if this isn’t a joke - new yorker style uses a diaresis when a word has a repeated vowel where the second vowel is part of a different syllable. coördinate, coöperate, and reëlect are probably the most common places where this comes up

https://www.newyorker.com/culture/culture-desk/the-curse-of-...

It is how you properly tell apart a coop which houses chickens from a coöp which is a business entity owned by its members

Ah yes, the diaresis will relieve those confused chicken farmers! A thousand thanks to The New Yorker.