Monday, March 10, 2008

Thought Experiment

This is interesting because of how it makes you think about how you think (I retyped it because the original copy is hard to read):

"How many of you have seen the puzzle with four cards?
B 5 2 J
Each card has a number on one side and letter on the other. Which cards do you have to turn over to test the rule that if there's a J on one side there's a 5 on the other side?
Something like 80 to 90 percent of college students get this wrong.

On the other hand, suppose you ask people the following: you say, you're a bouncer in a bar, and you want to make sure no one under 21 is drinking. Who do you have to check: someone who is drinking, someone who isn't drinking, someone who's over 21, or someone who's under 21?
And then, of course, almost everyone gets it right. Even though this problem is logically equivalent in every way to the other problem.
And this brings up a fundamental point about our brains. We're designed for spearing small animals. Not for proving theorems. This class is all about doing things that your brains are not designed for. The trick is to co-opt parts of your brain that evolved for something else: "You over there, you're supposed to track leopards leaping across the savannah? Well, now those leopards are going to be arbitrary vectors v in R3 space. Deal with it."

Incidentally, the analogy works like this:
B - Over 21
5 - Under 21
2 - Not Drinking
J - Drinking

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