1. 1st: Do Perception & Imagery Involve the Same Brain Mechanisms
1st: Do Perception & Imagery Involve the Same Brain Mechanisms? 2nd: Introduction to Problem Solving
Psychology 355: Cognitive Psychology Instructor: John Miyamoto 05/21/2018: Lecture 09-1
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2. Lecture probably ends here
Outline
Do perception and mental imagery involve the same brain mechanisms?
Review evidence from last week
Present evidence that sometimes perception and mental imagery do NOT involve the same brain mechanisms.
Introduction to problem solving
What is a problem (according to cognitive psychology)?
Basic concepts: Problem representation, moves and transformations
Algorithmic and insight problems
Restructuring a problem
Problem constraints
Lecture probably ends here
Psych 355, Miyamoto, Spr '18
Review: Do Perception & Imagery Involve the Same Brain Mechanisms?

3. Do Perception & Imagery Involve Similar Brain Mechanisms?
Mental imagery plays a functional role in cognitive processing.
Evidence that the Answer is "Yes"
Perception of "H" and mental image of "H" are both able to prime the processing of a target letter "H" (Farah's experiment with image priming)
Single cell studies find cells in temporal lobe that are excited by perception of a baseball and a mental image of a baseball.
fMRI study of faces and places finds double dissociation between:
FFA and PPA responses to perception of faces and places.
FFA and PPA responses to imagining faces and places.
Kosslyn found that TMS causes similar disruption of judgments based on perception of shapes and mental images of shapes. (See Goldstein, p. 287 and Figure on p. 288)
This assumption is an important background assumption, but does not directly pertain to whether perception and imagery involve similar brain mechanisms.
Same pattern of double dissociation in both cases.
Psych 355, Miyamoto, Spr '18
Same Slide without Sequenced Entry

4. Do Perception & Imagery Involve Similar Brain Mechanisms?
Mental imagery plays a functional role in cognitive processing.
Evidence that the Answer is "Yes"
Perception of "H" and mental image of "H" are both able to prime the processing of a target letter "H" (Farah's experiment with image priming)
Single cell studies find cells in temporal lobe that are excited by perception of a baseball and a mental image of a baseball.
fMRI study of faces and places finds double dissociation between:
FFA and PPA responses to perception of faces and places.
FFA and PPA responses to imagining faces and places.
Kosslyn found that TMS causes similar disruption of judgments based on perception of shapes and mental images of shapes. (See Goldstein, p. 287 and Figure on p. 288)
This assumption is an important background assumption, but does not directly pertain to whether perception and imagery involve similar brain mechanisms.
Same pattern of double dissociation in both cases.
Psych 355, Miyamoto, Spr '18
Transition to Question: Do Neuro-Impairments have Similar Effects on P & I?

5. Do Neurological Impairments Have Similar Effects on Perception and Imagery?
Before discussing the evidence, a brief reminder about unilateral neglect.
Evidence for "No" Answer:
Then, puzzling evidence that neurological impairments do NOT always have similar effects on perception and mental imagery.
Reminder re Unilateral Neglect – Transition to Unilateral Neglect in Imagery
Psych 355, Miyamoto, Spr '18

6. Hemispatial Neglect (Goldstein calls this "unilateral neglect")
Hemispatial Neglect (Unilateral Neglect): A deficit of attention in which one entire half of a visual scene is simply ignored.
The cause of unilateral neglect is often a stroke that has interrupted the flow of blood to the right parietal lobe.
Figure to the right: Patient’s copy of an image (model) shows systematic deficits.
This slide is based on instructional material that was downloaded from the Pearson Publishers website ( for Smith & Kosslyn (2006; ISBN ).
The patient’s copy neglects the left side of the visual field (opposite to the side of brain damage).
Psych 355, Miyamoto, Spr '18
Unilateral Neglect in Perception & Images

7. Left Unilateral Neglect in Perception & Images
Bisiach, E., & Luzzatti, C. (1978). Unilateral neglect of representational space. Cortex, 14,
(Scene was the Piazza del Duomo in Milan, viewed from a particular location)
Patient with left unilateral neglect.
Neglect occurs when patient is looking at a scene.
Neglect occurs when patient imagines a scene.
In this case, the pattern is the same for perception and mental images.
“Duomo” is pronounced do-mo.
Psych 355, Miyamoto, Spr '18
Transition to Question: Are Perception & Imagery Always Similar?

