“Coherent” means clear, logical, and easy to understand, with all the parts fitting together well. It can also describe things that stick together or are closely connected.
It comes from Latin “cohaerentem,” the present participle of “cohaerere,” meaning “to stick together,” from “co-” (together) and “haerere” (to cling). The idea of physical sticking became mental or logical sticking.
When your ideas are coherent, they’re literally “stuck together” in the listener’s mind instead of falling apart. Physics even uses “coherent light” for laser beams whose waves line up perfectly—logic and light sharing the same metaphor.
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