Lost in the Latin Quarter, I ended up, literally, at the foot of Michel de Montaigne.

A bronze statue of this French Renaissance philosopher — balding, with a beatific smile, cape draped over his shoulders, slender legs crossed — sits on the Rue des Ecoles in Paris, opposite the Sorbonne.

He was blackish green with the exception of the tip of his right shoe, which gleamed from having been inadvertently polished by the touch of countless hands. Why? I didn’t know. But assuming his foot was a kind of community talisman, I gave it a rub before continuing on my way.

It is a tradition among students, I would later learn, to touch the shoe of Montaigne with the hope that doing so brings them luck on their exams.

I was already lucky: I didn’t have a map. If I did I wouldn’t have seen the philosopher (by the sculptor Paul Landowski) or benefited from any additional good fortune that may have been transmitted through his foot. I wouldn’t have lingered before bookstore windows or passed Square Paul Langevin, where the blossoming branches of cherry trees reached over the fence, spilling petals like pink confetti.

The ubiquity of map and navigation apps these days can be a boon, but it also means that pedestrians can easily choose efficiency at the expense of discovery.

"We travel for romance, we travel for architecture and we travel to be lost," the writer Ray Bradbury said in a 1990 interview with Rob Couteau. "There’s nothing better than to walk around Paris and not know where in hell you are."

This is true of not only Paris, but also most any city in Europe if one hopes to have the kind of chance encounters that make a vacation more than a game of hopscotch among landmarks.

My iPhone finds the most direct route to anything I wish to see, which is why I turn it off. Keeping it on would mean missing out on countless small streets and dead ends, all those quiet, beautiful lanes and impasses with names I don’t remember.

Paper maps, which are rarer these days, can also get in the way.

"There are map people whose joy is to lavish more attention on the sheets of colored paper than on the colored land rolling by," John Steinbeck wrote in "Travels With Charley: In Search of America." "Another kind of traveler requires to know in terms of maps exactly where he is pinpointed every moment, as though there were some kind of safety in black and red lines, in dotted indications and squirming blue of lakes and the shadings that indicate mountains. It is not so with me. I was born lost and take no pleasure in being found."

It is by being a wanderer, and not, to borrow a term from Steinbeck, a "mapifier," that one is most likely to stumble upon less frequented haunts.

Off Dublin’s Dame Street, through a stone arch near City Hall, past the Treasury Block building and a parking lot, around a corner and onto what looks like a service road, there is a wall of stones. On and on this gray wall goes with stones that are fat, wide, narrow and tall, and then — a gate.

There, through decorative whorls of black iron, one sees a vast, green oblong field ringed with benches and crisscrossed with paving stones in a ribbony Celtic-inspired design. On the wall that leads to the field, which dates to 1680, are the words: "Dubh Linn Garden." Step inside, as I did one June afternoon, and you’ll be on the site of the former black pool, or "dubhlinn," from which Dublin gets its name.

On that same trip, again mapless, I wandered by centuries-old Georgian houses with Crayola-color doors and, by chance, wound up at No. 1 Merrion Square, where Oscar Wilde lived as a child, from 1855 to 1878, and where his mother held salons attended by the likes of Bram Stoker. Yeats lived nearby, at No. 82.

Other aimless walks through Dublin were less historical but no less enjoyable: With little regard for time or where I would go next, I strolled through the Victorian park, St. Stephen’s Green, one morning, stopping to watch a man at the lip of a lake feed two white swans and a flock of fuzzy cygnets.

Freedom is being guided by a mood, not a map. One winter, in Italy, I arrived in Bologna for the day without a plan, having driven from Flor­ence with a friend.

Overhead, garland arches were wrapped with gold ribbons in anticipation of Christmas and, on the streets below, a chocolate festival with edible wrenches, bolts and other tools jumbled amid stalls of marshmallow rabbits and owls.

In the spring, in the Netherlands, a bus ride to Keukenhof from Amsterdam allowed me to spend an afternoon lost beside snaky rivers of grape hyacinth and tulip fields that blanketed the land like red and yellow quilts.

In the summer, in Spain, I got disoriented in Barcelona trying to find my way back to my hotel from Barceloneta Beach and was instead swept up into some sort of flag-waving celebration.

Even a trip to the most touristy spot can feel personal and spontaneous if you forgo turn-by-turn navigation. I advise glancing at a map to determine the general direction you wish to walk, then winging it.

By doing just that in Paris, I didn’t see the Eiffel Tower grow closer from a cool distance. Rather, I was instantly dwarfed by it when I happened to glance skyward from a street in the shadow of the tower’s lattice belly.

Similarly, my inability to figure out how to get beyond the roundabout to the Arc de Triomphe made my (eventual) arrival there that much sweeter. I walked the last of more than 250 steps to the terrace and sat on the cool limestone to watch the sun disappear, with the avenues of Paris fanned out around me like pleats of a skirt frozen in mid­twirl: east toward Sacri-Coeur, west toward the woods of Bois de Boulogne, north to the Levallois-Perret cemetery, south to the Sorbonne and the lucky foot of Montaigne.

Stepanie Rosenbloom, New York Times

© 2015 The New York Times Company