What is “information”? Entire courses are given on information theory so we cannot do it justice here. But its basic features are so simple–and so important–that it is tempting to try. My favorite definition of information is due to Gregory Bateson [Bateson, 1973]: “Information is a difference that makes a difference.” Information is about surprise, ways in which an expectation has been violated in some way. If I tell you that your grade is based on (1) a final and (2) a midterm, you wouldn’t be very surprised. But if I tell you that your grade will also depend on (3) how long you can stand on one foot without moving, you probably would be surprised. There’s more information in that part of my message. We can demonstrate this in terms of a conversation you might have after a class with someone who missed class that day. “What did you learn in class today?” they will ask. “Oh, not much really,” you’d say in the first case, because you–and your friend’s–expectations about grading (not to mention your friend’s expectation that you can be relied on to convey the information; cf. Section 8.2.1) have been confirmed. But in the second case you’d have to reply, “You won’t believe this; part of our grade is based on how long we can stand on one foot!” You’ve learned something; you’ve gained information.