Mark and his classmate Ming talk about paradoxes again in the common room of their dorm.

    Ming: Mark, can you tell me some of those famous paradoxes you mentioned?

    Mark: Happy to. We already talked about one, called "The Liar's Paradox."

    Ming: Oh, yeah. If I say, "I always lie," then I must be lying, and therefore I sometimes tell the truth. That's a paradox.

    Mark: Right. The statement contains its own contradiction.

    Ming: Got it. What's another one?

    Mark: One of the most famous among mathematicians is called "Russell's Paradox," after the British philosopher and mathematician Bertrand Russell.

    Ming: Can you explain it?

    Mark: I wish I could! It's very complex. It's part of something in math called "set theory," the study of things that are parts of sets of things.

    Ming: I'm confused already! Let's do another one!

    Mark: Sure. Some of the oldest are called, "Zeno's Paradoxes," after an ancient Greek philosopher. One of them is called "The Dichotomy Paradox."

    Ming: What's a dichotomy?

    Mark: It basically means "cutting something in half," and that's the basis of the paradox. Let's say you want to go to the cafeteria.

    Ming: I do! I'm hungry!

    Mark: But first you have to go halfway, right?

    Ming: Right.

    Mark: And before that, you have to go a quarter of the way, or half of the half.

    Ming: Sure.

    Mark: And before that, you have to go an eighth, a sixteenth, a thirty-second…

    Ming: Oh! I see what's going to happen--I'll never get there!

    Mark: That's right--you'll starve! In math, we can keep cutting things in half infinitely.

    Ming: But I know I can go to the cafeteria! I do it all the time!

    Mark: That's why it's a paradox.

    Ming: Wow! This is fun! One more?

    Mark: This is a good one. It's called "The Surprise Test."

    Ming: This doesn't sound good…

    Mark: Just listen: The teacher says, "Next week I'm going to give you a test, but I won't tell you which day. I guarantee it will be a surprise."

    Ming: I hate that!

    Mark: So Bob, a clever student, says, "It can't be on Friday. Because if it is--Friday is the only day left after the other four, so I won't be surprised."

    Ming: I get it.

    Mark: Then, Bob thinks, it can't be on Thursday either. Because if it doesn't happen by Wednesday, Thursday won't be a surprise.

    Ming: I see where this is going. Bob will eliminate every day of the week.

    Mark: That's right! So, when the teacher gives the test on Wednesday--

    Ming: Surprise!

    Mark: Yes, and what the teacher said came true!

    Ming: Now that's a paradox I can understand--even if I don't like it!

    Mark: Geez, Ming, don't take it personally!