Kevin Levine explains the concept of BioShock Infinite on his blog:
There are two core principles for us that define a BioShock game. First, it has to be set in a world that is both fantastical and yet also grounded in the human experience. Second, it has to provide gamers with a large set of tools, and then set them loose in an environment that empowers them to solve problems in their own way.
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So when we started the sequel, we said to ourselves: “We want to expand on those core principles, but beyond that, there are no sacred cows. Everything else that people know or think they know about BioShock is open for negotiation.”
You will find yourself in a completely new world. Columbia is not an unknown secret city at the bottom of the sea. It’s a creation of an America transforming from a regional agrarian collection of states into a world power with global reach.
You now play an actual character, and not a cypher who is unaware of his own identity. You are Booker Dewitt, a particular character with an established history, with a voice you will hear as he talks to himself and others in the game.
You’ve come to Columbia for a reason: to find a mysterious young woman named Elizabeth and bring her safely out of the city. She will travel with you, interact with you, and react to the situations you cause to happen, and through your relationship with her, we’re able to tell the story of this new and amazing world.
This world of Columbia presents radical differences in scale from what you are used to. You’re not crawling through corridors on the ocean floor, claustrophobic with the weight of the ocean bearing down on you. Instead you find yourself navigating through huge environments, zipping around on Sky-Lines at eighty miles per hour and getting into firefights at ranges of two thousand yards.