This chapter discusses a perspective on designing interaction by quantifying information that reduces the computer's uncertainty about the user's goal. We begin with how to quantify uncertainty and information using Shannon's information-theoretic terms and how to optimize decisions under uncertainty using an expected utility function with Bayesian Experimental Design. We then describe the BIG framework-Bayesian Information Gain-where the computer "runs experiments" on the user by sending feedback that maximizes the expected gain of information by the computer, and uses the users' subsequent input to update its knowledge as interaction progresses. We demonstrate a BIG application to multiscale navigation, discuss some limitations of the BIG framework and conclude with future possibilities.