The proverb appears in the Ming novel Water Margin, attributed to Shi Nai'an: those with destiny meet across a thousand li; those without it pass face to face without meeting. The root concept is Buddhist: pratyaya, the conditions that bring about effects, entering China around the first century CE and localizing into yuan, the specific condition that binds people, family, friends, lovers, even the stranger you meet once. Yuanfen is not luck and not choice; it is the accounting of why this person.
Yuanfen does quiet work: it dignifies coincidences into relationships, and it lets people release failed ones, we had no yuan, without assigning blame. It is fate as a gentle administrative layer over a vast population where most encounters are once-only. The subway couplet is the folk proof: two strangers share a rail daily and stay strangers; two others meet across an airport and stay for life. Distance is not the variable. Yuan is.
The claim: recommendation engines are industrialized yuan, systems that compute which strangers across a thousand li should meet, and the proverb's mystery has been converted into match scoring, destiny as a service. Verdict: the mapping is exact enough to be uncomfortable, affinity prediction is a real industry. But the original concept's irreducibility is its point: yuanfen named the residue no calculus captures. When the residue reaches zero, the proverb will be obsolete, and so will the surprise that made it worth saying.
If meetings are fated, what is the free will for?