8. Are Perception & Imagery Always Similar?
Figure (p. 284). (a) Pictures incorrectly labeled by CK who had visual agnosia. (b) Drawings from memory by CK. From study by Behrmann, Moscovitch, & Winocur (1994).
Due to brain injury, Patient CK has visual agnosia (inability to recognize objects)
Figure (a) – incorrect identifications
Asparagus labeled “rose twig with thorns”
Dart labeled “feather duster”
Tennis racquet labeled “fencer’s mask”
Figure (b) – drawings from memory
Outline of England
Guitar
If you show CK his drawings at a later time, he cannot recognize (label) what they are.
(a)
(b)
Psych 355, Miyamoto, Spr '18
Dissociations Between Perception & Imagery

9. Dissociations Between Imagery & Perception
Case
Perception
Imagery
Guariglia (1993) OK
Unilateral neglect
Farah et al. (1993): Patient RM
OK: Recognizes objects & can draw pictures of objects
POOR: Can't draw objects from memory or answer questions that require mental imagery
Behrmann et al. (1994): Patient CK
POOR: Visual agnosia (can't recognize objects)
OK: Can draw objects from memory
Psych 355, Miyamoto, Spr '18
Same Slide without Emphasis Rectangles

10. Dissociations Between Imagery & Perception
Case
Perception
Imagery
Guariglia (1993) OK
Unilateral neglect
Farah et al. (1993): Patient RM
OK: Recognizes objects & can draw pictures of objects
POOR: Can't draw objects from memory or answer questions that require mental imagery
Behrmann et al. (1994): Patient CK
POOR: Visual agnosia (can't recognize objects)
OK: Can draw objects from memory
Diagram Showing Bottom Up & Top Down Processing of Images
Psych 355, Miyamoto, Spr '18

11. When Are Perception & Imagery Similar? When Are They Different?
Behrmann et al. (1994) point out that perception is more bottom up; Imagery is more top down.
Same Slide with Explanation of Behrmann’s Hypothesis
Psych 355, Miyamoto, Spr '18

12. When Are Perception & Imagery Similar? When Are They Different?
Hypothesis:
CK's injury blocks the bottom up input for object perception.
RM injury blocks the top down construction of a mental image.
Psych 355, Miyamoto, Spr '18
Conclusion - END

13. Conclusion
Mental manipulation of images is similar to perception of scenes as they undergo the analogous physical alterations.
Perception and imagery engage similar cognitive processes, but they are not perfectly equivalent.
Perception has more bottom-up influence than imagery.
Imagery has more top-down influence than perception.
Introduction to Problem Solving
Psych 355, Miyamoto, Spr '18

14. Introduction to Problem Solving
What is a “problem” (according to the cognitive psychology)?
Information processing versus Gestalt approach to problem solving. Algorithmic problems & insight problems
Tower of Hanoi – an example of an algorithmic problem
Insight problems
Problem representation
Problem restructuring
Problem isomorphs
Lecture probably ends here
Psych 355, Miyamoto, Spr '18
Definition of Problem Solving

15. Definition of Problem Solving
A problem exists when the present state differs from a goal state. The problem is to change the present state into the goal state.
Initial state
Goal state
Permissible "moves" – ways to change the problem state from the initial state towards the goal state.
Interesting problems are situations where it is not obvious how to change the initial state into the goal state.
Cognitive psychology of problem solving –
How do people solve problems?
What causes difficulties in problem solving?
Can cognitive psychology help people become better problem solvers?
Psych 355, Miyamoto, Spr '18
Examples of Problem Solving Situations

16. Problem Solving - Examples
Math problems, physics problems, science problems generally.
Initial state: The given information in the problem.
Goal state: The “answer” or solution to the problem.
Practical problems, e.g., arranging furniture, building a mechanical device.
Winning strategies in games, business, public health, law & war.
Psych 355, Miyamoto, Spr '18
Key Ideas in Theory of Problem Solving

17. Key Ideas in the Psychology of Problem Solving
Problem representation – The mental representation of the problem that the problem solver manipulates while trying to solve the problem.
Initial state
Goal state
Moves or transformations. Constraints and rules.
Insight problems & algorithmic problems
Restructuring a problem representation
Set
Functional fixedness
Psych 355, Miyamoto, Spr '18
Algorithmic vs Insight Problems

18. Algorithmic Problems versus Insight Problems
Algorithmic problems: The initial problem state can be transformed to the goal state by a systematic procedure.
Example: The Tower of Hanoi
Example: Solving a long division problem
Insight problems require mental restructuring of the problem representation to get a solution.
Circle problem
Mutilated checkerboard problem
Algorithmic and insight problems require somewhat different psychological processes to solve them.
Psych 355, Miyamoto, Spr '18
Tower of Hanoi – Example of an Algorithmic Problem

