The Story of Psychology (106 page)

The obvious first step: M must be 1, since no two digits—S + M in this case—can add up to more than 19, even with a carry.
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Simon and Newell had volunteers talk out loud as they worked on such a puzzle, recorded everything they said, and afterward diagrammed the steps of their thought process in the form of a search track of moves, decisions at forks with more than one option, wrong choices pursued to dead ends, reversals to try another route from the last fork, and so on.

Simon and Newell made particular use of chess, a vastly more complex problem than either the Tower or cryptarithmetic. In a typical chess game of sixty moves, at each step there are on average thirty possible moves; to “look ahead” only three moves would mean visualizing twenty-seven thousand possibilities. A key question for Simon and Newell was how chess players deal with such impossibly large sets of
contingencies. The answer: A skilled chess player does not consider all the possible moves he might make next and all the moves his opponent might make in response but only those few moves that make good sense and that follow elementary guidelines like “Guard the King” and “Don’t give away a piece for one of lesser value.” In short, the chess player makes a heuristic search—one guided by broad strategic principles of good sense—rather than a thorough but uninformed one.

The Newell and Simon theory of problem solving—for alphabetical reasons Newell’s name is first on their joint publications—on which they worked for another fifteen years is that problem solving is a search for a route from an
initial state
to a
goal.
To get there, the problem solver has to find a
path
through a
problem space
made up of all possible states he might arrive at by making all the moves that obey the
path constraints
(rules or conditions of the domain).

In most such searches, the possibilities multiply geometrically, since each decision point offers two or more possibilities, each of which leads to another decision point offering another set of possibilities. In the sixty moves of an average chess game, each move, as already mentioned, has an average of thirty alternatives; the total number of paths in a game is 30
⁶⁰
—30 million trillion trillion trillion trillion trillion trillion—a number totally beyond human comprehension. Accordingly, as Simon and Newell’s research demonstrated, problem solvers, in finding their way through such problem spaces, make no effort to look at every possibility.

In the massive tome they published in 1972 and straightforwardly called
Human Problem Solving
, Newell and Simon presented what they considered its general characteristics. Among them:
⁷⁵

In a relatively recent review of problem-solving theory, Keith Holyoak offers a homely example of means-end analysis. Your goal is to have your living room freshly painted. The subgoal nearest that goal is the condition in which you can paint it, but that requires you to have paint and a brush, so you must first reach the earlier subgoal of buying them. To do so requires reaching the even earlier subgoal of being at a hardware store. So it goes, backward chaining until you have a complete strategy by which to move from your present state to the state of having a painted living room.
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As major an achievement as Newell and Simon’s theory of problem solving was, it dealt only with deductive reasoning. Moreover, it considered only “knowledge-poor” problem solving—the kind applicable to puzzles, games, and abstract problems. To what extent the method described problem solving in knowledge-rich domains—the sciences, business, or law, for instance—was unclear.

For the past several decades, therefore, a number of researchers have been expanding the investigation of reasoning. Some have studied the psychological tendencies on which deductive and inductive reasoning are based; some whether either form, or some other, is what we use in everyday reasoning; some the differences in the kinds of reasoning used by experts and by novices in knowledge-rich situations. These investigations
have produced a wealth of insights into the formerly invisible workings of the reasoning human mind. Here are a few of the highlights:

Deductive reasoning:
The traditional idea, going back to Aristotle, is that there are two kinds of reasoning, deduction and induction. Deduction extracts a further belief from one that is given; that is, if the premise or premises are true, so is the conclusion, since it is necessarily included in them. From the premises of Aristotle’s classic syllogism

it follows that

This kind of reasoning is tight, strong, easy to follow, and fully convincing. It is exemplified by proofs of logic and geometry theorems.

Yet many other syllogisms that have only two premises and contain only three terms are not so transparent; some are so difficult that most people cannot draw a valid conclusion from them. Philip Johnson-Laird, who has done research on the psychology of deduction, gives an example that he has used in the laboratory. Imagine that in a room there are some archaeologists, biologists, and chess players, and that these two statements are true:

What, if anything, follows from those premises? Johnson-Laird has found that few people can give the right answer.
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*
Why not? He believes that the ease of drawing the valid conclusion in the Socrates syllogism and the difficulty of doing so in the archaeologist syllogism are due to the way the arguments are represented in the mind—the “mental models” we create of them, a theory he has been developing and testing ever since.
⁷⁸

People with formal training in logic usually visualize such arguments in the form of geometrical diagrams, the two premises being represented
by circles, one inside the other, or overlapping it, or separate. But Johnson-Laird’s theory, based on his research and validated by a computer simulation, is that people without such training use a more homespun model. In the Socrates syllogism, they unconsciously imagine a number of people, all mortal, imagine Socrates as related to that group, and then cast about for any other possibility (anyone outside the set—possibly Socrates). There being no such possibility, they correctly conclude that Socrates is mortal.

