‘… the only way to learn an unknown language is to interact with a native speaker, and by that I mean asking questions, holding a conversation, that sort of thing. Without that, it’s simply not possible, so if you want to learn the aliens’ language, someone with training in field linguistics – whether it’s me or someone else – will have to talk with an alien. Recorings alone aren’t sufficient.
-- Dr. Banks (Part 1)

Importance: With this quote, Dr. Banks firmly lays down the law to the reticent Colonel Weber: the only way she will do what he is asking her to do (establish communication with the visiting aliens) is that if she is allowed to set up a face-to-face relationship with them. This establishes Dr. Banks as a committed, responsible, strong-minded, and science-minded central character.

It looked like a barrel suspended at the intersection of seven limbs … any of its limbs could serve as...
-- Narration (Dr. Banks) (Part 2)