How Much Information Did You Convey?
"I like turtles" conveys more or less information depending on the question: a yes/no question has 2 plausible replies, an open-ended one has a billion. Information theory, explained with turtles.
Transcript
"You just said 'I like turtles.' How much information did you convey?" [Table] "Do you like turtles?" → I like turtles / I don't like turtles: roughly 2 plausible replies · "What reptiles do you like?" → chameleons, snakes, geckos, crocodiles: roughly 15 · "Tell me about yourself." → My elbow bends both ways / I can't keep up with rap lyrics / I saw a monkey on the subway / I've never tried orange juice: roughly 1,000,000,000 · (more information as you go down)
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Free for classrooms, worksheets, slides and other non-commercial use under CC BY-NC 4.0, with credit to Ben Orlin.
Cartoon by Ben Orlin, Math with Bad Drawings. https://cartoons.mathwithbaddrawings.com/2022-04-05-how-much-information-did-you-convey/ (CC BY-NC 4.0)