Why Good Thoughts Block Better Ones

Abstract

In a classic 1942 experiment, American psychologist Abraham Luchins asked volunteers to do some basic math by picturing water jugs in their mind. Given three empty containers, for example, each with a different capacity 21, 127 and three units of water the participants had to figure out how to transfer liquid between the containers to measure out precisely 100 units. They could fill and empty each jug as many times as they wanted, but they had to fill the vessels to their limits. The solution was to first fill the second jug to its capacity of 127 units, then empty it into the first to remove 21 units, leaving 106, and finally to fill the third jug twice to subtract six units for a remainder of 100. Luchins presented his volunteers with several more problems that could be solved with essentially the same three steps; they made quick work of them. Yet when he gave them a problem with a simpler and faster solution than the previous tasks, they failed to see it.

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74 Scientific American, March 2014 Photograph by Tktk Tktk

March 2014, ScientificAmerican.com 75
Why
Good
Thoughts
Illustration by Danny Schwartz
By Merim Bilalić and Peter McLeod
While we are working through a problem,
the brain’s tendency to stick with familiar ideas
can literally blind us to superior solutions
Block
Better
Ones
psychology

76 Scientific American, March 2014
  1942 ,    
asked volunteers to do some basic math by picturing water jugs in their mind. Given three
empty containers, for example, each with a dierent capacity—21, 127 and three units of water—
the participants had to figure out how to transfer liquid between the containers to measure out
precisely 100 units. They could fill and empty each jug as many times as they wanted, but they
had to fill the vessels to their limits. The solution was to first fill the second jug to its capacity of
127 units, then empty it into the first to remove 21 units, leaving 106, and finally to fill the third
jug twice to subtract six units for a remainder of 100. Luchins presented his volunteers with
several more problems that could be solved with essentially the same three steps; they made
quick work of them. Yet when he gave them a problem with a simpler and faster solution than
the previous tasks, they failed to see it.
This time, Luchins asked the participants to measure out 20
units of water using containers that could hold 23, 49 and three
liquid units. The solution is obvious, right? Simply fill the first
jug and empty it into the third one: 23 – 3 = 20. Yet many people
in Luchins’s experiment persisted to solve the easier problem the
old way, emptying the second container into the first and then
into the third twice: 49 – 23 – 3 – 3 = 20. And when Luchins gave
them a problem that had a two-step solution—but could not be
solved using the three-step method to which the volunteers had
become accustomed—they gave up, saying it was impossible.
The water jug experiment is one of the most famous exam-
ples of the Einstellung eect: the human brain’s dogged tenden-
cy to stick with a familiar solution to a problem—the one that
first comes to mind—and to ignore alternatives. Often this type
of thinking is a useful heuristic. Once you have hit on a success-
ful method to, say, peel garlic, there is no point in trying an ar -
ray of dierent techniques every time you need a new clove. The
trouble with this cognitive shortcut, however, is that it some-
times blinds people to more ecient or appropriate solutions
than the ones they already know.
Building on Luchins’s early work, psychologists replicated
the Einstellung eect in many dierent laboratory studies with
both novices and experts exercising a range of mental abilities,
but exactly how and why it happened was never clear. Recently,
by recording the eye movements of highly skilled chess players,
we have solved the mystery. It turns out that people under the
influence of this cognitive shortcut are literally blind to certain
details in their environment that could provide them with a
more eective solution. New research also suggests that many
dierent cognitive biases discovered by psychologists over the
years—those in the courtroom and the hospital, for instance—
are in fact variations of the Einstellung eect.
BACK TO SQUARE ONE
     1990, psychologists have studied the
Einstellung eect by recruiting chess players of varying skill lev-
els, from amateur to grand master. In such experiments, re -
searchers have presented players with specific arrangements of
chess pieces on virtual chessboards and asked them to achieve a
checkmate in as few moves as possible. Our own studies, for in -
stance, provided expert chess players with scenarios in which
they could accomplish a checkmate using a well-known sequence
IN BRIEF
The Einstellung eect is the brain’s tendency to stick
with the most familiar solution to a problem and
stubbornly ignore alternatives.
Psychologists have known about this mental phe-
nomenon since the 1940s, but only now do they have
a solid understanding of how it happens.
In recent eye-tracking experiments, familiar ideas
blinded chess players to areas of a chessboard that
would have provided clues to better solutions.
In
Merim Bilali´c is a professor of cognitive science at the University
of Klagenfurt in Austria and a senior research fellow at the Uni-
versity of Tübingen in Germany. His research on the Einstellung
eect won the British Psychological Society’s Award for Outstanding
Doctoral Research Contributions to Psychology in 2008.
Peter McLeod is an emeritus fellow at Queen’s College at
the University of Oxford. He is chair of the Oxford Foundation
for Theoretical Neuroscience and Articial Intelligence.

