The traditional 關 is built around 門 mén, the same two-leaf gate that frames its inverse 開 (to open). Where 開 shows two hands lifting a latch, 關 shows the latch dropped: an inner element of crossed cords or a bolt threaded through hooks, sealing the gate shut. The Shuōwén Jiězì gives the gloss directly: 以木横持門戶也 (yǐ mù héng chí mén hù yě), "a piece of wood held crosswise to hold the gate." The character is a picture of the bar in place.

From that physical image the word fans out along two paths that modern Chinese still keeps separate, even as it uses the same character for both. The first path stays close to the gesture: to close, to shut, to seal off. A door is closed (关门), a light is switched off (关灯), a shop is shut down (关店), a person is locked up (关起来). Anything that was open and is now sealed takes 关.

The second path leaves the household and goes to the borderlands. The same wooden bar that closes a gate also closes a mountain pass, and in classical China these passes were the points where empires controlled movement. 关 became the noun for any such checkpoint: 关口 (guānkǒu, a strategic pass), 关隘 (guān'ài, a narrow defile), 海关 (hǎiguān, the customs office). The most famous of all is 山海关 Shānhǎi Guān, "Mountain-Sea Pass," the eastern terminus of the Great Wall where the rampart meets the Bohai Sea, controlling the corridor between Manchuria and the North China Plain. The Manchu armies forced their way through it in 1644 and ended the Ming dynasty in a single passage.

From "the pass that controls movement between two regions" comes the third meaning, the most abstract and the most culturally loaded: relation, connection, concern. To be 关 to something is to stand at the pass between yourself and it. 关系 (guānxi, relationship), 关于 (guānyú, regarding), 关心 (guānxīn, to care about), 有关 (yǒuguān, related to), 关键 (guānjiàn, key, the critical hinge): every one of them is built on the image of the pass. What you care about is what stands at the gate of your attention.

The simplified 关 keeps none of the gate frame. The 1956 reform replaced the entire 門-based structure with 丷 (a stylized "eight" stroke pair) over 天 (heaven), an arrangement borrowed from a Song-period cursive shorthand. The result is visually unrelated to the original picture, which is why the traditional 關 is worth holding in mind whenever the modern verb appears.

The semantic leap from "door-bolt" to "mountain pass" is small once you stand at one. A pass is the place where geography itself acts as a gate: two cliffs or two mountain ranges close down to a single corridor, and whoever holds the corridor controls passage between the regions on either side. Imperial China built fortified guardposts at every such corridor and called them 关. The word is both the geography and the institution.

三个最有名的关 stand out. 山海关 Shānhǎi Guān, the Mountain-Sea Pass, sits where the Great Wall meets the Bohai Sea on the Hebei coast, controlling the narrow strip between Mongolia and the Central Plains. 函谷关 Hánggǔ Guān, the Hangu Pass in modern Henan, was the gate between the Wei River valley (Qin's heartland) and the eastern states; legend has 老子 Lǎozǐ riding west through it on a green ox, leaving the Daodejing with the gatekeeper before vanishing into the mountains. 嘉峪关 Jiāyù Guān stands at the western end of the Great Wall in Gansu, the last fortified gate before the Gobi and the Silk Road.

From these literal passes, 关 became any threshold of control. 海关 (hǎiguān) is the customs office, the sea-pass through which goods enter and leave a country. 难关 (nánguān, "difficult pass") names any obstacle a person must struggle through: an exam, a financial crisis, an illness. 过关 (guò guān, to pass the pass) is the standard verb for clearing any test, gate, or hurdle: customs, an exam, a level in a video game. The metaphor is one of the most productive in the language.

Hold the traditional 關 in mind: the gate frame 門 with a wooden bolt threaded through it. That bar in place is the entire character. Drop the bar and you have closed the gate; place that gate at a mountain corridor and you have built a frontier pass; place the same gate between two people and you have built a relationship. The journey from "shut the door" to 关心 (turning the heart toward someone) is the same gate moving from a household to the borderlands to the social world.

The simplified 关 lost the gate frame, but the metaphor still does the work. When you hear 关电视, picture the bolt dropping across the gate of the television. When you hear 关于这个问题, picture the gate of attention swinging open onto the question. When you hear 关心, picture the heart standing at the gate, turned outward toward someone else.

Pair it always with 开 (kāi): hands lifting the bar versus the bar dropped. The 开关 (kāiguān) on every wall in your house is these two characters in disguise, and the social network you live inside is the same image extended to 关系.