Why children are better (or at least
more open-minded) scientists than
adults are: Search, temperature
and the origins of human
cognition.
Alison Gopnik
Dept. of Psychology
UC Berkeley
The Probabilistic Models
Approach to Causal Learning
Abstract structured representations of causal
knowledge with systematic relations to data
Intuitive theories –Gopnik & Meltzoff, 1997
Causal Bayes nets- Spirtes, Glymour and Scheines, 1993,
Pearl 2000, Woodward 2003, Gopnik et al. 2004
Hierarchical causal Bayes nets and probabilistic logicGriffiths and Tenebaum 2007, Goodman 2010
Probabilistic Models and Cognitive
Development
• Gopnik 2012 Science
• Gopnik & Wellman 2012 Psychological
Bulletin
Unanswered Questions
• How do children search through all the
possible hypotheses?
• Do children learn higher-order causal
principles as well as specific causal
relationships?
• Why do children sometimes appear so
irrational?
• Are there developmental differences ?
The Sampling Hypothesis
Denison, Bonawitz, Gopnik, &
Griffiths, Cognition, 2013
Why Childhood?: Longer Childhood,
Bigger Brain, Smarter Animal
Quokka vs. Opposum
Weisbecker & Goswami, PNAS 2010
Fossil Dental Evidence For Immaturity
Regression of predicted versus actual age for eight fossil juveniles and 36 recent (living)
humans.
Smith T M et al. PNAS 2010;107:20923-20928
©2010 by National Academy of Sciences
Exploration vs. Exploitation
• Search and temperature
• Childhood is evolution’s way of
performing simulated annealing
Inferring Abstract Laws:
Lucas, Gopnik & Griffiths
• Framework theories
• Hierarchical Bayes-nets (Griffiths &
Tenenbaum)
• The blessing of abstraction (Goodman)
Which objects are blickets?
Is D a blicket? Is E a blicket? Is F a blicket?
What if you also saw these
events?
“Or“ Training
“And” Training
Test
Functional Form Procedure: “OR” and “AND” Test
Trial
D
D+F
E
D
D
D+E+F
D+F
Functional Form Procedure:
“OR” and “AND” Conditions
Do think the circle
is a blicket or not a
blicket?
CIRCLE
DIAMOND
BALL
Functional Form Procedure:
“OR” and “AND” Conditions
Which of these
should we use to
make the machine
turn on?
CIRCLE
DIAMOND
BALL
Intervention Question
“BASELINE” Test Trial 1 Results:
Percentage of Participants who think D and F are Blickets
1
0.9
*
______
***
______
0.8
0.7
0.6
D
0.5
F
0.4
0.3
0.2
0.1
0
Children
Adults
N = 24
N = 26
“OR” Test Trial Results:
1
0.9
Percentage of Participants who think D and F are Blickets
**
_____
***
______
0.8
0.7
0.6
D
0.5
F
0.4
0.3
0.2
0.1
0
Children
Adults
N = 25
N = 28
“AND” Test Trial Results:
Percentage of Participants who think D and F are Blickets
1
**
_____
0.9
0.8
0.7
0.6
D
0.5
F
0.4
0.3
0.2
0.1
0
Children
Adults
N = 25
N = 24
“BASELINE” Intervention 1 Results:
Percentage of Single vs. Multiple Object Interventions
0.9
0.8
0.7
0.6
0.5
Single
0.4
Multiple
0.3
0.2
0.1
0
Children
N = 22
Adults
N = 26
“OR” Intervention Results:
Percentage of Single vs. Multiple Object Interventions
1
0.9
0.8
0.7
0.6
Single
0.5
Multiple
0.4
0.3
0.2
0.1
0
Children
Adults
N = 25
N = 28
“AND” Intervention Results:
Percentage of Single vs. Multiple Object Interventions
0.9
**
_______________________________________
0.8
0.7
0.6
0.5
Single
0.4
Multiple
0.3
0.2
0.1
0
Children
Adults
N = 25
N = 24
“BASELINE” Intervention 1 Results:
F v. DF v. DEF Interventions
0.9
0.8
**
___________________
***
___________________
0.7
0.6
0.5
F
DF
0.4
DEF
0.3
0.2
0.1
0
Children
Adults
N = 22
N = 26
“OR” Intervention Results:
0.9
0.8
F v. DF v. DEF Interventions
***
___________________
***
___________________
0.7
0.6
0.5
F
DF
0.4
DEF
0.3
0.2
0.1
0
Children
Adults
N = 25
N = 28
“AND” Intervention Results:
F v. DF v. DEF Interventions
***
_______________________________
0.6
*
__________________
**
________
0.5
0.4
**
_______________
F
0.3
DF
DEF
0.2
0.1
0
Children
N = 25
Adults
N = 24
Tulver Flowers
Tulver “AND” Test Trial Results:
Percentage of Adults who think D and F are Tulvers
N = 28
N = 27
Adult “AND” Intervention Results:
Percentage of Single vs. Multiple Object Interventions
Adult “AND” Intervention Results:
F v. DF v. DEF Interventions
N = 28
N = 27
Learning Higher-Order Causal
Relations: Walker & Gopnik,
Psychological Science In press
• ,
• Learn causal properties of objects between 19- and
24-months
(Gopnik, 2012; Sobel & Kirkham, 2006; Meltzoff, Waismeyer & Gopnik, 2012)
• Determine whether
effects were caused by
their own actions at
16-months
(Gweon & Shchulz, 2011)
Relational Reasoning in
Non-Human Primates
• Failure as evidence for key difference in human
cognition (Penn, Holyoke, & Povinelli, 2008)
• Depends on culture/language (Gentner, 2010)
• Not a qualitative difference (Premack, 1988)
• Primates can learn
– Hundreds of trials
(Premack, 1988)
– Learning to use words
for “same” and “different”
(Premack, 1983)
Experiment 1
Match-to-Sample
• 46 participants
• 18- to 24-month-olds (mean 20.9 mos.)
