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algorithm. A systematic, step-by-step problem-solving strategy that is guaranteed
to produce a solution.
heuristic. A rule of thumb that allows one to make judgments that are quick but
often in error.
If algorithms are guaranteed to produce solutions, why not use them all the time?
The reason is that algorithms are not always available—and sometimes they take too
much time to be practical. Thus, chess experts do not consider all the possible moves
on the board, because there are simply too many of them. This strategy is fine for
computer chess programs made to evaluate millions of positions and moves per
second. But great players must rely instead on heuristics, such as “Get control of the
center of the board.”
Some heuristics are general, in that they can be used to solve a wide range of
problems. One important general heuristic is the means-end analysis (Newell &
Simon, 1972). This involves breaking a larger problem into a series of subgoals. For
example, let’s say you are starting a new job Monday and have to get to work on
time. You could solve this problem by driving your car to work, but your car needs
repair. So, you set a subgoal of getting your car repaired. But this might require other
subgoals, such as finding a mechanic. For some problems, the nested subgoals can
get quite complex and involved. In fact, unless people carefully evaluate whether
each step brings them closer to the endpoint, it is possible to lose track of what part
of the problem is actually being solved (Simon, 1975).
means-end analysis. A problem-solving heuristic that involves breaking down a
larger problem into a series of subgoals.
Another powerful problem-solving heuristic consists of the use of analogies. If
you have previously solved some problem that seems similar to a new one, you can
use the old solution as a model. The trick is to recognize that the second problem
resembles the first. Analogical thinking plays a central role in science, where the
heart has been likened to a pump, the brain to a computer, the eye to a camera,
molecules to billiard balls, the phone to an ear, and the spinning earth to a slowing
toy top. Research shows that people are quicker to grasp and use new scientific
concepts when these concepts are taught by analogy than when they are explained
in literal terms (Donnelly & McDaniel, 1993)—and that the shorter the “mental leap” is
between two problems, because they are similar in obvious ways, the more effective
is the analogy for teaching said concepts (Chen, 2002; Holyoak & Thagard, 1997).
Diagrams and animated displays may be particularly useful for getting people to
notice the analogical link between problems.
analogy. A problem-solving heuristic that involves using an old solution as a
model for a new, similar problem.
Creativity is also associated with analogical thinking when participants are tasked
with making connections that require a longer “mental leap” (Barnett & Ceci, 2002;
Bowdle & Gentner, 2005). For example, try solving the problem of connecting
furnace:coal with stomach:food. Did you find the connection? A furnace burns coal,
whereas a stomach “burns” (i.e., metabolizes) food. Another connection you might
have thought of is fuel. Food and coal are both referred to as fuel, whereas a furnace
and stomach both use fuel to create energy. Green and colleagues (2012) presented
problems such as this while imaging the brain. They argued that connecting distant
items reflects creative thinking and seems to be associated with activity in the
frontopolar cortex of the brain.
Insight
When people struggle with a problem, they usually try to monitor their progress to
evaluate whether they’re closing in on a solution (Kotovsky, Hayes, & Simon, 1985).
But have you ever puzzled over something, felt as if you were stumped, and then
come up with the answer abruptly, out of the blue, as if a light bulb flashed inside your
head? Aha! If so, then you have experienced problem solving by insight, a process
in which the solution pops to mind all of a sudden—and in which the problem solver
doesn’t realize the solution is coming and cannot describe what he or she was
thinking at the time (Sternberg & Davidson, 1999).
insight. A form of problem solving in which the solution seems to pop to mind all
of a sudden.
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Insight is something we cannot reproduce since it is impossible to describe how
the sudden solution was developed.
iStock.com/Igor Vershinsky
Insight is an experience that seems to arise whenever people at an impasse relax
the way they approach a problem, reframe it, switch from one strategy to another,
remove a mental block, or identify an analogy from a prior experience (Knoblich &
Ohlsson, 1999; Ohlsson, 2011; Simon, 1989). Some researchers claim that these
apparent flashes of insight actually result from a gradual, step-by-step process—but
that sometimes we’re just not aware of the progress we are making (Weisberg, 1992).
Others find that certain types of tasks seem to promote a special form of problem
solving that has a sudden, all-or-none quality (Smith & Kounios, 1996). Is insight
gradual but nonconscious, or is it truly sudden? It’s hard to know for sure. Weisberg
(2015) argues that both claims should be combined to understand how insight works.
