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When we communicate one thing, we often unavoidably send other messages. To start with a simple example, imagine that Ian says to Barry, "My mother's name is Karen." From Ian's communication, Barry learns more than just the underlying bit of information (mom's name). The communication also lets Barry know that: (a) Ian knows his mom's name, and (b) Ian knows that Barry knows Ian's mom's name.

What is less well understood is that when we teach, we learn. When Ian tells Barry about his mom, Ian learns several things.

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