-----------------------------------------------------------• Created a causal version of Premack’s (1983)
match-to-sample task
– Observe an abstract relational pattern (AA’, BB’,
CC’ lead to a reward)
– Select between AB (object match) and DD
(relational match)
Match-to-Sample Trial
1a
35
Match-to-Sample Trial
1b
Match-to-Sample Trial
2a
Match-to-Sample Trial
2b
Match-to-Sample Trial
3a
Match-to-Sample Trial
3b
Match-to-Sample Test
Trial 1
Test Blocks
Familiar
Novel
Distractor
Novel
Paired
41
Match-to-Sample Test
Trial 2
Test Blocks
Familiar
Novel
Distractor
Novel
Paired
42
Percentage of Infants who
Selected the Pair
Results: Match-to-Sample
1
*
0.8
0.6
0.4
0.2
0
18-20 months
21-24 months
18- to 24-month-olds, t(45) = 2.47, p<.02**
18-20 month olds: p=.72
21-23 month olds: p<.02**
Significant difference between age groups: p<.05**
43
Experiment 1a: Control
• Due to “matching” the experimenter’s
selection or a baseline preference for pairs?
• 21 participants total
• 21- to 24-month-olds (mean = 22.4 mos.)
--------------------------------------------------------------• Occlude the 2nd object in the pair
• No evidence for relational property “same”
• Prediction: random selection on test items
44
Control Trial 1a
Control Trial 1b
Control Trial 2a
Control Trial 2b
Control Trial 3a
Control Trial 3b
Control Test Trial
Test Blocks
Familiar
Novel
Distractor
Novel
Paired
Percentage of Infants who
Selected the Pair
Results: Control Experiment
1
0.8
*
0.6
0.4
0.2
0
21-24 mos EXP 1
21-24 mos EXP 2
21- to 24-month-olds in Experiment 1: p<.02
21- to 24-month-olds in Experiment 2: p=.65 (ns)
Significant diff. between infants in Exp 1 and Exp 2: p<.05
Experiment 2:
Relational Match-to-Sample
• 2 conditions: “same” and “different”
• 38 participants, 19 per condition
• Age: 18- to 30-months (mean 25.8 mos.)
----------------------------------------------------------• Present + and - evidence for the relation
“same” or “different”
• Evidence presented as pairs of objects
• Single test trial
“Same” Trial 1
“Same” Trial 2
“Same” Trial 3
“Same” Trial 4
“Same” Condition Test Trial
“Different” Trial 1
“Different” Trial 2
“Different” Trial 3
“Different” Trial 4
“Different” Condition Test Trial
Percent Infants who
Selected the Correct Pair
Results: RMTS
*
1
0.8
0.6
0.4
0.2
0
18- to 24-month-olds
25- to 30-month-olds
Median split (younger: mean = 22.8; older: mean = 28.7)
18-24 month olds: p=.08 (one-tail); p=.16 (two-tail)
25-30 month olds: p<.001 (two-tail exact binomial test)
No significant diff between age groups, p=.58
Summary and Discussion
• Infants can learn abstract relational causal
principles (same/different) and use them to
guide action
• Appears very early in development
• May help explain how children acquire
abstract causal knowledge
U-Shaped Curve?
• Piloting: older children pass the “same”
condition, but fail the “different” condition
• Older children doing WORSE than younger
children?
