理 lǐ is a pictophonetic compound: the jade radical 王/玉 carries the meaning, and the right-hand element 里 lǐ carries the sound. The left side is 王, the standing form of 玉 yù (jade), the same element that runs down the side of 玛 and 珠. Its meaning here is the natural veining inside a piece of jade, the streaks and grain that a carver reads and follows when deciding where to cut. So the earliest sense of 理 is concrete: the texture or grain of a stone, the lines already there to be worked along.

From "the grain you cut along" the character climbs steadily into the abstract:

1. Texture, grain. The literal veins of a material: 纹理 wénlǐ (texture; grain), 肌理 jīlǐ (the texture of flesh or a surface).
2. Principle, reason, the inner pattern. The grain extended to the order running through any thing or argument: 道理 dàoli (sense; the way of a thing), 理由 lǐyóu (a reason), 真理 zhēnlǐ (truth).
3. To put in order, to manage. To work along the grain rather than against it, hence to tidy and to govern: 管理 guǎnlǐ (to manage), 整理 zhěnglǐ (to sort; to tidy), 处理 chǔlǐ (to handle).
4. To heed, to attend to. Often in the negative: 不理 bù lǐ (to ignore; to pay no mind).

In later Chinese thought 理 became one of the great philosophical words. The Neo-Confucian thinkers raised it to mean cosmic principle, the rational pattern underlying all things, paired against 气 qì, the matter and energy that principle organizes. To "investigate the principle of things" (穷理 qióng lǐ) was the scholar's path to understanding. The thread from jade to cosmos holds throughout: 理 is the order already in a thing, the grain you find rather than the shape you impose.

The same 理 that names a thing's inner grain also names the act of working with that grain. To 理 something is to bring it into order along its natural lines, hence the whole family of verbs of managing, sorting, and handling. 整理 zhěnglǐ is to tidy and arrange, putting scattered things back into their places. 处理 chǔlǐ is to deal with or dispose of a matter, to handle a problem to its end. 管理 guǎnlǐ is to administer and run, the word behind every "manager" and "management" in modern Chinese. Even a haircut is 理发 lǐfà, literally to put the hair in order.

The image underneath is the carver again: you do not force the jade, you read its veins and cut along them. Good management, in the logic of the word, is less about imposing a shape than about finding the order already latent in things and following it.

Hold a piece of jade up to the light and look at the veins running through it. Those lines are 理, the grain. The radical 王 on the left is the jade itself, and the carver's whole art is to read that grain and cut along it, never against it.

Now let the image widen. Follow the grain in a stone and you get texture (纹理). Follow the grain in an argument and you get its sense and reason (道理). Follow the grain in a tangled affair and you set it in order (整理, 处理, 管理). Follow the grain of the whole world and you reach the cosmic principle the philosophers called 理. Wherever you meet 理, look for the pattern already there, the line you are meant to find and follow rather than force.