Is this an illustration of a young or old woman?

Leonardo da Vinci always assumed that his first way of looking at a problem was too biased toward his usual way of thinking. He would always look at a problem from at least three different perspectives to get a better understanding. It has been my observation that people who pride themselves on their ability to think logically and analytically ignore his advice and trust their usual way of thinking

Peter Cathcart Wason was a cognitive psychologist at University College, London who pioneered the Psychology of Reasoning. He progressed explanations as to why people make certain consistent mistakes in logical reasoning. The problem described below is a variation on the Wason selection task that was devised by Peter Wason. The Wason selection task was originally developed as a test of logical reasoning, but it has increasingly been used by psychologists to analyze the structure of human reasoning.

Consider the following problem. Four cards are laid out with their faces displaying respectively, an E, a K, a 4 and a 7.

You are told that each card has a letter on one side and a number on the other. You are then given a rule, whose truth you are expected to evaluate. The rule is: “If a card has a vowel on one side, then it has an even number on the other.” You are then allowed to turn over two, but only two, cards in order to determine whether the rule is correct as stated.

Which two cards do you turn over?

If you worked this problem silently, you will almost certainly miss it, as have the large percentage of subjects to whom it has been presented. Most subjects realize that there is no need to select the card bearing the consonant, since it is irrelevant to the rule; they also appreciate that it is essential to turn over the card with the vowel, for an odd number opposite would prove the rule incorrect.

The wording of the problem determines the perspective most people mentally default to almost immediately. Most people assume that the object is to examine the cards to ascertain that if a card has a vowel on one side, then it has an even number on the other; and if a card has an even number on one side, then it has a vowel on the other side. This assumption leads them to make the fatal error of picking the card with the even number, because the even number is mentioned in the rule. But, in fact, it is irrelevant whether there is a vowel or a consonant on the other side, since the rule does not take a stand on what must be opposite to even numbers.

On the other hand, it is essential to pick the card with the odd number on it. If that card has a consonant on it, the result is irrelevant. If, however, the card has a vowel on it, the rule in question has been proved incorrect, for the card must (according to the rule) have an even (and not an odd) number on it.

The content of this specific problem influenced the way we constructed our perception of the problem. This perception created the assumption that leads to error. This should give one pause about mentally defaulting to first impressions.

“If a card has a vowel on one side, then it has an even number on the other.” Here we are working with letters and numbers. Transposing the words to read “If a card has an even number on one side, then……….” Clarifies the problem and gives us a different perspective on even numbered cards. It becomes apparent that what even numbered cards have on the other side has no significance. The rule is only concerned with cards that have vowels on one side.

Sigmund Freud would “reframe” something to transform its meaning by putting it into a different framework or context than it has previously been perceived. For example, by reframing the “unconscious” as a part of him that was “infantile,” Freud began to help his patients change the way they thought and reacted to their own behavior.

The important thing is not to persist with one way of looking at the problem. Consider the following interesting twist, again using four cards. This time, however, we reframe the problem by substituting journeys and modes of transportation for letters and numbers. Each card has a city on one side and a mode of transportation on the other.

LOS ANGELES NEW YORK AIRPLANE CAR

This time, the cards have printed on them the legends, respectively, Los Angeles, New York, airplane, and car; and the rule is reframed to read: “Every time I go to Los Angeles, I travel by airplane. While this rule is identical to the number-letter version, it poses little difficulty for individuals. In fact, now 80 percent of subjects immediately realize the need to turn over the card with “car” on it.

Apparently, one realizes that if the card with “car” on it has the name “Los Angeles” on the back, the rule has been proved incorrect; whereas it is immaterial what it says on the back of the airplane since, as far as the rule is concerned, one can go to New York any way one wants.

Why is it that 80 percent of subjects get this problem right, whereas only 10 percent know which cards to turn over in the vowel-number version? By changing the content (cities and modes of transportation substituted for letters and numbers), we restructured the problem, which dramatically changed our reasoning. The structure of a problem colors our perspective and the way we think.

The significant point about this test is that we are incredibly bad at it. And it doesn’t make much difference what the level of education is of the person taking the test. Moreover, even training in formal logic seems to make little difference to a person’s performance. The mistake that we tend to make is fairly standard. People almost always recognize that they have to pick up the card with the vowel, but they fail to see that they also have to pick up the card with the odd number. They think instead that they have to pick up the card with the even number.

One of the most interesting things about this phenomenon is that even when the correct answer is pointed out, people feel resistance to it. It apparently feels “right” that the card with the even number should be picked up. It feels right because your initial perspective is biased toward the usual way of thinking. It is only when you look at it from different perspectives that you get a deeper understanding of the problem.

**MICHAEL MICHALKO**

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