analogical reasoning psychology 355: cognitive psychology instructor: john miyamoto 05/27 /2015:...

Analogical Reasoning

Psychology 355: Cognitive Psychology

Instructor: John Miyamoto

05/27/2015: Lecture 09-4

This Powerpoint presentation may contain macros that were used to create the slides. The macros aren’t needed to view the slides. If necessary, you can disable the macros without any change to the presentation.

Outline

Analogical Reasoning – What helps or hinders the discovery of useful analogies?

• Examples of analogies

• Structural definition of an analogy

• Studies of the discovery of analogiesWhat are the cognitive processes during discovery of useful analogies?

• Experiments on analogies that influence decisions

Psych 355, Miyamoto, Spr '15 2

Lecture probably ends here

Examples of Analogical Reasoning


Examples of Analogical Reasoning

• Is the current international political instability analogous to the

political situation that preceded World War I?

• Is a successful business enterprise 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"

"plane" is to "air" as "boat" is to ____

Why Are We Interested in Analogical Reasoning?


Why Are We Interested In Analogical Reasoning?

• Seeing useful analogies is one of the basic mechanisms of

problem solving.

• Analogies influence decisions. o Is the current instability in the Ukraine analogous to the German annexation

of Austria in 1938? o 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


The Structure of an Analogy

• Source (Base Problem): Typically,

a well understood problem or

system to which an analogy is made.

(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. (structure of the atom)

• Representation: A description of the structure of the source and the target.

Main Steps in the Mental Construction of an Analogy

Source TargetAtomSolar System


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


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 ray cannot be high intensity because that would destroy healthy tissue.

• Gick & Holyoak (1983): With no other hints, about 10% of subjects (University of Michigan undergrads) produced the convergence solution.

Psych 355, Miyamoto, Spr '15 8Analogical Transfer


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. o Train subjects on one problem. (Referred to as the "base problem.")o 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


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:o How many subjects (%) solve the target problem after seeing

the base problem? o How many subjects (%) solve the target problem without seeing

the base problem first?

Base Problem: The Fortress Problem


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 Analogies – Red Adair & Arrow Diagram


Other Base Analogies

• Red Adair Problem: (Red Adair was famous for being able to put out burning oil wells)

o Need to put out a burning oil well but can't deliver enough water from any one position.

o 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


Gick & Holyoak: Study of Analogical Transfer

• Base Problem: The Fortress Problem• Target Problem: The Radiation Problem

Three Conditions

1. Subjects are not shown the base problem.

Subject attempt to solve the target problem.o This condition tests for the rate of spontaneous solutions to the target problem.

Same Slide with Condition 2 Added




Three Conditions


Subject attempt to solve the target problem.

2. Subjects are shown the base problem.

Subject attempt to solve the target problem.o 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




Three Conditions



2. Subjects are shown the base 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.o 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)


• 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 Increase Three Conditions

10% 1. Control: No base problem, no hint

30% +20% 2. Base problem, no hint

75% +45% 3. Base problem + hint

Summary of Results (Gick & Holyoak, 1980, 1983)


• These results show that noticing the analogy is a separate step from constructing the analogy. (Condition 3 is better than Condition 2.)


% Solutions Increase Three Conditions

10% 1. Control: No base problem, no hint

30% +20% 2. Base problem, no hint

75% +45% 3. Base problem + hint


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. o Evidence for this is given by the Lightbulb Problem (next).

Lightbulb Problem – Standard Version


Effect of Superficial Features

Lightbulb Problem (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. o Excellent transfer! Recall that the Fortress Problem transferred

to the Radiation Problem 30% of the time.

Comparing Effects of Superficial Features & Structural Features


Effects of 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:

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 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


Results of 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


Superficial Feature Structural Feature

ProblemMedium of Action

Why One Strong Beam/Attack Not Possible

Analogical Transfer Successful?

Radiation Problem X-ray beamOne strong x-ray beam will injure the intervening tissue.

sourceproblem

Fortress Problem Attack by troopsOne strong attacking army will detonate mines on roads.

poor

Lightbulb Problem (Insufficient Intensity Version)

Laser beamHigh intensity laser not available poor

Lightbulb Problem (Fragile Glass Version)

Laser beamHigh intensity laser will break the glass. good


Comparison of Features Among the Problems


Superficial Feature Structural Feature

ProblemMedium of Action

Why One Strong Beam/Attack Not Possible

Analogical Transfer Successful?

Radiation Problem X-ray beamOne strong x-ray beam will injure the intervening tissue.

sourceproblem

Fortress Problem Attack by troopsOne strong attacking army will detonate mines on roads.

poor

Lightbulb Problem (Insufficient Intensity Version)

Laser beamHigh intensity laser not available poor

Lightbulb Problem (Fragile Glass Version)

Laser beamHigh intensity laser will break the glass. good

What Influences the Likelihood of Analogical Transfer?




Structural Similarities Analogical Transfer

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).



Gick and Holyoak (1983):o Subjects read the fortress story and the "Red Adair" story. o Subjects were asked to write a brief summary describing as clearly

as possible the ways in which the stories were similar. o Subjects' problem summaries were rated by independent raters

for quality of the description of the convergence schema. o 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




Structural Similarities +

Induction of a Problem Schema

Analogical Transfer

Summary re Analogical Transfer


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.o 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

29Psych 355, Miyamoto, Spr '15

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:o Subjects were 20 male sportswriters from the staffs of the Oakland Tribune,

the San Jose Mercury News, the Merced Sun Star, and the Palo Alto Time. o Subjects read a description of a hypothetical player. o Subjects predict the future success of the player 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.


Example of a Player Description in Gilovich’s Study

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 as his school’s most outstanding player.

FYI: Drew Pearson was a famous wide receiver (different position). Gene Upshaw was a famous offensive guard (same position).

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


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 a scenario:

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 on the Goldstein textbook.


Question: Should the U.S. intervene to help Country B?

• Two prototypes of US military interventiono World War II: Appeasement of Hitler leads to genocide & terrible war.o 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


Phrase WW II Neutral Vietnam

The room in which the subject was supposedly briefed about the crisis was called the _____.

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 invasion

quickstrike invasion


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


Phrase WW II Neutral Vietnam

The room in which the subject was supposedly briefed about the crisis was called the _____.

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 invasion



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

Dependent Variables (Ratings) & Results


Results: Superficial Features Affect Availability of Analogies

• Subjects were 42 Stanford undergraduates who were enrolled in a

political science course.o 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. o Rate: How likely is it that the crisis would turn into a major world problem

involving more countries than A, B, and the US.o 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 '15 36Ubiquity of Analogies in Real-World Problem Solving


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 knowno Notice that real-world problem solvers often have a lot of practice

looking for useful analogies in their area of expertise.o 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


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. o 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

analogical reasoning psychology 355: cognitive psychology instructor: john miyamoto 05/27 /2015:...

Documents

understood problem

target test problem

quotation structure

russian marriage problem

basic mechanisms of

discovery of useful

atom analogous

analogysource base problem