Last Thursday, as President Obama was prepping for his first summit in the California desert with China’s new leader, Xi Jinping, the Olshans were having our final dinner with Wenrui (“When-Ray”), our Chinese homestay student.

Wenrui came to stay with us in January for what we all thought would be a few weeks. But her mother’s visa was more troublesome to renew than anyone imagined. Weeks became months, and months became the entire school semester.

We had an inkling this would happen. The United States has become much more difficult to enter in the past few years, even for successful businesspeople like Wenrui’s mother. Bureaucracies tend to stiffen as tension develops between countries, and recently, as China has begun to flex its economic and military muscles, the United States has responded by tightening its borders.

Incorporating Wenrui into our day-to-day lives wasn’t terribly difficult. After all, what’s one extra person in the back seat on the rides to and from school, or one extra plate at the dinner table? Factor in the two to three extra hours it took her each night to power through her homework — all in a foreign language — and there were times when Wenrui seemed practically invisible.

The visa troubles, and the separation they entailed, were much harder on Wenrui and her family, despite the Internet technology that let them talk to each other — and even see each other’s faces — practically for free, almost every night. To be on one’s own at sixteen, in a foreign country, would be a tall order for anyone, no matter how accommodating the school, or how hospitable the homestay.

So it was with palpable excitement that Wenrui sat down to dinner with us that final night. To mark the occasion, I’d made Gong Bao chicken, one of her favorite dishes, but I noticed that she wasn’t eating as much as usual.

When I asked if she felt okay, she put her hand to her throat. “I have a — I don’t know what you call it — in my throat. There are sores. I thought it was going to be okay, but then the salt made it dry…”

I didn’t really understand what she meant, but over the course of our five months together, I’d learned to have an open mind about her health concerns. At times, it seemed that Wenrui had an entirely different body from ours, with different innards, workings — and remedies.

Even so, we reflexively offered her some typical American palliatives for a sore throat: an ice cube; some ice cream; tea with honey; Ibuprofin.

She graciously turned them down, one by one, her eyes widening a bit in panic when we got to the Ibuprofin.

“Oh, no,” she said, “I’ll be fine.”

At that point, as a distraction more than anything, I asked her what she did in China for a sore throat.

“I had one once before like this,” she said. “My grandmother, who likes traditional medicine, took me to a traditional doctor. He made me bleed. You know, with a tool.”

“Hold up,” I said. “Made you bleed? As in, bloodletting?”

Wenrui nodded. “It’s pretty common.” She went on to describe the procedure, which involved the doctor’s puncturing her skin with a hooked needle and making a trail of wounds below her throat. “It hurt a lot!” she said. “In the end, it looked like a kind of necklace.”

But it worked.

Another time, Wenrui told us about a cure that sounded straight out of the Dark Ages: Chinese “cupping;” i.e., the application of glass or bamboo cups to the skin, which are then heated with flame to create a partial vacuum. The heat and vacuum are supposed to promote better subcutaneous “flow,” although flow of what, exactly, is a little mysterious. One thing was certain: they left nasty, plum-sized welts on the flesh, and sometimes minor burns.

In the West, we’re very proud of our modern, science-based medicine, but we should remember that bloodletting and cupping were mainstays of Western treatment for centuries, perhaps even millennia. My mother-in-law has vivid memories of being cupped in Portugal as a child for treatment of tuberculosis.

But we’ve moved on. We look back at the bloodletting of our first President, who was bled copiously in the final days before his death, as a kind of misguided barbarism. But George Washington had access to the finest healthcare of his day; his doctors were merely acting on their training and experience.

These treatments — at least in the West — were based on an archaic understanding of the body. Cupping and bloodletting were thought to address problems with the bodily “humors,” the four fluids — blood, phlegm, yellow bile, and black bile — that needed to be kept in balance for good health. Each of the humors corresponded to a physical element — earth, air, fire, or water — and had a seasonal correlation: hot, cold, wet, or dry.

In the West, the idea of humors didn’t survive the Enlightenment, with its emphasis on rigorous scientific observation. A thing that couldn’t be seen or measured couldn’t be said to exist.

But China has deeper respect for ancestral wisdom. Traditional medicine survives — and thrives — side by side with modern medical facilities. Addressing the flow of chi, or “body energy,” remains the foundation of treatment for most ailments. Never mind that there’s no way to map it with an MRI: it’s real to Chinese doctors and patients; therefore it’s treatable.

Consult a Chinese medical manual and you’ll find prescriptions for exotic maladies like “stagnant blood,” “wind-dryness,” “excess heat,” “liver yang rising,” and “liver fire blazing.”

These ailments may sound strange — even highly dubious — to Western ears. But as we’ve learned from Wenrui, what people believe in, heals them.

On either side of the Pacific, medicine involves a healthy dose of faith.