March 2014, ScientificAmerican.com 77
called “smothered mate.” In this five-step maneuver, the queen is
sacrificed to draw one of the opponent’s pieces onto a square to
block o the king’s escape route. The players also had the option
to checkmate the king in just three moves with a much less fa -
miliar sequence. As in Luchins’s water jug studies, most of the
players failed to find the more ecient solution.
During some of these studies, we asked the players what was
going through their mind. They said they had found the smoth-
ered mate solution and insisted they were searching for a short-
er one, to no avail. But the verbal reports oered no insight into
why they could not find the swifter solution. In 2007 we decided
to try something a little more objective: tracking eye move-
ments with an infrared camera. Which part of the board people
looked at and how long they looked at dierent areas would un -
equivocally tell us which aspects of the problem they were notic-
ing and ignoring.
In this experiment, we followed the gaze of five expert chess
players as they examined a board that could be solved either with
the longer smothered mate maneuver or with the shorter three-
move sequence. After an average of 37 seconds, all the players
insisted that the smothered mate was the speediest possible way
to corner the king. When we presented them with a board that
could be solved only with the three-sequence move, however, they
found it with no problem. And when we told the players that this
same swift checkmate had been possible in the previous chess-
board, they were shocked. “No, it is impossible,” one player ex -
claimed. “It is a dierent problem; it must be. I would have noticed
such a simple solution.” Clearly, the mere possibility of the smoth-
ered mate move was stubbornly masking alternative solutions. In
fact, the Einstellung eect was powerful enough to temporarily
lower ex pert chess masters to the level of much weaker players.
The infrared camera revealed that even when the players
said they were looking for a faster solution—and indeed believed
they were doing so—they did not actually shift their gaze away
from the squares they had already identified as part of the
smothered mate move. In contrast, when presented with the
one-solution chessboard, players initially looked at the squares
and pieces important for the smothered mate and, once they
realized it would not work, directed their attention toward oth-
er squares and soon hit on the shorter solution.
BASIS FOR BIAS
  , Heather Sheridan of the University of South-
ampton in England and Eyal M. Reingold of the University of
Toronto published studies that corroborate and complement
our eye-tracking experiments. They presented 17 novice and 17
expert chess players with two dierent situations. In one sce-
nario, a familiar checkmate maneuver such as the smothered
mate was advantageous but second best to a distinct and less
ob vious solution. In the second situation, the more familiar se -
quence would be a clear blunder. As in our experiments, once
amateurs and master chess players locked onto the helpful fa -
miliar maneuver, their eyes rarely drifted to squares that would
clue them in to the better solution. When the well-known se -
quence was obviously a mistake, however, all the experts, and
most of the novices, detected the alternative.
The Einstellung eect is by no means limited to controlled
experiments in the lab or even to mentally challenging games
like chess. Rather it is the basis for many cognitive biases. Eng-
lish philosopher, scientist and essayist Francis Bacon was espe-
cially eloquent about one of the most common forms of cogni tive
bias in his 1620 book Novum Organum: “The human un der-
standing when it has once adopted an opinion ... draws all
things else to support and agree with it. And though there be a
greater number and weight of instances to be found on the other
side, yet these it either neglects or despises, or else by some dis-
tinction sets aside and rejects. .. . Men .. . mark the events where
they are fulfilled, but where they fail, though this happen much
oftener, neglect and pass them by. But with far more subtlety
does this mischief insinuate itself into philosophy and the sci-
ences, in which the first conclusion colours and brings into con-
formity with itself all that comes after.”
In the 1960s English psychologist Peter Wason gave this par-
ticular bias a name: “confirmation bias.” In controlled experi-
ments, he demonstrated that even when people attempt to test
theories in an objective way, they tend to seek evidence that con-
firms their ideas and to ignore anything that contradicts them.
In The Mismeasure of Man, for example, Stephen Jay Gould
of Harvard University reanalyzed data cited by researchers try-
ing to estimate the relative intelligence of dierent racial
groups, social classes and sexes by measuring the volumes of
their skulls or weighing their brains, on the assumption that
intelligence was correlated with brain size. Gould uncovered
massive data distortion. On discovering that French brains were
on average smaller than their German counterparts, French
neurologist Paul Broca explained away the discrepancy as a re -
sult of the dierence in average body size between citizens of
the two nations. After all, he could not accept that the French
were less intelligent than the Germans. Yet when he found that
women’s brains were smaller than those in men’s noggins, he
did not apply the same correction for body size, because he did
not have any problem with the idea that women were less intel-
ligent than men.
Somewhat surprisingly, Gould concluded that Broca and
others like him were not as reprehensible as we might think. “In
most cases discussed in this book we can be fairly certain that
biases ... were unknowingly influential and that scientists be -
lieved they were pursuing unsullied truth,” Gould wrote. In oth-
er words, just as we observed in our chess experiments, com-
fortably familiar ideas blinded Broca and his contemporaries to
the errors in their reasoning. Here is the real danger of the Ein-
stellung eect. We may believe that we are thinking in an open-
minded way, completely unaware that our brain is selectively
directing attention away from aspects of our environment that
could inspire new thoughts. Any data that do not fit the solution
or theory we have already clung to are ignored or discarded.
The surreptitious nature of confirmation bias has unfortu-
nate consequences in everyday life, as documented in studies on
decision making among doctors and juries. In a review of errors
in medical thought, physician Jerome Groopman noted that in
most cases of misdiagnosis, “the doctors didn’t stumble because
of their ignorance of clinical facts; rather, they missed diagnoses
because they fell into cognitive traps.” When doctors inherit a
patient from another doctor, for example, the first clinician’s di -
agnosis can blind the second to important and contradictory
de tails of the patient’s health that might change the diagnosis. It
is easier to just accept the diagnosis—the “solution”—that is al -
ready in front of them than to rethink the entire situation. Simi-

