At first, it seemed like we'd come to the mosque for nothing.

My Chinese friend and I were spending the National Day holiday in Xining, Qinghai province - a destination delightfully free of crowds thanks to the province's far-west location and sparse population.

The mosque was huge and architecturally imposing, with square minarets at its front corners and Arabic script on the eaves of the Chinese temple-style roofs inside.

But an elderly man wearing an exquisitely fine white taqiyah, the brimless cap worn by many Muslim men, was not inviting. Polite but firm, he waved us away, muttering "closed" and "holiday" and "religious ritual".

I was surprised - everything else nearby was open and bustling. Maybe the mosque was closed to me, the foreigner? And why would there be a "religious ritual" for the secular holiday?

I learned, thanks to my friend who translated these questions and the answers, that the holiday was the Muslim Festival of Sacrifice, celebrated annually during the haj ritual and only coincidentally falling during China's National Day week this year. As the explanation unfolded, I recognized a story I'd known since childhood: God tested Abraham by demanding that he sacrifice his son, Isaac. Once Abraham's faith was proven, God intervened at the last moment - sparing Isaac and giving Abraham a lamb to slaughter as a sacrifice instead.

In Arabic, Abraham becomes Ibrahim and Isaac becomes Isma'il. But except for the names, the narrative is the same across three religious faiths: Judaism, Christianity and Islam.

While the story was familiar, some of its manifestations that day were startling. My grandfather was a country farmer, but the next generations of my family have been city folks, and I wasn't prepared to look down a side alley near the mosque and see a sheep getting its throat cut on the sidewalk, no matter how reverently. In fact, for the rest of the afternoon I saw pop-eyed sheep and yaks - clearly smelling blood - resisting against their rope leads as they were tugged along cobbled walkways to meet the blade. By dusk, quite a pile of hides had been presented at the mosque gates as offerings, while the meat presumably went to dinner tables.

But hearing a story central to my own faith told through Muslim eyes was thought-provoking, especially at a time when fear of militant Islamists has led many in other faiths, especially in the West, to see all Muslims as extremists. When we see Muslims as individuals with values we share - rather than an alien concept - they are easier to understand and accept.

That is the beauty of all people-to-people exchanges, which have been central to the diplomacy of China, the United States and Europe in recent years. Friendship groups and embassies organize all sorts of events to promote this, and I've enjoyed attending cross-cultural fashion shows, tours of remote parts of China, Oktoberfest parties for Chinese followers of the German embassy on Sina Weibo and more international food festivals than I can count.

Perhaps the cross-cultural event that's been the most fun for me: I joined a group from China Post on a trip to Denmark. One of its designers, Shen Jiahong, had designed four stamps that luminously illustrated Hans Christian Andersen stories, and we all went to Andersen's hometown of Odense for the stamp-issuing ceremony. It was fascinating to watch and occasionally help my new Chinese friends find good shopping (among other things, Denmark makes great amber), local points of interest and - very important - local sources of Chinese food.

While organized cultural exchanges have great merit, I've found that more random encounters with individuals are the best way to get to know people who are different from ourselves.

That is if we are open to those encounters.