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I thought blue always meant blue. No, I didn't. It started out as meaning "yellow" and evolved into "white" and hence in Old English to “pale” and “the colour of bruised skin”. It was actually re-borrowed in its modern sense from French.
Some didn't even have a proper word for blue. Ancient Greeks for example. Poor Homer had to call the colour of the sea "Wine Coloured" ;)
Why do we sometimes feel blue? Because of Zeus! Blue was related to rain or storms, and Zeus would make rain when he was sad or crying, and a storm when he was angry.
What about the Blue Moon? It used to have a meaning of something that was absurd. The origin of Blue Moon is steeped in folklore and it suggests something that, in fact, never happens, as in this pamphlet from 1528:
Yf they say the mone is blewe,
We must beleve that it is true.
A kind of "at the Greek calends" :)) Anyway, good news: It used to be "never", and today it is "very rarely"! Impossible things do happen!
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Oh, I nearly forgot... It also has a meaning bordering on indelicacy: blue as "obscene, indecent" (and therefore a blue joke, a blue movie, a secret stash of blue mags even); it is recorded from the 19th century, and the sense connection is unclear... I am very curious, but nowdays much etymological research is done ;) I might even give a hand one day...
Still many interesting things to be said about blue, but I'll be back!