It has led to adventures we never expected - but will never forget.
Last spring, while touring the westernmost section of China's Great Wall at Yangguan Pass, we happened upon "Mike," a 7-year-old parked in the shadow of a rampart, regaling passersby with tales of ancient China.
The Silk Road, the trade route linking China with medieval Europe, ran through this part of Gansu Province, and Mike knew its history well.
He wore a blue jogging suit with a name badge pinned to his chest and sported one of those haircuts that mark a stylish Chinese kid - short around the ears with a dark tuft above his forehead. But he spoke with the brisk authority of a college professor, and we couldn't help but stop to listen, lagging behind as our tour group went on.
Mike ("I won't bother you with my Chinese name because you would never be able to remember it") grabbed our hands and led us around the ramparts. He chattered about the doings of folks in these parts in olden times, and said his grandparents were about our age.
His badge wasn't official, he told us sheepishly. He was a volunteer, much too young to be a real guide. But his English was perfect, without an accent. He said he taught himself by playing computer games and watching Western cartoons on TV.
Meanwhile, his father stood off to the side, grinning broadly, and the real guides passed by with stiff, indulgent smiles.
We only tripped him up once. Accidentally.
When we described the scuppers that let rainwater run off the ramparts as being "kind of like a bathtub drain," he looked at us as though we were from outer space.
We tried to explain, but computer-game English apparently doesn't include bathtub.
Others in our group may have learned more official Silk Road history. But they missed Mike.
On another trip, a few years ago, we arranged to stay at a kibbutz in the Galilee region of Israel. Orthodox Jews ran a hotel, farm, and furniture factory there.
"Why would you want to stay at an Orthodox kibbutz?" Jewish friends asked. "They're so conservative."
Because something that wouldn't happen in a Jerusalem Marriott might happen there, we said.
Sure enough, a woman who spent weekends at the kibbutz asked us to share Shabbat supper, a weekly religious ritual, with her family in her apartment overlooking the Western Wall in Jerusalem.
The wall, a remnant of the wall that enclosed the Jews' ancient temple, is the holiest site in Judaism. People have been living in the warrens in that part of the Old City for millennia.
We were thrilled by the promise of a rare and unforgettable experience. As candles were lit and prayers said, we heard a commotion coming from the direction of the wall.
Ramadan services at the nearby Al-Aqsa Mosque were breaking up, and Muslims were pouring into the Old Oity. At the same time, truckloads of Israeli soldiers were gathering in the plaza below us.
We watched from a balcony as Muslim celebrators fired rifle shots into the air to mark the end of the day's fast. And young Israeli soldiers answered with a few rounds of their own, as if to say they had the situation in hand.
We'll never forget the gunpowder smell wafting up on clouds of rifle smoke. We were a bit unnerved, but it was obviously not a violent exchange. Yet, we would never have experienced it if we hadn't accepted an invitation to spend Shabbat with a new friend from the kibbutz.
Serendipity struck again last fall when we stopped to chat with a woman selling roast chicken and sausages at the farmers market in Vevey, Switzerland.
"What are you doing here?" she chastised. "They're bringing the cows down from the high meadows today in L'Etivaz. You have to see the cows coming back. You can see the market tomorrow. Go. Hurry."
Every spring, the dairy farmers in the Swiss alpine villages drive their cows to the high mountain meadows to graze. And every fall, they drive them back down to winter in the villages.
The Swiss call the homecoming Desalpe. It's an earthy festival that guidebooks often don't list because the dates vary.
We dashed to the railway station to catch the little green train that climbed into the alpine region through forests just beginning to turn color. A bus took us the final few miles to the village.
L'Etivaz, a wide spot in the road with a handful of businesses, was decorated with Desalpe banners and plastic flowers. There were raucous beer gardens, sausage and cheese booths, stone-throwing contests, and concerts by herdsmen blowing long wooden alpenhorns or swinging enormous cowbells.
Everything stopped when the cows appeared on the winding mountain road above the village. We joined the folks who rushed to the roadside for a close-up view.
The village erupted with the clamor of cowbells, moos, and cheering people. The cows, bedecked in floral bonnets and massive bells, were prodded along by smiling farm boys and girls.
And then it was over. The locals went back to their beer, and we lowland visitors rushed for buses and trains to take us back down the mountain.
That's the travel magic - the serendipity - we now crave.
We just had to retire and learn to slow down to let it happen.
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