In the archaeologist syllogism, however, they imagine and try out first one, then another, and finally a third model, of increasing difficulty (we will spare ourselves the details). Some people rely on the first, unable to see that the second invalidates it, and others the second, not seeing that it, too, is discredited by the third and most difficult—which leads to the only valid conclusion.
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Mental modeling is not the only source of erroneous deductions. Experiments have shown that even where the form of a syllogism is simple and its mental model easy to create, people are apt to be misled by their beliefs and information. One research team asked a group of subjects whether these two syllogisms were logically correct:

More people thought the first one logically correct than did the second, although the two are identical in structure, differing only in the substitution of the nonsense word “opprobines” for “automobiles.” They were misled by their knowledge of automobiles; knowing the conclusion of the first syllogism to be true, they thought the argument logically correct. But it is not, as they could see in the case of opprobines, about which they knew nothing and where they could recognize that there is no necessary overlap between opprobines and things with a motor.
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Inductive reasoning:
By contrast, inductive reasoning is loose and inexact. It moves from specific beliefs to broader ones, that is, from limited cases to generalizations. From “Socrates is mortal,” “Aristotle is mortal,”
and other instances, one infers, with a degree of confidence based on the number of cases, that “all men are mortal,” although even a single case to the contrary would invalidate that conclusion.

A good deal of important human reasoning is of this type. Categorization and concept formation, crucial to thinking, are the products of induction, as seen in studies of how children arrive at categories and concepts. All the higher knowledge humankind possesses about the world—everything from the inevitability of death to the laws of planetary motion and galactic formation—is the product of the derivation of generalizations from a mass of particulars.

Induction is also the reasoning used where pattern recognition is the key to solving a problem. A simple example:

What number comes next?

2 3 5 6 9 10 14 15 ——

A ten-year-old can answer correctly after a while; an adult can see the pattern and the answer (20) in a minute or less. It is the very reasoning process employed by economists, public health officials, telephone system planners, and many others whose recognition of patterns is critically important to the survival of modern society.

(Disconcertingly, researchers have found that many people frequently fail to reason inductively from incoming information. All too often, we notice and add to our memory store only what supports a strongly held belief, ignoring any that does not. Psychologists call this “confirmation bias.” Dan Russell and Warren Jones gave subjects materials to read, some confirming and some disproving the existence of ESP. Afterward, believers in ESP remembered the confirming materials 100 percent of the time but the negative materials only 39 percent of the time, while skeptics remembered both kinds about 90 percent of the time.
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)

Much of our reasoning combines deduction and induction, each of which serves its own purposes. How we came by both kinds of reasoning ability has been explained, at least hypothetically, by evolutionary psychology: Both methods are assets in the struggle to survive and were the products of natural selection.
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The hypothesis seems validated by a recent study using PET scans: When subjects were asked to solve problems requiring deduction, two small areas on the right side of the brain showed increased activity; when the problems required inductive thinking,
two brain structures on the left side showed it.
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Natural selection, in short, developed brain structures capable of both kinds of reasoning.

Probabilistic reasoning:
The human mind’s abilities are the product of evolutionary selection, but we have lived in advanced civilized societies too short a time to have developed an inherited ability for sound reasoning about statistical likelihoods, though it is often called for in modern life.

Daniel Kahneman and Amos Tversky, who did much of the basic work in this area, asked a group of subjects which they would prefer: a sure gain of $80, or an 85 percent chance of winning $100 along with a 15 percent chance of winning nothing. Most people preferred the sure gain of $80, although statistically the average yield of the risky choice is $85. Kahneman and Tversky concluded that people are “risk-averse”: They prefer a sure thing even when a risky thing is the better bet.

Turning to the obverse situation, Kahneman and Tversky asked another group of subjects whether they would prefer a sure loss of $80 or an 85 percent chance of losing $100 along with a 15 percent chance of losing nothing. This time a large majority preferred the gamble to the sure thing even though, on average, the gamble is costlier. Kahneman and Tversky’s conclusion: When choosing between gains, people are risk-averse; when choosing between losses, they are risk-seeking—and in both cases are likely to make poor judgments.
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An even more disquieting finding came from a later experiment in which they posed two versions of a public-health problem to groups of college students. The versions are mathematically identical but different in wording. The first version: