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Analogical Reasoning
Psychology 355: Cognitive Psychology
Instructor: John Miyamoto
05/23/2018: Lecture 09-3
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Outline of the Analogical Reasoning Topic
• What are analogies? Why are they useful in problem solving?
• Structural definition of an analogy
• Discovery of analogies: What are the cognitive processes during
discovery of useful analogies?
• Influence of analogies on decisions
Psych 355, Miyamoto, Spr '18 2 Examples of Analogical Reasoning
Psych 355, Miyamoto, Spr '18 3
Examples of Analogical Reasoning
• Is the current international political instability analogous
to the political situation that preceded World War I?
• Is a successful business analogous to a successful football team?
• Is the mutilated checkerboard problem analogous
to the Russian marriage problem?
• Is the structure of an atom analogous to the structure
of the solar system?
• "pony" is to "horse" as ____ is to "cow"
"bird" is to "air" as "fish" is to _____.
Why Are We Interested in Analogical Reasoning?
Psych 355, Miyamoto, Spr '18 4
Why Are We Interested In Analogical Reasoning?
• Seeing useful analogies is one of the basic mechanisms
of problem solving.
• Analogies influence decisions.
♦ Is the current instability in Ukraine and Crimea analogous to the German
annexation of Austria in 1938?
♦ Maureen Dowd writing in the New York Times (January 17, 2010) about
President Obama’s reluctance to support gay marriage:
“Obama sees himself as such a huge change that he can be
cautious about other societal changes. But what he doesn’t
realize is that legalizing gay marriage is like electing a black
president. Before you do it, it seems inconceivable. Once
it’s done, you can’t remember what all the fuss was about.”
[Italics added to the quotation]
Structure of an Analogy
Psych 355, Miyamoto, Spr '18 5
The Structure of an Analogy
• Source (Base Problem): Typically,
a well understood problem or system
to which an analogy is made.
♦ E.g., structure of the solar system
Example: The structure of an atom is analogous to the structure of the solar system.
• Target (Test Problem): Typically, a less understood problem or
system about which we can learn by analogy to the source. • E.g., structure of the atom
• Representation: The structure of the source and the target.
• Mapping: A correspondence between the source structure
and the target structure
Main Steps in the Mental Construction of an Analogy
Source Target
Atom Solar System
Psych 355, Miyamoto, Spr '18 6
Main Steps in the Mental Construction of an Analogy
• Create representations of the source and target.
• Noticing: Noticing that a potential analogy exists.
• Mapping: Constructing a correspondence between
the representations of the source and the target.
• Application: Applying the mapping from source to target,
i.e., drawing inferences about the target based
on what is known about the source.
Dunker’s Radiation Problem - Outline
Psych 355, Miyamoto, Spr '18 7
Dunker's Radiation Problem - Outline
• Doctor must kill a tumor in a patient's stomach.
Surgery is not possible.
• There is a ray that can kill the tumor.
• In high dosages it will kill the tumor, but it will also kill
healthy tissue in front of the tumor.
• In low dosages, it won't harm the healthy tissue, but it also won't kill
the tumor.
• Question: How can the doctor kill the tumor without killing
the healthy tissue?
The Convergence Solution
Convergence Solution for the Radiation Problem
• Beam the ray at the tumor from many
different angles.
• All rays should have low intensity, but the
combination of rays at point of intersection
(at the tumor) will have high intensity. ----------------------------------
• The convergence solution respects the constraint
that the ray cannot be high intensity.
• Gick & Holyoak (1983): With no other hints, about 10% of subjects
(University of Michigan undergrads) produced the convergence
solution.
Psych 355, Miyamoto, Spr '18 8 Analogical Transfer
Psych 355, Miyamoto, Spr '18 9
Analogical Transfer
• Analogical transfer – seeing analogies and using the analogies to solve
a new problem.
• Gick and Holyoak studied whether exposure to analogous problems
and their solutions would help people solve the radiation problem.
♦ Train subjects on one problem. (Referred to as the "base problem.")
♦ Test subjects on another problem that is analogous to the first problem.
(Referred to as the "target" or "test" problem.)
Gick & Holyoak on Analogical Transfer – Basic Idea
Psych 355, Miyamoto, Spr '18 10
Gick & Holyoak's Study of Analogical Transfer
Step 1: Train subjects to solve (or at least think about)
one or more base problems (source for an analogy).