But that understanding cannot come from participant reports alone. Consider
research by Janet Metcalfe and David Wiebe (1987), for example. They had subjects
work on different types of problems and periodically rate how “warm” they were
getting on a seven-point scale. On multistep algebra problems, the ratings increased
steadily as subjects neared a solution. On insight problems, however, the warmth
ratings remained flat and low, then rose all at once, the moment subjects
encountered a solution. It’s interesting that when people working on insight problems
are asked to describe their thinking along the way, which brings the process into
consciousness, their problem-solving performance deteriorates (Schooler, Ohlsson, &
Brooks, 1993).
People often report that they tried unsuccessfully for hours to solve a problem and
then, after taking a break, came back and it “clicked”: An insight quickly converted
into a solution. The improved ability to solve a problem after taking a break from it is
called the incubation effect. One puzzle that psychologists have used to investigate
incubation effects in the laboratory is the “cheap-necklace problem,” shown in Figure
7.7. Try it for 5 minutes before reading on. Using this problem, Silveira (1971) tested
three groups of subjects. All groups worked on the same task for a total of 30
minutes. One group worked without a break. After 15 minutes, however, the second
group took a half-hour break and the third group took a 4-hour break. During these
rest periods, subjects were kept busy with other activities that prevented them from
continuing to work on the necklace problem. The results provided strong evidence for
incubation: Subjects who took a break were more likely to solve the problem than
those who did not. In fact, the longer the interlude, the better the performance. The
implication of this effect is clear. Sometimes it helps to take a break while trying to
solve problems that require a critical insight—as in the cheap-necklace problem,
where the key is to realize that you can’t link all four chains (Anderson, 1990).
incubation effect. Forming a solution to a problem as a result of taking a mental
break from it.
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Figure 7.7 The Cheap-Necklace Problem
LEARNING CHECK
Crash Project
Here’s the problem: Your computer has crashed, and you’ve lost the extremely
important psychology paper you were just finishing. Each of the following approaches
to recovering it falls under one of the four basic methods for solving problems: trial
and error (T), algorithm (A), heuristic (H), or insight (I). Identify the appropriate letter
for each.
(Answers: 1. H; 2. A; 3. H; 4. I; 5. T; 6. A.)
The history of science is filled with stories of discovery by flashes of insight. But is
insight necessarily the product of a great mind? Many psychologists believe that
other animals too are capable of insight, not just of trial-and-error problem solving.
Many years ago, Wolfgang Köhler (1925) claimed that a chimpanzee named Sultan
displayed insight in problem solving. Köhler put bananas and a long stick outside the
chimp’s cage, both out of reach, and put a short stick inside the cage. Sultan poked at
the banana with the short stick, but it was too short to reach the fruit. After trying
repeatedly, he gave up, dropped the stick, and walked away. Then all of a sudden,
Sultan jumped up, picked up the short stick, and used it to get the longer stick—which
he used to get the banana. Did this episode reveal insight? Many researchers are
skeptical of such a claim and suggest that the apparent insight may be no more than
an accumulation of learned behaviors (Epstein, Kirshnit, Lanza, & Rubin, 1984). Yet
others agree with Köhler. Sociobiologist Edward O. Wilson tells a Sultan-like story of
a chimp trying to reach some leaves: “He sat and looked at the tree for a long time,
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and went over to a log. He dragged it over to the tree, propped it against the trunk,
then stood back and charged his ramp. It’s extremely difficult to explain that, other
than to say the chimp was consciously thinking” (Begley & Ramo, 1993).
“Blind Spots” in Problem Solving
Using trial and error, algorithms, heuristics, and insight, people often display a
remarkable capacity to solve problems. As we have experienced time and again,
however, our competencies are often compromised by certain “blind spots.” To
appreciate some of these shortcomings, try the problems in Figures 7.8 and 7.9
before reading on. The solutions are revealed later on in the section.
Figure 7.8 The Nine-Dot Problem
Figure 7.9 Duncker’s Candle Problem Monica Wierzbicki/Body Scientific Intl.
Representation Failures
For many years, problem-solving researchers have used the “nine-dot problem”
presented in Figure 7.8 (Burnham & Davis, 1969; MacGregor, Ormerod, & Chronicle,
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2001; Öllinger, Jones, & Knoblich, 2014). This problem is notoriously difficult, and it
seems to illustrate that failure often results from an incorrect problem representation.