19. The Tower of Hanoi (A Problem with an Algorithmic Solution)
We will discuss algorithmic problems tomorrow.
Long division is an example of an algorithmic problem
Multiplying two numbers is an algorithmic problem.
Finding the square root of a positive number is an algorithmic problem.
Tower of Hanoi is an algorithmic problem – there is a logically adequate strategy that will always solve this problem.
Psych 355, Miyamoto, Spr '18
General Idea of an Insight Problem

20. General Idea of an Insight Problem
The solution of insight problems usually depends on finding a new way to represent the problem.
Ideas from Gestalt Psychology
The mind searches for structure in perception
The mind searches for structure in problem solving
Mental Representation of a Problem
The Problem Representation =
Finding a New Way to Represent a Problem
Restructuring the Problem Representation =
Psych 355, Miyamoto, Spr '18
Solving the Circle Problem by Restructuring the Problem Representation

21. The Circle Problem: An Example of an Insight Problem
Given:
radius r = 1
length of a = 0.9
line b is perpendicular to line a
Question: What is the length of x?
Hint: Change the problem representation.
#Section:
plot.jm(x=c(-100, 100), y = c(-100, 120), axes=F)
ellipse(c(0,0), width=160, ht = 160, lwd=2)
lines(c(0,0), c(-80, 80), lwd=2)
lines(c(-80, 80), c(0,0), lwd=2)
tt <- pi/6
rr <- 80
aa <- -cos(tt)*rr
bb <- sin(tt)*rr
#lines(c(0, aa), c(0, bb), lwd=2)
lines(c(aa,aa), c(0, bb), lwd=2)
lines(c(aa, 0), c(bb,bb), lwd=2)
lines(c(aa, 0), c(0,bb), lwd=2)
text(x = aa + 5, y = bb/1.95, "a", cex=1.5)
text(x = -2 + aa/2, y = bb/2 - 7, "x", cex=1.5)
text(x = 40, y = -7, "r", cex=1.5)
text(x = c(-80), y = (95),
c(paste("r = 1.0, a = ", round(aa/80 , dig=1))), cex=2, adj=0)
text(x = c(-80), y = (120), "What is the length of x?", cex=2, adj=0)
#lines(c(0, aa), c(0, bb), lwd=2, lty=2)
#EndSection:
Initial Representation
Psych 355, Miyamoto, Spr '18
Restructuring the Representation of the Circle Problem

22. Restructuring the Representation of the Circle Problem
If r = 1, a = 0.9, and a and b are perpendicular, what is the length of x?
Solution: Add dashed line that connects the opposite corners.
Alternative representation: The answer is obvious: x = r = 1.
Alternative problem representation makes the solution obvious.
Solutions to insight problems often depend on a “trick”.
Here the trick is to change the problem representation.
#Section:
plot.jm(x=c(-100, 100), y = c(-100, 120), axes=F)
ellipse(c(0,0), width=160, ht = 160, lwd=2)
lines(c(0,0), c(-80, 80), lwd=2)
lines(c(-80, 80), c(0,0), lwd=2)
tt <- pi/6
rr <- 80
aa <- -cos(tt)*rr
bb <- sin(tt)*rr
#lines(c(0, aa), c(0, bb), lwd=2)
lines(c(aa,aa), c(0, bb), lwd=2)
lines(c(aa, 0), c(bb,bb), lwd=2)
lines(c(aa, 0), c(0,bb), lwd=2)
text(x = aa + 5, y = bb/1.95, "a", cex=1.5)
text(x = -2 + aa/2, y = bb/2 - 7, "x", cex=1.5)
text(x = 40, y = -7, "r", cex=1.5)
text(x = c(-80), y = (95),
c(paste("r = 1.0, a = ", round(aa/80 , dig=1))), cex=2, adj=0)
text(x = c(-80), y = (120), "What is the length of x?", cex=2, adj=0)
#lines(c(0, aa), c(0, bb), lwd=2, lty=2)
#EndSection:
Alternate Representation for the Circle Problem
Psych 355, Miyamoto, Spr '18
Another Insight Problem – the Mutilated Checkerboard Problem - Probable END