Step 2: Subjects are asked to solve the Radiation Problem
(target problem).
Compare the following two measures:
♦ How many subjects (%) solve the target problem without seeing
the base problem first?
♦ How many subjects (%) solve the target problem after seeing
the base problem?
Base Problem: The Fortress Problem
Psych 355, Miyamoto, Spr '18 11
Base Problem: Duncker's Fortress Problem
• A general needs to capture
a fortress with his army.
• An attack by his entire army
would capture the fortress, but
the roads are mined.
• Since the dictator needs to move his workers to and from the fortress,
the mines are set to let small bodies of men pass over them safely,
• Any large force would detonate the mines.
• How can the general attack the fortress with all of his army?
Other Base Problems – Red Adair & Arrow Diagram
Psych 355, Miyamoto, Spr '18 12
Other Base Problems
• Red Adair Problem: (Red Adair was famous for being
able to put out burning oil wells)
♦ Need to put out a burning oil well
but can't deliver enough water from
any one position.
♦ Convergence Solution: Direct streams
of water at the well from many directions.
• Arrow Diagram: In some conditions,
subjects were given an arrow diagram
to see if that would be helpful.
Three Conditions in the Experiment on Analogical Transfer
Psych 355, Miyamoto, Spr '18 13
Gick & Holyoak: Study of Analogical Transfer
Base Problem: The Fortress Problem
Target Problem: The Radiation Problem
Three Experimental Conditions
1. Subjects are not shown the base problem.
Subject attempt to solve the target problem.
♦ This condition tests for the rate of spontaneous solutions to the target problem.
Same Slide with Condition 2 Added
Psych 355, Miyamoto, Spr '18 14
Gick & Holyoak: Study of Analogical Transfer
Base Problem: The Fortress Problem
Target Problem: The Radiation Problem
Three Experimental Conditions
1. Subjects are not shown the base problem.
Subject attempt to solve the target problem.
2. Subjects are shown the base problem.
Subject attempt to solve the target problem.
♦ This condition tests for the rate of spontaneous use of the analogy of the base
problem when attempting to solve the target problem.
Same Slide with Condition 3 Added
Psych 355, Miyamoto, Spr '18 15
Gick & Holyoak: Study of Analogical Transfer
Base Problem: The Fortress Problem
Target Problem: The Radiation Problem
Three Experimental Conditions
1. Subjects are not shown the base problem.
Subject attempt to solve the target problem.
2. Subjects are shown the base problem.
Subject attempt to solve the target problem.
3. Subjects are shown the base problem plus a hint that
the base problem may be useful when working on the
next problem.. Subject attempt to solve the target problem.
♦ This condition tests for the rate of using the analogy when the subjects
are informed that it may be useful.
Results of Gick & Holyoak's Study
Summary of Results (Gick & Holyoak, 1980, 1983)
Psych 355, Miyamoto, Spr '18 16
• These results show that noticing the analogy is a separate step from
constructing the analogy. (Condition 3 is better than Condition 2.)
Same Slide with Emphasis Rectangles
% Solutions Three Conditions
10% 1. Control: No base problem, no hint
30% 2. Base problem, no hint
75% 3. Base problem + hint
Summary of Results (Gick & Holyoak, 1980, 1983)
Psych 355, Miyamoto, Spr '18 17
• These results show that noticing the analogy is a separate step from
constructing the analogy. (Condition 3 is much better than Condition 2.)
Noticing Analogies: Effects of Superficial Similarities
% Solutions Three Conditions
10% 1. Control: No base problem, no hint
30% 2. Base problem, no hint
75% 3. Base problem + hint
Psych 355, Miyamoto, Spr '18 18
Noticing Analogies: The Effects of Superficial Similarities
How to increase the rate at which people notice an analogy?
Hypothesis: People are more likely to notice an analogy
if the base and target problem share superficial features.
♦ Evidence for this is given by the Lightbulb Problem (next).
Lightbulb Problem – Standard Version
Psych 355, Miyamoto, Spr '18 19
Effect of Superficial Features
Lightbulb Problem (Fragile Glass Version; see Goldstein, pp. 352)
Ruth must repair an expensive lightbulb. The filament is broken.