Even though the instructions say nothing about staying inside an imaginary square
formed from the dots, almost everyone behaves as though the outside dots form a
boundary that cannot be crossed (to understand why, review the Gestalt principles of
perceptual grouping discussed in the chapter on sensation and perception and think
about your typical way of solving problems that required you to connect the dots). If
you don’t mentally handicap yourself in this way, the solution is simple. But people do,
which is what makes the problem so difficult. Is this tendency to represent problems
narrowly limited to clever laboratory puzzles and brainteasers? Sadly, no. As we’ll
learn in the Treatment and Interventions chapter, cognitively oriented clinical
psychologists find that people often suffer needlessly because they conceptualize
problems in ways that make them seem insurmountable.
Mental Set
The nine-dot problem can also illustrate a mental set, the desire to use strategies
that have worked in the past to solve a current problem. When trying to solve the
nine-dot problem, our minds can easily go back to a time when we were given
problems that required us to connect the dots. Do you remember the last time you
had to draw a straight line between two points? You were probably in elementary
school. When connecting the dots, you learned that connecting lines were never
drawn outside of the dots. You were also taught that when you color a picture with
crayons, you are supposed to stay in the lines. Thus, your mental set from
elementary school may have been the reason it never occurred to you to drag the line
beyond the dot.
mental set. Incorporating a strategy that worked in the past.
Functional Fixedness
The “candle problem” in Figure 7.9 illustrates a more specific type of
representation failure. The difficulty in this case is one of functional fixedness, a
tendency to think of objects only in terms of their usual functions. In a way, our brains
almost become locked into how they view an object and its use. In the candle
problem, for example, you’d struggle for as long as you recognized the thumbtack
box as only a container, not as a possible shelf. A brick is a brick, but it can also be
used as a paperweight. Finding creative new solutions to practical problems often
requires that we think open-mindedly—or, as they say, “outside the box”—in order to
imagine unusual uses for common objects (Sternberg & Lubart, 1991; Weisberg,
1986).
functional fixedness. The tendency to think of objects only in terms of their usual
functions, a limitation that disrupts problem solving.
The Confirmation Bias
The nine-dot and candle problems are tricky not because they are intellectually
demanding but because people tend to be overly rigid in their thinking. But there’s
more. Once we think we have a solution, we fall prey to confirmation bias, a
tendency to look only for evidence that will verify our beliefs—which can prevent us
from realizing that we are in error. This bias is pervasive and has a negative influence
on the way people approach the problems in their daily lives (Nickerson, 1998).
confirmation bias. The inclination to search only for evidence that will verify
one’s beliefs.
To demonstrate, Peter Wason (1960) gave students a three-number sequence, 2-
4-6, and challenged them to figure out the rule he had used to generate this set. How
should they proceed? By making up their own sequences and asking the
experimenter to indicate whether or not they fit the rule. Subjects were told they could
test as many sequences as they wanted and to state the rule only if they felt certain
that they knew it. The task was straightforward and the rule behind 2-4-6 was easy:
any three increasing numbers. Yet out of 29 subjects, only 6 discovered the correct
rule without first seizing on one that was incorrect. What happened was this: Subjects
would start with an initial hypothesis (adding by 2s, even numbers, skipping numbers)
and then search only for confirming evidence. Thinking that the rule was “adding by
2s,” a subject might test 6-8-10, 50-52-54, 21-23-25, and so on, yet never try
disconfirming sets such as 6-8-4 or 3-2-1. When all the sequences fit, the subject
would proudly and with confidence announce the wrong rule.
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Description
Figure 7.10 Solution to the Cheap-Necklace Problem
Description
Figure 7.11 Solution to the Nine-Dot Problem
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Description
Figure 7.12 Solution to Duncker’s Candle Problem Monica Wierzbicki/Body
Scientific Intl.
The Representativeness Heuristic
One rule of thumb that people use to make probability estimates is the
representativeness heuristic—the tendency to judge the likelihood of an event’s
occurring by how typical it seems (Kahneman & Tversky, 1973). Like other heuristics,
this one enables us to make quick judgments. With speed, however, comes bias and
a possible loss of accuracy. For example, which sequence of boys (B) and girls (G)
would you say is more likely to occur in a family with six children: (1) B,G,B,G,B,G; (2)
B,B,B,G,G,G; or (3) G,B,B,G,G,B? These sequences are all equally likely. Yet most
people say that the third is more likely than the others because it looks typical of a
random sequence.
representativeness heuristic. A tendency to estimate the likelihood of an event
in terms of how typical it seems.
