For example, in English the word right (opposite of left) and right (privileges, as in human rights) are homonyms. In Spanish, derecho/a also means both of those things. Don’t the concepts behind those words predate the cross-pollination of the two languages? Why do they share this homonym quality?
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That said, look at Latin:
The “privileges” that you see in derecho and right are an extension of what Latin already associated with dexter - things that are proper to do or to get. For example if I got a right to freedom, that means that it’s fitting for me to get freedom, you know?
Based on that odds are that Spanish simply inherited the association, and kept it as such even after borrowing izquierdo from Basque and shifting directus→derecho from “straight” to “right”. While English borrowed it, either from Latin or some Gallo-Romance language.
And overall you’ll see a fair bit of that in the Western European languages, regardless of phylogenetic association, since languages clustered near each other (i.e. a Sprachbund) will often borrow concepts and associations from either each other or from a common source.
Also, note that right “as side” and “as privilege” are not homonyms. Those aren’t different words from different sources, it’s the same word with two different meanings, this is called polysemy. The same applies to derecho.
So that’s why “straight on” and “on the right” are the maddeningly confusable “a derecha” and “en derecho”. Such a pain when following directions.
It could be worse.
That word was originally a verb, it’s the perfect participle of Latin dirigo “to lay straight”, “to direct”, “to steer”. The verb itself kicked the bucket; if it didn’t, it would’ve been something like *dereger in Spanish, with the past participle *derecho.
So “driven straight to the right” would’ve become *“derecho en derecho a la derecha”.
(Thankfully the verb got replaced by its own reborrowed version dirigir “to drive”, “to direct”, so the sentence is a bit less maddening: dirigido en derecho a la derecha.)
[inb4 I’m not a native speaker so if anyone finds a mistake please do tell me out. I’m a bit too prone to portuñol.]