23. Another Insight Problem – Mutilated Checkerboard Problem
End lecture here?
Problem: Cover the mutilated checkerboard with domino pieces so that every domino covers two squares OR if this is impossible, explain why it is impossible. The domino pieces must always be perpendicular or parallel to the sides of the board - they cannot be placed in a diagonal position.
See ‘e:\p355\hnd10-1a.doc’ and ‘e:\p355\hnd10-1b.doc’ for code for making mutilated checkerboards.
#Section:
plot.jm(c(-1, 9), c(-1, 10), axes=F)
j.dark <- colors()[82]
j.light <- 8
for (i in 1:4) for (j in 1:8) {
II <- (i - 1)*2 + .5
JJ <- j - .5
if (j %in% c(1,3,5,7)) j.col <- j.light else j.col <- j.dark
if (i != 1 | j != 8) rectan(c(JJ,II), width=1, ht=1, col=j.col) }
II <- (i - 1)*
if (j %in% c(2,4,6,8)) j.col <- j.light else j.col <- j.dark
if (i != 4 | j != 1) rectan(c(JJ,II), width=1, ht=1, col=j.col)
lines(c(0,0), c(0, 7), lwd=3)
lines(c(0,1), c(7, 7), lwd=3)
lines(c(1,1), c(7, 8), lwd=3)
lines(c(1,8), c(8, 8), lwd=3)
lines(c(8,8), c(8, 1), lwd=3)
lines(c(8,7), c(1, 1), lwd=3)
lines(c(7,7), c(1, 0), lwd=3)
lines(c(7,0), c(0, 0), lwd=3)
rectan(c(1,9), width = 1.6, ht=.6, col = colors()[chip.col])
text(2, 9, "= domino piece", cex=2,adj=0)
#EndSection:
Psych 355, Miyamoto, Spr '18
Failed Attempt to Solve the Mutilated Checkerboard Problem

24. Failed Attempt at Solving the Mutilated Checkerboard Problem
Problem: Cover the mutilated checkerboard with domino pieces so that every domino covers two squares OR if this is impossible, explain why it is impossible.
Failure!
This is not a solution!
FACT: It is impossible to cover the mutilated checkerboard with dominoes.
Why is it impossible?
#Section:
plot.jm(c(-1, 9), c(-1, 10), axes=F)
j.dark <- colors()[82]
j.light <- 8
for (i in 1:4) for (j in 1:8) {
II <- (i - 1)*2 + .5
JJ <- j - .5
if (j %in% c(1,3,5,7)) j.col <- j.light else j.col <- j.dark
if (i != 1 | j != 8) rectan(c(JJ,II), width=1, ht=1, col=j.col) }
II <- (i - 1)*
if (j %in% c(2,4,6,8)) j.col <- j.light else j.col <- j.dark
if (i != 4 | j != 1) rectan(c(JJ,II), width=1, ht=1, col=j.col)
lines(c(0,0), c(0, 7), lwd=3)
lines(c(0,1), c(7, 7), lwd=3)
lines(c(1,1), c(7, 8), lwd=3)
lines(c(1,8), c(8, 8), lwd=3)
lines(c(8,8), c(8, 1), lwd=3)
lines(c(8,7), c(1, 1), lwd=3)
lines(c(7,7), c(1, 0), lwd=3)
lines(c(7,0), c(0, 0), lwd=3)
rectan(c(1,9), width = 1.6, ht=.6, col = colors()[chip.col])
text(2, 9, "= domino piece", cex=2,adj=0)
#EndSection:
Psych 355, Miyamoto, Spr '18
Solution to the Mutilated Checkerboard Problem

25. Solution to the Mutilated Checkerboard Problem
Problem: Cover the checkerboard with domino pieces so that every domino covers two squares OR if this is impossible, explain why it is impossible.
A Solution is Impossible!
A domino piece always covers one dark square and one light square. Therefore any solution covers an equal number of dark and light squares.
The mutilated checkerboard has 30 dark squares and 32 light squares so it is impossible to cover an equal number of dark and light squares.
Easy Version of the Mutilated Checkerboard Problem – The Matchmaker Problem
Psych 355, Miyamoto, Spr '18

