A strange thing happened to me the other day as I waited at a traffic light in Beijing.

I'd just watched a leaf fall from a willow tree somewhere between Wusi Dajie and Di'anmennei Avenue. It was the middle of a hot afternoon and even the leaf seemed tired. It was the first falling leaf I'd noticed of the autumn. As I played with the brakes on my bicycle, a fella pulled up beside me on a late-model moped — average build, baseball cap covering what I estimated to be a balding head, a pair of smart spectacles on his face — "Have you been to the Great Wall of China?" he asked, apropos of nothing, in an accent you wouldn't find out of place in the halls of Westminster Palace.

Now, there's nothing particularly strange about any of that — we were both men on our way to some place. Why not talk about the Great Wall along the way? But the very night before, the same man had stopped beside my daughter and me as we waited for a taxi on the edge of the Guozijian hutong alley.

"Have you been to the Great Wall of China?" he'd asked then as well, sitting stationary on his moped, staring into the distance. "Are you kiddin' me?" I'd replied, "One of the best things I've ever seen. The craftsmanship, like, something else."

He said nothing in reply, didn't even acknowledge my words, as if I'd never said them. He stayed where he was, looking to be either checking something or taking notes on his phone, taking small frequent bites at a chocolate bar he held in his other hand, until a horn behind him sounded and he had to take off into the hutong.

So when I saw this man again the next afternoon in a city where I could count the people I knew on one hand, it felt like seeing an old mate I hadn't met in decades. "What are the chances," I thought, "in a city of more than 20 million people, of seeing the same stranger twice in two days in two different parts of town and him asking the same question, 'Have you been to the Great Wall of China?'"

The second time he asked it, I attempted an air of familiarity, "We were there last week tongzhi (comrade)," and I lifted my arms into the sky for emphasis, "and it was marvelous. Might go back next weekend. You don't remember me?"

But my new friend gave away no sign of recognition. Again, he said nothing to my answer. When the lights changed, he was immediately off into the distance, not looking back.

I haven't seen my friend again, but now I'm seeing the leaves falling everywhere — on Huixin East Road, along the Liangma River. They're all still green but they're falling anyway.

One of the first things I noticed about Beijing were these big luxurious willows spreading their cover over the populace. The first day I got here, as I came in from the Beijing Capital Airport off the madness on the Fourth Ring Road, the trees made me feel a bit less mesmerized. Cycling through the dog days of dashu (Major Heat), the breeze you'd catch as you picked up speed down a treelined street gave you a new lease on life.

In solar terms, my daughter, Rosa, flew into Beijing in the middle of liqiu (Start of Autumn) and left for university again after the start of chushu (End of Heat). I'm writing this on the cusp of bailu (White Dew). … White Dew, what a name for a season. In Ireland, we'd be in the month of Mean Fomhair (the middle of the harvest), and White Dew might be something we'd be drinking.

While Rosa was here and we were out and about on the bikes, I let her take the lead, as her navigating skills are better than mine. They say, because Beijing is built on a central axis, you can't get lost in it. I can disprove that claim.

So whether we were following the Xiaoyuehe and the Bahe canals, heading out to the Bird's Nest or looking for the Silk Market, Rosa took the lead while I followed, trying to judge what the right distance between us should be.

Before she left for university in Scotland, I asked her again about the man on the moped, "What about your man? The fella who was asking about the Great Wall twice in 12 hours. That was weird, wasn't it? Do you think he devotes himself to keeping an inventory of who in Beijing, at any given time, has seen the Great Wall and who hasn't?"

"Daddy, maybe he's just really unlucky."

"What do you mean?" I asked, eyeing her up warily.

"Well, maybe the man's been out trying to practice his English and the two people he's met were both you."