Twisted or woven together in a complicated way; closely connected or dependent on each other.
From 'inter-' (between, among) + 'twined' (twisted). The 'twine' part comes from Old English 'twinn' (thread), and 'inter-' is Latin for 'between,' creating a word for things twisted together with each other.
When you see DNA strands in pictures, they're literally intertwined—two helixes twisted around each other—and that's why we use this word for complicated relationships where two people or ideas are so wrapped up together you can't separate them anymore.
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