we looked for a restaurant. A few turns, a few bridges later we came upon a trattoria that played reggae music and served us spaghetti with clam sauce and fried calamari. We left 15 minutes before concert time.

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We walked and walked, positive the church was around the next bend. We may have gone in circles, it's hard to tell. Our map was little help because it named only some streets. For the first time, I felt panic, a sense that there was no reasoned way of negotiating this maze. It was only with the help of an Italian man that we finally found the church again. We arrived 30 minutes after the concert started.

The frustration, though, melted away inside the church, all white marble, frozen angels and Tintoretto-like paintings.

But it also had its jolt of the unexpected: a black skull-and-crossbones imbedded in its otherwise pristine floor.

Curiouser and curiouser.

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