A high intensity laser can repair the filament, but it will break the
glass.
Solution: Beam many low intensity lasers at the filament from
many different directions.
Holyoak & Koh (1987):
• Subjects who were only given the Lightbulb Problem
solved it 10% of the time.
• Subjects who were first saw the Radiation Problem and
its solution solved the Lightbulb Problem 81% of the time.
♦ Excellent transfer! Recall that the Fortress Problem transferred
to the Radiation Problem 30% of the time.
Comparing Effects of Superficial Features & Structural Features
Psych 355, Miyamoto, Spr '18 20
Effects of Superficial Features versus Structural Features
• Subjects first saw the Radiation Problem and its solution.
They then tried to solve a version of the Lightbulb Problem.
Lightbulb Problem (Fragile Glass Version) – shares
both superficial & structural features with the Radiation Problem:
Ruth must repair an expensive lightbulb. The filament is broken.
A high intensity laser can repair the filament, but it will break the glass.
(Same as scenario on preceding slide.)
Lightbulb Problem (Insufficient Intensity Version) – shares
superficial BUT NOT structural features with the Radiation Problem:
Ruth must repair an expensive lightbulb. The filament is broken.
A high intensity laser can repair the filament, but she doesn’t have one.
She only has low intensity lasers available to her.
Solution for both versions: Beam many low intensity lasers at the
filament from many different directions.
Results for Two Versions of the Lightbulb Problem
Psych 355, Miyamoto, Spr '18 21
Results: Superficial Features versus Structural Features
Subjects first saw the Radiation Problem and its solution.
They then tried to solve one version of the Lightbulb Problem.
Lightbulb Problem (Fragile Glass Version) –
shares both superficial & structural features with the Radiation Problem:
Lightbulb Problem (Insufficient Intensity Version) –
shares superficial BUT NOT structural features with the Radiation Problem:
Results:
% Solution Version
69% Fragile Glass Version
33% Insufficient Intensity Version
Comparison of Features for Different Problems
Superficial Similarities
+
Structural Similarities
Analogical Transfer
Comparison of Features Among the Problems
Psych 355, Miyamoto, Spr '18 22
Superficial Feature Structural Feature
Problem Medium of
Action
Why One Strong
Beam/Attack
Not Possible
Analogical
Transfer
Successful?
Radiation Problem X-ray beam
One strong x-ray beam will
injure the intervening
tissue.
Radiation problem
is the source
problem
Fortress Problem Attack
by troops
One strong attacking army
will detonate mines on
roads.
poor
Lightbulb Problem (Insufficient Intensity
Version)
Laser beam High intensity laser
not available poor
Lightbulb Problem (Fragile Glass
Version)
Laser beam High intensity laser
will break the glass. good
Same Slide with Emphasis Rectangles
Superficial Feature Structural Feature
Problem Medium of
Action
Why One Strong
Beam/Line of Attack
Not Possible
Analogical
Transfer
Successful?
Radiation Problem X-ray beam
One strong x-ray beam will
injure the intervening
tissue.
Radiation problem
is the source
problem
Fortress Problem Attack
by troops
One strong attacking army
will detonate mines on
roads.
poor
Lightbulb Problem (Insufficient Intensity
Version)
Laser beam High intensity laser
not available poor
Lightbulb Problem (Fragile Glass
Version)
Laser beam High intensity laser
will break the glass. good
Comparison of Features Among the Problems
Psych 355, Miyamoto, Spr '18 23 What Influences the Likelihood of Analogical Transfer?
What Influences the Likelihood of Analogical Transfer?
Psych 355, Miyamoto, Spr '18 24
Superficial Similarities
+ Structural Similarities
Analogical Transfer
Schema Induction in Problem Solving
The relationship depicted on this slide needs to be modified.
See diagram below that includes the effect of schema induction.
Psych 355, Miyamoto, Spr '18 25
Schema Induction in Problem Solving
A problem schema is an abstraction of the similarities
between many problem solutions. It is a general description
of how problems of a given kind can be solved.
• Does having a good problem schema makes it more likely
that one will see an analogy?
Experiment on Schema Induction + Results
Schema induction is not discussed in Goldstein, but it is an important concept
in the study of analogical reasoning.
• Gick and Holyoak (1983) introduced idea of schema induction
in analogical reasoning.