The problem with this heuristic is that it often leads us to ignore numerical
probabilities, or “base rates.” Now that you’ve considered the boy-girl sequence
example, contemplate this scenario. Suppose there’s a group of 30 engineers and 70
lawyers. In that group, a random selection of one person results in a discussion with
a conservative man named Jack, who enjoys mathematical puzzles and has no
interest in social or political issues. Question: Is Jack a lawyer or an engineer? When
Kahneman and Tversky (1973) presented this item to subjects, most guessed that
Jack was an engineer (because he seemed to fit the stereotyped image of an
engineer)—even though he came from a group containing a 70 percent majority of
lawyers. In this instance, representativeness overwhelmed the more predictive base
rate. Do you think your consideration of the boy-girl sequence example made you
more aware of this flaw in thinking and, as a result, helped you to avoid the flaw that
Kahneman and Tversky’s participants made?
The Availability Heuristic
Another mental shortcut that people use is the availability heuristic, the
tendency to estimate the likelihood of an event based on how easily instances of that
event come to mind. To demonstrate, Tversky and Kahneman (1973) asked subjects
to judge whether there are more words in English that begin with the letter K or the
letter T. To answer this question, subjects tried to think of words that started with
each letter. More words came to mind that started with T, so most subjects correctly
chose T as the answer. In this case, the availability heuristic was useful. It sure beat
counting up all the relevant words in the dictionary.
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availability heuristic. A tendency to estimate the likelihood of an event in terms
of how easily instances of it can be recalled.
As demonstrated, the availability heuristic enables us to make judgments that are
quick and easy. But often, these judgments are in error. For example, Tversky and
Kahneman asked some subjects the following question: Which is more common,
words that start with the letter K or words that contain K as the third letter? It turns out
the English language contains many more words with K as the third letter than as the
first. Yet out of 152 subjects, 105 guessed it to be the other way around. The reason
for this disparity is that it’s easier to bring to mind words that start with K, so these are
judged more common.
Dramatic airline disasters are so memorable that people overestimate the risks of
flying. In fact, mile for mile, travelers are far more likely to die in a car crash than on a
commercial flight.
iStock.com/porpeller
The letter-estimation bias is harmless, but the availability heuristic can lead us
astray in important ways—as when uncommon events pop easily to mind because
they are very recent or highly emotional. One possible consequence concerns the
perception of risk. Which is a more likely cause of death in the United States:
drowning in a pool or fatal injury due to a cataclysmic storm such as a tornado or
hurricane? The truth is that swimming pools are much riskier—with the odds at 1 in
5,271—than cataclysmic storms—with the odds at 1 in 62,288 (Insurance Information
Institute, 2016). However, the media posts more stories about storm fatalities than
swimming pool drownings. Thus, people who are asked to guess the major causes of
death tend to overestimate the number of those who die as a result of events that are
highly publicized such as shootings, fires, floods, terrorist bombings, accidents, and
other dramatic events—and to underestimate the number of deaths caused by heart
attacks, diabetes, and other mundane and less memorable events (Slovic, Fischoff, &
Lichtenstein, 1982). Made relevant by current fears of terrorism, research shows that
people’s perceptions of risk are affected more by fear, anxiety, and other emotions
than by cold probabilities (Slovic, 2000; Tannenbaum et al., 2015).
Anchoring Effects
Using the availability heuristic, people are influenced in their judgments by the
facts that are most available in memory—and they fail to make adjustments to
compensate for that bias. A related phenomenon is the anchoring effect, the
tendency to use one stimulus as an “anchor,” or reference point, in judging a second
stimulus.
anchoring effect. The tendency to use an initial value as an “anchor,” or
reference point, in making a new numerical estimate.
