Hannah Bates was a colonist on Moab IV, a member of the genetically-engineered and socially isolated Human Genome colony. As one of the leading scientists in her society, she was an expert on biosphere homeostasis and theoretical physics.
In 2368, when a stellar core fragment of a collapsed neutron star threatened to destroy the colony, its leader, Aaron Conor, accepted help from the Federation. Exposure to the technology on board the USS Enterprise-D showed Bates how much more advanced the Humans outside her society had become. Her experiences there, in particular her collaboration with Geordi La Forge, who would have never been "allowed" to be born on the colony due to his blindness and yet demonstrated a technical skill at least equal to her own, challenged many of her beliefs about the colony. For his part, Commander La Forge gently challenged the colony's belief system by stating that regardless of his disability, he could still contribute something substantive to his society.
Further, as Bates and La Forge collaborated on a solution to the problem of the core fragment, they both realized that the answer to the problem was based in the technology on which La Forge's VISOR was based. Upon hearing this, La Forge laughed and said that if the solution to the problem was part of a technology designed for a blind man who would never have existed in her society, what else could her people have missed out on by being closed off from other societies.
Desperate to prolong her contact with the outside world, Bates even attempted to convince the society and the crew of the Enterprise-D that the earthquakes caused by the core fragment had damaged the colony's artificial biosphere and it would have to be evacuated despite their efforts. La Forge, however, knew she had fabricated the evidence and convinced her to abandon her efforts. Eventually, Bates requested asylum aboard the Enterprise-D and was granted it. Her departure encouraged others to go and, in all, 23 colonists left. The damage to the engineered society, as each person fulfilled important roles that were not easily replaceable, would take generations to heal. (TNG: "The Masterpiece Society")