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December 29, 2003

My lucky number is pi

An interesting article on irrationality, inter alia. "In short, the evolutionary design features of the human brain may well hold the key to our penchant for logic as well as illogic."

Consider the following problems:

Problem 1:

"Imagine that you are confronted with four cards. Each has a letter of the alphabet on one side and a number on the other. You are also told this rule: If there is a vowel on one side, there must be an even number on the other. Your job is to determine which (if any) of the cards must be turned over in order to determine whether the rule is being followed. However, you must only turn over those cards that require turning over. Let's say that the four cards are as follows:

T 6 E 9

Which ones should you turn over?

Problem 2:

You are a bartender at a nightclub where the legal drinking age is 21. Your job is to make sure that this rule is followed: People younger than 21 must not be drinking alcohol. Toward that end, you can ask individuals their age, or check what they are drinking, but you are required not to be any more intrusive than is absolutely necessary. You are confronted with four different situations, as shown below. In which case (if any) should you ask a patron his or her age, or find out what beverage is being consumed?

#1 -Drinking Water
#2 -Over 21
#3 -Drinking Beer
#4 -Under 21

Did you find one problem easier than the other? Answers and speculation within.

"Answers:

Problem 1:

Most people realize that they don't have to inspect the other side of card T. However, a large proportion respond that the 6 should be inspected. They are wrong: The rule says that if one side is a vowel, the other must be an even number, but nothing about whether an even number must be accompanied by a vowel. (The side opposite a 6 could be a vowel or a consonant; either way, the rule is not violated.) Most people also agree that the E must be turned over, since if the other side is not an even number, the rule would be violated. But many people do not realize that the 9 must also be inspected: If its flip side is a vowel, then the rule is violated. So, the correct answer to the above Wason Test is that T and 6 should not be turned over, but E and 9 should be. Fewer than 20 percent of respondents get it right.

Problem 2:

Nearly everyone finds this problem easy. You needn't check the age of person 1, the water drinker. Similarly, there is no reason to examine the beverage of person 2, who is over 21. But obviously, you had better check the age of person 3, who is drinking beer, just as you need to check the beverage of person 4, who is underage. The point is that this problem set, which is nearly always answered correctly, is logically identical to the earlier set, the one that causes considerable head scratching, not to mention incorrect answers.

Why is the second problem set so easy, and the first so difficult? This question has been intensively studied by the evolutionary psychologist Leda Cosmides. Her answer is that the key isn't logic itself -- after all, the two problems are logically equivalent -- but how they are positioned in a world of social and biological reality. Thus, whereas the first is a matter of pure reason, disconnected from reality, the second plays into issues of truth telling and the detection of social cheaters. The human mind, Cosmides points out, is not adapted to solve rarified problems of logic, but is quite refined and powerful when it comes to dealing with matters of cheating and deception. In short, our rationality is bounded by what our brains were constructed -- that is, evolved -- to do. "


Posted by martin at 10:24 AM