Imagine being asked, “What proportion of African nations are in the United
Nations?” Think about it. What would be your estimate? Now suppose that before
answering this question, the experimenter spun a roulette wheel marked with
numbers from 1 to 100. You think the outcome of the spin is random, but actually the
wheel is rigged to stop either at 10 or at 65. At that point, the experimenter asks, “Is
the proportion of African nations in the United Nations above or below the wheel
number? Then what, specifically, is your estimate?” As a result of this procedure,
subjects vary their estimates according to the numerical reference point provided by
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the wheel number. Those for whom 10 was the initial anchor estimated that 25
percent of African nations were in the U.N. Among those given 65 as an anchor, the
estimate was 45 percent. Even though subjects assumed the wheel number to be
arbitrary, it served as a starting point for their numerical estimates (Kahneman et al.,
1982). Additional studies have confirmed that anchoring effects are common and
powerful—even with our own judgments about memory performance (Yang, Sun, &
Shanks, 2017). Thus, numerical reference points bias judgments of events even
among people who are offered prizes to be accurate and among those who say
afterward that they were not influenced by the anchor (Wilson, Houston, Brekke, &
Etling, 1996).
LEARNING CHECK
Blind Spots and Biases
Don’t let blind spots in problem solving or biases in judgment prevent you from
seeing which description best matches each term in the left column.
(Answers: 1. d; 2. c; 3. b; 4. g; 5. f; 6. e; 7. a.)
What’s Your Prediction?
If anchoring leads us to set high or low reference points, what are the
implications? Can trial lawyers raise or lower the amount of money that juries award
by stating large or small amounts? Would juries deem lawyers as greedy, and react
against it? Or, are juries so focused on evidence that they disregard what lawyers ask
for?
Mollie Marti and Roselle Wissler (2000) presented mock jurors with a case of a
dock worker who fell and was badly injured, and who sued the trucking company
responsible for the accident. There was no dispute that the company was at fault;
jurors only had to decide how much money to award the worker for pain and
suffering. In one version of the case, the plaintiff’s lawyer did not state a figure. In
other versions, he asked for $750,000, $1.5 million, or $5 million. Make a prediction:
What effect do you think the requests had?
When no request was made, jurors gave an average of $680,000. Did the larger
requests lead jurors to award more, less, or the same? Demonstrating an anchoring
effect, Figure 7.13 shows that the more the lawyer asked for, the more he got. In fact,
one follow-up study showed that jurors awarded even more when the lawyer sought
$15 million. Bennett (2014) argues that the anchoring effect occurs “even when the
anchor is incomplete, inaccurate, irrelevant, implausible, or even random” (p. 489).
Bennett also reviews anchoring research across a wide range of fields such as
medicine, real estate, psychology, and finances. In this way, the anchoring effect can
have quite the impact on things such as the punishment given to a guilty party, the
amount of money a home sells for, and investments. Thanks to anchoring effects, you
can sometimes get what you ask for.
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Description
Figure 7.13 Anchoring Effects Source: Marti, M. W., & Wissler, R. L. (2000). Be
careful what you ask for: The effect of anchors on personal-injury damages awards.
Journal of Experimental Psychology: Applied, 6(2), 91–103.
https://doi.org/10.1037/1076-898X.6.2.91
LANGUAGE
LEARNING OBJECTIVES
Define language, and recognize its properties.
Determine if you agree with the saying, “All humans speak in the same
tongue.”
Identify the universal properties of all languages.
Describe how language emerges.
Language is a form of communication consisting of a system of sounds, words,
meanings, and rules for their combination. Language is also a defining and adaptive
milestone in human evolution. Linguist Noam Chomsky (1972) argued that the human
brain is biologically hardwired for the acquisition of language. Thus, all cultures have
language, all languages have certain structural properties (such as nouns and verbs)
in common, and children all over the world learn to fluently speak the language they
hear, at about the same age, and without much effort or instruction.
language. A form of communication consisting of sounds, words, meanings, and
rules for their combination.
When it comes to language, it’s clear that some form of learning occurs—but it’s
also clear that humans are born with a unique sensitivity to the sounds and structures
of speech (MacWhinney, 1998). Terrence Deacon (1998) has argued that the human
brain and language have coevolved over millions of years. Steven Pinker (1994)
believes that the ability to learn, speak, and understand language is a powerful
instinct, tightly woven into the human experience. “All over the world,” he notes,
“members of our species fashion their breath into hisses and hums and squeaks and
pops and listen to others do the same.... We humans are fitted with a means of
sharing our ideas, in all their unfathomable vastness” (Pinker, 1999, p. 1). In the
coming sections, we will consider the unique properties of “language” and, finally, the
relationship between thought and language.
Characteristics of Human Language
According to Ethnologue (2018), there are roughly 7,097 spoken languages
worldwide, to say nothing of the different dialects within each language. When all the
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