• Gentner and Goldin-Meadow (2003) developed similar idea
of analogical encoding (discussed in Goldstein, pp. 353 - 354).
Psych 355, Miyamoto, Spr '18 26
Schema Induction in Problem Solving
Gick and Holyoak (1983):
♦ Subjects read the fortress story and the "Red Adair" story.
♦ Subjects were asked to write a brief summary describing
as clearly as possible the ways in which the stories were similar.
♦ Subjects' problem summaries were rated by independent raters
for quality of the description of the convergence schema.
♦ Subjects then attempted to solve the radiation problem.
RESULTS: % Successful Solutions
Rated Quality of Schema to the Radiation Problem
"good" 91%
"intermediate" 40%
"poor" 30%
• Having a good problem schema correlates with seeing the analogy
between the source problems and the target problem.
Summary re Schema Induction
What Influences the Likelihood of Analogical Transfer?
Psych 355, Miyamoto, Spr '18 27
Superficial Similarities
+ Structural Similarities
+ Induction of a
Problem Schema
Analogical Transfer
Summary re Analogical Transfer
Psych 355, Miyamoto, Spr '18 28
Summary re Analogical Transfer
• Noticing that a potential analogy exists is more difficult than
applying an analogy once it has been noticed.
• Superficial features and deeper structural relationships influence
the likelihood of noticing an analogy.
• Discovering a schema for an analogy is promoted by seeing
multiple examples of the base problem.
♦ Examples: Gick and Holyoak (1983) described in preceding slides;
Gentner and Goldin-Meadow (2003) as discussed in Goldstein, pp. 353 -
354.
• Possibly end lecture here?
Gilovich – Superficial Associations Influence Judgment
Psych 355, Miyamoto, Spr '18 29
Gilovich – Superficial Associations Influence Judgment
Gilovich, T. (1981). Seeing the past in the present: The effect of associations to familiar events on
judgments and decisions. Journal of Personality and Social Psychology, 40, 797-808.
• Basic argument: Superficial associations to past experience
influence judgment.
• Experiment:
♦ Subjects were 20 male sportswriters
(the Oakland Tribune; the San Jose Mercury News; the Merced Sun Star; the Palo Alto Time).
♦ Subjects read a description of a hypothetical player.
♦ Subjects predicted the future success of college players in pro football on
a 9-point scale from:
1 = fails to make a pro team to 9 = star/superstar
Example of a Player Description and Experimental Results
FYI: The Gilovich study was not discussed on the Goldstein textbook.
Psych 355, Miyamoto, Spr '18 30
Example of a Player Description in Gilovich’s Study
Gilovich – Superficial Features Influence Policy Analogies
Results: Average Ratings of Tim B's Chances in Pro Football Rating
Award named for famous player who played the SAME position. 6.44
Award named for famous player who played DIFFERENT position. 4.80
Offensive Guard: Tim B. 6'3". 260 lbs. 5.0 speed in the 40. Good strength and
body control. Has a quick, strong charge that enables him to move opponents off
the line of scrimmage. Will need to learn to pass block since his college ran the Veer.
Tim won the award for football excellence.
FYI: Drew Pearson was a famous wide receiver (different position).
Gene Upshaw was a famous offensive guard (same position).
Psych 355, Miyamoto, Spr '18 31
Do Superficial Features Affect Availability of Analogies?
Gilovich, T. (1981). Seeing the past in the present: The effect of associations to familiar events on
judgments and decisions. Journal of Personality and Social Psychology, 40, 797-808.
• Basic structure of the scenarios:
Country A is threatening to invade
its peaceful neighbor, Country B.
Neither country is strategically
important. Country B has asked
the U.S. for help.
• Question: Should the U.S. intervene
to help Country B?
Two Prototypes of American Military Intervention
FYI: This Gilovich study was not discussed
in the Goldstein textbook.
Psych 355, Miyamoto, Spr '18 32
Question: Should the U.S. intervene to help Country B?
• Two prototypes of US military intervention
♦ World War II: Appeasement of Hitler leads to genocide & terrible war.
♦ Vietnam: Intervention leads to long, painful war.
• Research Question:
Can we manipulate the description of the situation
to make the WW II or Vietnam analogy more available?
