Sarah asked if there's a connection between the word am עם - nation, and the root עמם, as found in the word amum עמום, meaning "dim" or "dark".
While they look similar, they're not related. As I quoted from Horowitz in the discussion about the letter ayin:
Ancient Hebrew had two different ayin sounds. These sounds were represented in our alphabet by the letter ayin. One was a harsh, heavy ayin. This is now lost, and no longer used in Hebrew. The other was a soft, mild ayin. When the Greek Jews translated the Bible into Greek, they had to transliterate Hebrew names having the harsh ayin in it. They used the Greek letter gamma for it - so you can imagine how hard a sound it must have been.
So we can see from Klein's etymology of the two words that they each come from a different "ayin".
Regarding the root עמם meaning dark or dim, Klein writes that it is cognate with the Arabic ghamma, meaning "he covered, veiled, concealed."
As far as am, Klein says it comes from a distinct root עמם, meaning "to join, connect", and is cognate with the Arabic verb 'amma. Am meant "those united" or "those related". A related word is im עם - meaning "together with".