pupil (eye), moo (cow sound)
牟 centers on the idea of a cow's sound (moo) and, by extension, the pupil of the eye, which resembles a dark, round shape like a cow's eye or the sound itself.
牟 is thought to combine 厶 (a pictograph of a cow's head or horns) with 牛 (cow), reinforcing the bovine association. The meaning 'pupil' may derive from the round, dark shape of a cow's eye.
The top 厶 looks like a cow's horns, and the bottom 牛 is a cow. Together they make the sound 'moo' and also suggest the round pupil of a cow's eye.
For ボウ, imagine a cow mooing with a deep, low 'bow' sound: bow -> ボウ, and the cow's pupil stares back at you.
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