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Cognition refers, quite simply, to thinking. There are the obvious applications of conscious reasoning—doing taxes, playing chess, deconstructing Macbeth—but thought takes many subtler forms, such as interpreting sensory input, guiding physical actions, and empathizing with others.
A bias is a tendency, inclination, or prejudice toward or against something or someone. Some biases are positive and helpful—like choosing to only eat foods that are considered healthy, or staying away from someone who has knowingly caused harm to you or others.