26. Easy Version of the Mutilate Checkerboard Problem The Russian Marriage Problem (a.k.a. the Matchmaker Problem)
Hayes, 1978: [wording slightly altered below]
In a small Russian village, there were 32 bachelors and 32 unmarried women. A matchmaker arranges 32 highly satisfactory marriages. The village was happy and proud. One night, two bachelors got drunk and killed each other. Can the matchmaker come up with heterosexual marriages (one man, one woman) among the 62 survivors?
#Section:
plot.jm(c(-1, 9), c(-1, 10), axes=F)
j.dark <- 8 #colors()[82]
j.light <- 8
for (i in 1:4) for (j in 1:8) {
II <- (i - 1)*2 + .5
JJ <- j - .5
if (j %in% c(1,3,5,7)) j.col <- j.light else j.col <- j.dark
if (j %in% c(1,3,5,7)) j.tx <- "Woman" else j.tx <- "Man"
rectan(c(JJ,II), width=1, ht=1, col=j.col)
text(JJ, II, j.tx) }
II <- (i - 1)*
if (j %in% c(2,4,6,8)) j.col <- j.light else j.col <- j.dark
if (j %in% c(2,4,6,8)) j.tx <- "Woman" else j.tx <- "Man"
rectan(center=c(4,4), width=8, ht=8, lwd=3)
rectan(c(1* , ), width=1, ht=1, col="darkblue", density = 25, angle = 0)
rectan(c(1* , ), width=1, ht=1, col="darkblue", density = 25, angle = 0)
#EndSection:
There are 30 men and 32 women. Obviously there is no way to match them into a complete set of heterosexual couples.
Psych 355, Miyamoto, Spr '18
Mutilated Checkerboard Problem & Russian Marriage Problem Are Isomorphs

27. Monday, 21 May, 2018: The Lecture Ended Here
Psych 355, Miyamoto, Spr '18

28. Mutilated Checkerboard Problem & Russian Marriage Problem
#Section:
plot.jm(c(-1, 9), c(-1, 10), axes=F)
j.dark <- 8 #colors()[82]
j.light <- 8
for (i in 1:4) for (j in 1:8) {
II <- (i - 1)*2 + .5
JJ <- j - .5
if (j %in% c(1,3,5,7)) j.col <- j.light else j.col <- j.dark
if (j %in% c(1,3,5,7)) j.tx <- "Woman" else j.tx <- "Man"
rectan(c(JJ,II), width=1, ht=1, col=j.col)
text(JJ, II, j.tx) }
II <- (i - 1)*
if (j %in% c(2,4,6,8)) j.col <- j.light else j.col <- j.dark
if (j %in% c(2,4,6,8)) j.tx <- "Woman" else j.tx <- "Man"
rectan(center=c(4,4), width=8, ht=8, lwd=3)
rectan(c(1* , ), width=1, ht=1, col="darkblue", density = 25, angle = 0)
rectan(c(1* , ), width=1, ht=1, col="darkblue", density = 25, angle = 0)
#EndSection:
The multilated checkerboard problem and the Russian marriage problem are problem isomorphs.
Problem Isomorphs: Problems that differ superficially but have identical logical structure.
Psych 355, Miyamoto, Spr '18
Concept of Problem Isomorphs

29. Concept of Problem Isomorphs
Problem isomorphs – structurally identical versions of a problem.
Basic fact about problem isomorphs: Some versions of a problem are harder to solve than other versions of the problem.
What is the psychological difference between the mutilated checkerboard problem and the matchmaker problem?
Kaplan and Simon: It is easier to solve the Russian marriage problem than the mutilated checkerboard problem, presumably because the Russian marriage version makes the importance of pairing men with women obvious. (See next slide)
Basic meaning of “morph” is “form” or “shape”.
Psych 355, Miyamoto, Spr '18
Four Isomorphic Versions of the Mutilated Checkerboard Problem

30. Kaplan & Simon: Four Isomorphic Versions of the Mutilated Checkerboard Problem
Blank board is hardest problem.
“Bread”/“Butter” word labels are easiest problem.
Colored & “Pink”/“Black” word labels are intermediate difficulty.
The salience of the pairing affects difficulty.
Blank (hardest)
Colored (intermediate)
See ‘e:\p355\rcode\mutilated checkerboard.doc’ for the R-code.
“Pink” & “Black” Word Labels (intermediate)
“Bread” & “Butter” (easiest)
Psych 355, Miyamoto, Spr '18
Conclusions re Problem Representation

31. Conclusion re Problem Representation
Some problem representations make problem solving easier than other problem representations.
Solving an insight problem often depends on finding a problem representation that make it obvious how to find the solution.
Examples that support these claims:
Mutilated checkerboard problem; Russian marriage problem; other isomorphic versions.
Circle problem. .
Psych 355, Miyamoto, Spr '18
Cheap Necklace Problem – An Example of a False Constraint