How To Approach Problems

How To Approach Problems:

Once we have settled on a perspective, we close off but one line of thought. Certain kinds of ideas occur to us, but only those kinds and no others. Have you ever looked closely at the wheels on a railroad train? They are flanged. That is, they have a lip on the inside to prevent them from sliding off the track. Originally train wheels were not flanged–instead, the railroad tracks were. Because the problem of railroad safety had been expressed as: “How can the tracks be made safer for trains to ride on?” hundreds of thousands of miles of track were manufactured with an unnecessary steel lip. Only when the problem was redefined as: “How can the wheels be made to secure the track more securely?” was the flanged wheel invented.

One of the many ways in which we have become cognitively lazy is to accept our initial impression of the problem that it encounters. Once we settle on an initial perspective, we don’t seek alternative ways of looking at the problem. Like our first impression of people, our initial perspective on problems and situations are apt to be narrow and superficial. We see no more than we expect to see based on our past experiences in life, education and work.

Most of us look at a scene rather than look into it. People tend to think of perception as a passive process. We see, hear, smell, taste or feel stimuli that impinge upon our senses. We think that if we are at all objective, we record what is actually there. Yet perception is demonstrably an active rather than a passive process; it constructs rather than records “reality.” You construct how you choose to see the world.

THOUGHT EXPERIMENT

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

A B 4 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.

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. Leonardo Da Vinci wrote in his notebooks that one should always assume that your first impression of a problem is usually biased toward your usual way of thinking. He suggested looking at your problem in at least three different ways to get a better understanding.

“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 above thought experiment 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 mechanisms.

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.