• This would support a U-shape – acquiring
prior that “different” is a low probability
relation
• 30-48-month-olds (M=36.2 months)
Preliminary Results
1
0.8
0.6
0.4
0.2
0
Same
Different
Conclusions
• Yes, damn it, children are little scientists
• They may be better, or at least more
open-minded scientists than we are
• Apparent irrationalities may actually be
causal inference advantages
• Normative philosophical inquiries and
empirical psychological ones can be
mutually illuminating
Collaborators and Support
•
•
•
•
•
•
•
•
Clark Glymour
Tom Griffiths
Elizabeth Bonawitz
Caren Walker
Chris Lucas
Sophie Bridgers
NSF
The James S. McDonnell Foundation
Causal Learning Collaborative
Reasoning and Learning about Complex Causal
Structures: Backtracking/conditioning vs
Surgery/Intervening
Pretense and Causal Reasoning
Buchsbaum et al, Philosophical
Transactions of the Royal Society, ’12
• Counterfactuals in causal reasoning and
learning
• Intuitive link between causal
counterfactuals and pretense –
are they related?
Monkey’s Birthday
• Two within-subject phases
– Counterfactual phase
– Pretense phase
• 52 preschool age children
– 26 four year olds
– 26 three year olds
• “Birthday machine”
for Monkey’s birthday
Counterfactual Phase
• Introduced to “birthday machine” and two objects
– Plays happy birthday when “zando” is on top
– Does nothing when “not a zando” is on top
• Asked counterfactuals
– “if this one was not a zando
what would happen if we put
it on the machine?”
– “if this one was a zando,
what would happen if we put
it on the machine?”
Pretense Phase
• Confederate needs to borrow real machine and
objects
• Introduce box + two wood blocks for pretend
• How do we pretend to make the machine go?
– What do we pretend when
we put each block on the
machine?
– Reverse roles of blocks and
repeat
Expt. 2: Mean Correct on Counterfactual and Pretense Questions
4
3.5
***
3
2.5
2
***
1.5
1
0.5
0
Counterfactual
Pretense
Music
Exp 2: Average Score for Pretense Questions
2
1.5
1
0.5
Counterfactuals
Incorrect
0
Counterfactuals
Correct
Zando
Non-Zando
-0.5
-1
-1.5
-2
No Music
Partial Correlation Counterfactuals and Pretense
accounting for age, conservation, executive function: p < 0.05*, r =
Reasoning about Complex Causal
Structures in Pretense
Reasoning about Complex Causal
Structures in Pretense
• In this book, we are going to learn about my friend Katie’s
dog named Sparky and cat named Buster. Sparky and Buster
spend a lot of time in Katie’s backyard. Sometimes Sparky
barks. When Sparky barks, it makes Buster feel scared.
Other times, Sparky wags his tail. When Sparky wags his
tail, it makes Buster feel happy. When Buster is scared, his
fear makes him run up a tree to hide from Sparky. When
Buster is happy, his happiness makes him wrestle with
Sparky. When Sparky barks, his barking also makes the birds
fly out of the tree. When Sparky wags his tail, the wagging
makes the fleas on his tail dizzy. Sometimes there are
ladybugs in Katie’s backyard. Other times there are
butterflies in Katie’s backyard.
Reasoning about Complex Causal
Structures in Pretense
Bark
Ladybugs
Wag
Butterflies
Scared
Birds
Happy
Fleas
Run
Wrestle
Reasoning about Complex Causal
Structures in Pretense: Backtracking vs
Surgery
Preliminary Results
Proportion "Forward" Answers Consistent with
Story Structure
1
+
*
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
Counterfactual
Pretense
Preliminary Results
Proportion "Backtracking” Answers
1
0.9
*
**
0.8
0.7
+
0.6
0.5
0.4
0.3
0.2
0.1
0
Counterfactual
Pretense
Learning Higher-Order Causal
Relations, Walker & Gopnik
2012
Test Blocks
Familiar
Novel
Distractor
Novel
Paired
Test Blocks
Familiar
Novel
Distractor
Novel
Paired
Percentage of Infants who
Selected the Paired Block
Results: Experiment 1
1
*
0.8
0.6
0.4
0.2
0
18-20 months
18-20 month olds: p=.72
21-23 month olds: p<.02
Sig diff between age groups: p<.05
21-24 months
Test Blocks
Familiar
Novel
Distractor
Novel
Paired
Percentage of Infants who
Selected the Paired Block
Results: Experiment 1
vs.
2
*
1
0.8
0.6
0.4
0.2
0
21-24 mos EXP 1
21-24 mos EXP 2
21-23 month olds in Exp 1: p<.02
21-23 month olds in Exp 2: p=.72
Sig diff between infants in Exp 1 and Exp 2: p<.05
Summary and Discussion
• Preschool age children can reason about
counterfactuals for a novel causal
relationship
• Maintain and intervene on a newly
learned causal relationship within a
pretend scenario
• Flexibly reassign the causal roles of
pretend objects