Player B
One-Solution Problem
Two-Solution Problem
Move 1 Move 2 Move 3
Move 2 Move 3
Move 4 Move 5
Player APlayer B
Move 1
Player A
Two-Solution Problem
One-Solution Problem
40
30
20
10
0
Initial 10
seconds
Final 5
seconds
Percent of Time Spent
Looking at Key Squares
Problem-Solving Period
Middle
40
30
20
10
0
Initial 10
seconds
Final 5
seconds
Percent of Time Spent
Looking at Key Squares
Problem-Solving Period
Middle
A B C D E F G H
8
7
6
5
4
3
2
1
A B C D E F G H
8
7
6
5
4
3
2
1
Illustration by George Retseck
findings
Much More Than
Meets the Eye
The intellectually demanding game of chess
has proved a wonderful way for psychologists
to study the Einstellung eect—the brain’s ten-
dency to stick with solutions it already knows
rather than looking for potentially superior
ones. Experiments have shown that this cog-
nitive bias literally changes how even expert
chess players see the board in front of them.
Chess Masters Fail to See the Quickest Path to Victory
In a well-known ve-sequence move called smothered mate ( top, yellow ), player A
begins by moving his queen from E2 to E6, backing player B’s king into a corner. Player
A then repeatedly threatens to take B’s king with a knight, forcing player B to dodge.
As an act of deliberate sacrice, player A moves his queen adjacent to B’s king, allowing
player B to take the queen with a rook. To end the game, player A moves his knight to F7,
boxing in B’s king with no chance of escape. In recent experiments, psychologists presented
master chess players with the two-solution board shown above, which could be won using
either the smothered mate or a much swifter three-step solution ( middle, green ). The players
were told to achieve checkmate as quickly as possible, but once they recognized the smothered
mate as a possibility, they became seemingly incapable of noticing the more ecient strategy.
When presented with a nearly identical board on which the position of one bishop had shifted
( bottom, blue ), eliminating the smothered mate as an option, the players did recognize the
speedier solution, however.
See animations of chess moves at ScienticAmerican.com/mar2014/einstellung
SCIENTIFIC AMERICAN ONLINE

