Pop Quiz

Probability

If a million monkeys type on a million typewriters for an infinite amount of time, one of them will eventually produce the complete works of Shakespeare.

1. How does the number of monkeys affect the time it takes to produce results? What about the number of typewriters? If there are a million monkeys but only half a million typewriters, will the monkeys using the typewriters type faster, or will they type more slowly in a stubborn display of territoriality? What if there are two million typewriters?

2. Discuss the ethical implications of exploiting monkeys in this manner. Most people would agree that chaining monkeys to typewriters would be unacceptably cruel. Would a setup in which the monkeys are kept in an idyllic monkey preserve, identical to their natural habitat in every way (except for the presence of large numbers of typewriters that they are free to type on or not as they choose) be acceptable? Where do you draw the line?

3. How much typing paper will the monkeys go through each day? Where will this paper come from? Will vast areas of the monkey habitat need to be clear-cut in order to keep up with the demand for paper? Does this affect your answer to question 2?

4. A monkey produces a copy of Hamlet at time T0. A movie about that monkey’s life is released at time T1. A movie depicting a revisionist version of events, in which Hamlet was actually typed by a different monkey (which — spoiler alert! turns out to be a human in a monkey costume), comes out at time T2. Solve for T1 and T2. Extra credit: who plays the monkey in each movie? Who plays the guy in the monkey suit?

5. Is Rise of the Planet of the Apes available on Netflix? Why or why not?

Physics

Photo courtesy of Jens Vöckler

1. Quantum theory tells us that you can’t know the exact position and momentum of an object at the same time. The momentum of an object at rest is 0. What is the momentum of a parked car? Would you entrust your car to a “quantum” valet parking service?

2. Does God play dice with the universe? If so, who usually wins?

Philosophy

Alice and Bob own identical bicycles and park them near each other. One night, Charlie secretly switches the front tires on the two bikes. Each night after that, he switches another pair of parts, until the bike parked in Alice’s spot is made entirely of parts that were originally in Bob’s bike, and the bike parked in Bob’s spot is made entirely of parts that were originally in Alice’s bike.

1. Is this really the best practical joke that Charlie can come up with?

2. Giddy with success, Charlie fails to secure the bicycles properly on the last night. An hour after he leaves, one of the bikes falls over. Does it make a sound?

3. Charlie describes his antics to Alice and Bob, who decide to build a storage shed for their bikes in order to prevent people from tampering with them in the future. What color should they paint the bike shed?

4. Alice begins to notice that Bob has been acquiring more and more items — a desk lamp, a chair, several books — identical to things that she owns. Last week, she was surprised to see Bob in line behind her at the supermarket with a cart filled with the exact same groceries she was buying. Should she be concerned?

Video Review: Vinay and Maru Prove that P ≠ NP

P vs. NP is one of the most famous unsolved problems in math. Recently, mathematician Vinay Deolalikar circulated a paper that contained a possible solution to that problem. There’s been lots of discussion on the Internet about this paper; surprisingly, though, the companion video series has been largely ignored.

Maru
Maru

In Vinay and Maru Prove that P ≠ NP, Deolalikar presents the material from his paper with the assistance of Maru, who is possibly the most entertaining cat on YouTube. Each episode features video imagery of Maru with narration by Deolalikar. In Episode 1, Deolalikar defines what P ≠ NP means — basically, that the solutions to some problems are hard to find but easy to verify — while Maru interacts with a large cardboard box. Finding a way into the box is a difficult problem for Maru; eventually, he solves it and goes on to demonstrate (repeatedly) that verifying the solution is easy. Of course, the fact that Maru found the initial problem difficult doesn’t prove anything; it’s possible that someone could discover a simpler box-entry-finding algorithm tomorrow. Episode 1 gets two thumbs up from me — the narration is clear and informative, and Maru’s performance is outstanding.
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