Gilovich Experiment: Phrases Manipulated Across Conditions 1, 2 & 3
Phrases Manipulated Across Condition 1, 2 & 3
Psych 355, Miyamoto, Spr '18 33
Phrase WW II Neutral Vietnam
The decision was made in
_____ (location).
Winston Churchill
Hall
Abraham
Lincoln Hall Dean Rusk Hall
The current U.S. president was
from _____, the same state as
_____.
New York; FDR Virginia; William
H. Harrison Texas; LBJ
The impending invasion was
referred to as a _____. blitzkrieg quickstrike quickstrike
A pact between Country A and
Country F was called a _____
nonaggression
pact pact pact
In an emergency, U.S. troops
stationed in Country D could be
flown to Country B in _____.
troop transports troop transports Chinook
helicopters
Minorities in Country A were
fleeing _____.
via boxcars on
freight trains to
Country G
to Country G
via small boats
up the coast to
Country G
Same Slide Without Emphasis Rectangles
Phrases Manipulated Across Condition 1, 2 & 3
Psych 355, Miyamoto, Spr '18 34 Dependent Variables (Ratings) & Results
Phrase WW II Neutral Vietnam
The decision was made in
_____ (location).
Winston Churchill
Hall
Abraham
Lincoln Hall Dean Rusk Hall
The current U.S. president was
from _____, the same state as
_____.
New York; FDR Virginia; William
H. Harrison Texas; LBJ
The impending invasion was
referred to as a _____. blitzkrieg quickstrike quickstrike
A pact between Country A and
Country F was called a _____
nonaggression
pact pact pact
In an emergency, U.S. troops
stationed in Country D could be
flown to Country B in _____.
troop transports troop transports Chinook
helicopters
Minorities in Country A were
fleeing _____.
via boxcars on
freight trains to
Country G
to Country G
via small boats
up the coast to
Country G
Psych 355, Miyamoto, Spr '18 35
Results: Superficial Features Affect Availability of Analogies
• Subjects were 42 Stanford undergraduates who were enrolled in a
political science course.
♦ Rate: How successful would a US military intervention be in preventing a
takeover if a limited number of U.S. troops were sent to Country B.
♦ Rate: How likely is it that the crisis would turn into a major world problem
involving more countries than A, B, and the US.
♦ Rate your preferred policy on a scale from
1 = "hands off; appeal to U.N." to .....
9 = intervention.
• Results: Ratings were significantly more interventionist when scenario
contained WW II features than when it contained neutral or Vietnam
features. (Neutral & Vietnam conditions did not differ).
Interpretation of Results
Interpretation of Results
• Result: Non-relevant features that are associated with WW II or
Vietnam had an impact on subjects' judgments about what to do.
• Interpretation: The non-relevant features affected whether subjects
drew an analogy between WW II or Vietnam when deciding a course of
action.
♦ Note: The scenario never made a direct reference to “World War II”
or to “Vietnam.”
• Remember Gick & Holyoak found that superficial features
affect whether subjects notice an analogy.
Psych 355, Miyamoto, Spr '18 36 Ubiquity of Analogies in Real-World Problem Solving
Psych 355, Miyamoto, Spr '18 37
Analogies in Real-World Problem Solving Contexts
"In-vivo" problem solving research = naturalistic studies of problem
solving, e.g., in a microbiology lab or a design engineering group.
• Finding: Scientists and engineers often use analogies in their
discussions.
• Question: Why are analogies often used by problem solvers
in real-world situations, but not by psychology subjects in cognitive
laboratory situations?
• True answer not known
♦ Notice that real-world problem solvers often have a lot of practice
looking for useful analogies in their area of expertise.
♦ Perhaps in the real world, many people use analogies but only a few people
discover the analogies. Applying an analogy is easier than discovering the
analogy.
Summary re Analogical Reasoning – END
Psych 355, Miyamoto, Spr '18 38
Summary of Analogical Reasoning
• Analogies facilitate problem solving.
• Basic structure of an analogy: Source or base problem,
target problem, problem representation, noticing, mapping, application
• Subjects do not readily recognize the existence of analogies without
hints or suggestions. Subjects are influenced by superficial similarities,
but also by structural similarities.
• Schema induction facilitates analogical problem solving.
♦ Schema induction requires exposure to two or more instances of a problem
structure.
• Analogies occur often in the problem solving activities of scientists
when they are working on their research.
END