Analogical Reasoning

Transcription

1 Analogical Reasoning Psychology 355: Cognitive Psychology Instructor: John Miyamoto 05/23/2018: Lecture 09-3 Note: This Powerpoint presentation may contain macros that I wrote to help me create the slides. The macros aren t needed to view the slides. You can disable or delete the macros without any change to the presentation.

2 Psych 355, Miyamoto, Spr '18 2 Examples of Analogical Reasoning 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

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. Psych 355, Miyamoto, Spr '18 Why Are We Interested in Analogical Reasoning?

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] Psych 355, Miyamoto, Spr '18 Structure of an Analogy

5 The Structure of an Analogy Example: The structure of an atom is analogous to the structure of the solar system. Source (Base Problem): Typically, a well understood problem or system to which an analogy is made. E.g., structure of the solar system Solar System Source Atom Target 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 Psych 355, Miyamoto, Spr '18 5

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. Psych 355, Miyamoto, Spr '18 Dunker s Radiation Problem - Outline

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? Psych 355, Miyamoto, Spr '18 The Convergence Solution 7

8 Psych 355, Miyamoto, Spr '18 8 Analogical Transfer 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.

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.) Psych 355, Miyamoto, Spr '18 Gick & Holyoak on Analogical Transfer Basic Idea

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 10

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? Psych 355, Miyamoto, Spr '18 Other Base Problems Red Adair & Arrow Diagram 11

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. Psych 355, Miyamoto, Spr '18 Three Conditions in the Experiment on Analogical Transfer 12

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. Psych 355, Miyamoto, Spr '18 Same Slide with Condition 2 Added 13

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. Psych 355, Miyamoto, Spr '18 Same Slide with Condition 3 Added

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. Psych 355, Miyamoto, Spr '18 Results of Gick & Holyoak's Study

16 Summary of Results (Gick & Holyoak, 1980, 1983) % Solutions Three Conditions 10% 1. Control: No base problem, no hint 30% 2. Base problem, no hint 75% 3. Base problem + hint These results show that noticing the analogy is a separate step from constructing the analogy. (Condition 3 is better than Condition 2.) Psych 355, Miyamoto, Spr '18 Same Slide with Emphasis Rectangles

17 Summary of Results (Gick & Holyoak, 1980, 1983) % Solutions Three Conditions 10% 1. Control: No base problem, no hint 30% 2. Base problem, no hint 75% 3. Base problem + hint These results show that noticing the analogy is a separate step from constructing the analogy. (Condition 3 is much better than Condition 2.) Psych 355, Miyamoto, Spr '18 Noticing Analogies: Effects of Superficial Similarities

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). Psych 355, Miyamoto, Spr '18 Lightbulb Problem Standard Version

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. Psych 355, Miyamoto, Spr '18 Comparing Effects of Superficial Features & Structural Features

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. Psych 355, Miyamoto, Spr '18 Results for Two Versions of the Lightbulb Problem

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 Superficial Similarities + Structural Similarities Analogical Transfer Psych 355, Miyamoto, Spr '18 Comparison of Features for Different Problems

22 Comparison of Features Among the Problems 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 Psych 355, Miyamoto, Spr '18 22

23 Comparison of Features Among the Problems 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 Psych 355, Miyamoto, Spr '18 What Influences the Likelihood of Analogical Transfer? 23

24 What Influences the Likelihood of Analogical Transfer? Superficial Similarities + Structural Similarities Analogical Transfer 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 Schema Induction in Problem Solving 24

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? 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 ). Psych 355, Miyamoto, Spr '18 Experiment on Schema Induction + Results

26 Gick and Holyoak (1983): Schema Induction in Problem Solving 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: Rated Quality of Schema % Successful Solutions 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 Psych 355, Miyamoto, Spr '18 26

27 What Influences the Likelihood of Analogical Transfer? Superficial Similarities + Structural Similarities + Induction of a Problem Schema Analogical Transfer Psych 355, Miyamoto, Spr '18 Summary re Analogical Transfer 27

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 Possibly end lecture here? Gilovich Superficial Associations Influence Judgment Psych 355, Miyamoto, Spr '18 28

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, FYI: The Gilovich study was not discussed on the Goldstein textbook. 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 Psych 355, Miyamoto, Spr '18 29

30 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 for football excellence. FYI: Drew Pearson was a famous wide receiver (different position). Gene Upshaw was a famous offensive guard (same position). Results: Average Ratings of Tim B's Chances in Pro Football Rating Award named for famous player who played the SAME position Award named for famous player who played DIFFERENT position Gilovich Superficial Features Influence Policy Analogies Psych 355, Miyamoto, Spr '18 30

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, FYI: This Gilovich study was not discussed in the Goldstein textbook. 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? Psych 355, Miyamoto, Spr '18 Two Prototypes of American Military Intervention 31

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 Psych 355, Miyamoto, Spr '18 32

33 Phrases Manipulated Across Condition 1, 2 & 3 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 Same Slide Without Emphasis Rectangles 33

34 Phrases Manipulated Across Condition 1, 2 & 3 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 Dependent Variables (Ratings) & Results 34

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 Psych 355, Miyamoto, Spr '18 35

36 Psych 355, Miyamoto, Spr '18 Ubiquity of Analogies in Real-World Problem Solving 36 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.

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. Psych 355, Miyamoto, Spr '18 Summary re Analogical Reasoning END

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. Psych 355, Miyamoto, Spr '18 END