March 2014, ScientificAmerican.com 79
Player B
One-Solution Problem
Two-Solution Problem
Move 1 Move 2 Move 3
Move 2 Move 3
Move 4 Move 5
Player APlayer B
Move 1
Player A
Two-Solution Problem
One-Solution Problem
40
30
20
10
0
Initial 10
seconds
Final 5
seconds
Percent of Time Spent
Looking at Key Squares
Problem-Solving Period
Middle
40
30
20
10
0
Initial 10
seconds
Final 5
seconds
Percent of Time Spent
Looking at Key Squares
Problem-Solving Period
Middle
A B C D E F G H
8
7
6
5
4
3
2
1
A B C D E F G H
8
7
6
5
4
3
2
1
larly, radiologists examining chest x-rays often fixate on the first
abnormality they find and fail to notice further signs of illness
that should be obvious, such as a swelling that could indicate
cancer. If those secondary details are presented alone, however,
radiologists see them right away.
Related studies have revealed that jurors begin to decide
whether someone is innocent or guilty long before all the evi-
dence has been presented. In turn, their initial impressions of
the defendant change how they weigh subsequent evidence and
even their memory of evidence they saw before. Likewise, if an
interviewer finds a candidate to be physically attractive, he or
she will automatically perceive that person’s intelligence and
personality in a more positive light, and vice versa. These biases,
too, are driven by the Einstellung eect. It is easier to make a de -
cision about someone if one maintains a consistent view of that
person rather than sorting through contradictory evidence.
Can we learn to resist the Einstellung eect? Perhaps. In our
chess experiments and the follow-up experiments by Sheridan
and Reingold, some exceptionally skilled experts, such as grand
masters, did in fact spot the less obvious optimal solution even
when a slower but more familiar sequence of moves was possi-
ble. This suggests that the more expertise someone has in their
field—whether chess, science or medicine—the more immune
they are to cognitive bias.
But no one is completely impervious; even the grand mas-
ters failed when we made the situation tricky enough. Actively
remembering that you are susceptible to the Einstellung eect
is another way to counteract it. When considering the evidence
on, say, the relative contribution of man-made and naturally oc -
curring greenhouse gases to global temperature, remember that
if you already think you know the answer, you will not judge the
evidence objectively. Instead you will notice evidence that sup-
ports the opinion you already hold, evaluate it as stronger than
it really is and find it more memorable than evidence that does
not support your view.
We must try and learn to accept our errors if we sincerely want
to improve our ideas. English naturalist Charles Darwin came up
with a remarkably simple and eective technique to do just this.
“I had ... during many years, followed a golden rule, namely, that
whenever a published fact, a new observation or thought came
across me, which was opposed by my general results, to make a
memorandum of it without fail and at once,” he wrote. “For I
had found by experience that such facts and thoughts were far
more apt to escape from memory than favourable ones.”
The Explanation: Tunnel Vision
Eye-tracking devices revealed that as soon as chess players hit on the smothered
mate as a solution, they spent far more time looking at squares relevant to that
familiar maneuver ( orange ) than at squares pertinent to the more ecient
three-step sequence ( magenta ), despite insisting that they were searching for
alternatives. Conversely, when the smothered mate was not viable, the players’
gaze shifted to regions of the chessboard crucial to the swifter strategy.
More to explore
Why Good Thoughts Block Better Ones: The Mechanism of the Pernicious
Einstellung (Set) Eect. Merim Bilali´c, Peter McLeod and Fernand Gobet
in Cognition, Vol. 108, No. 3, pages 652–661; September 2008.
The Mechanism and Boundary Conditions of the Einstellung Eect in Chess:
Evidence from Eye Movements. Heather Sheridan and Eyal M. Reingold in
PLOS ONE, Vol. 8, No. 10, Article No. e75796; October 4, 2013.
www.plosone.org/article/info%3Adoi%2F10.1371%2Fjournal.pone.0075796
FroM our Archives
The Expert Mind. Philip E. Ross; August 2006.
The Science of Genius. Dean Keith Simonton; Scientic American Mind, November/
December 2012.