cognaction.org/denis
Analysis of the action dynamics of choice
Denis O'Hora
Psychology, National University of Ireland Galway
Rick Dale
Cognitive and Information Sciences
University of California, Merced
Petri Piiroinen
Mathematics, Statistics and Applied Mathematics
National University of Ireland Galway
cognaction.org/denis
Outline
• Rick: Brief introduction...
• Denis: Decisions, decisions, decisions
• Petri: Relevant concepts of nonlinear dynamics
• Denis: Mousetracker!
• Denis and Rick: Some other examples (MATLAB, R,
PsyScope, etc.)
• Petri: Dynamical systems analysis of trajectories
cognaction.org/denis
Outline
• Rick: Brief introduction...
• Denis: Decisions, decisions, decisions
• Petri: Relevant concepts of nonlinear dynamics
• Denis: Mousetracker!
• Denis and Rick: Some other examples (MATLAB, R,
PsyScope, etc.)
• Petri: Dynamical systems analysis of trajectories
cognaction.org/denis
Doing cognitive science by hand
Rick Dale
Cognitive and Information Sciences
UC Merced
cognaction.org/denis
What is the mind like?
• “Classical” conceptions of the mind as a sequence of
domain-specific discrete-state operations.
• Pylyshyn, Fodor, Markman, Dietrich, Carey, Spelke, Marcus, Pinker, ...
• Simmering dynamical conceptions have always been
around (e.g, Wiener, etc.), but activity in the past few
decades: The mind as living in an endless flux of
continuous energy, itself graded and parallel operating
under many constraints that guide structured behavior.
• Port & Van Gelder, 1995
cognaction.org/denis
Implications
Symbolic Computing System
Non-Symbolic System/Process
cognition
cognition
action
action
Neglect of action dynamics...
Continuous, non-ballistic movements...
(Spivey, Grosjean, & Knoblich, 2005)
Spoken-word recognition
phonological cohort “candle”
Curvature
“Click the candy...”
“Graded spatial attraction toward phonological competitors
visible in averaged trajectories...”
(Spivey, Grosjean, & Knoblich, 2005)
Spivey & Dale, 2006
choice 1
choice 2
RT in ms
choice 1
choice 2
curvature
complexity
vacillation
movement
time
dnx/dt
initiation
time
Evaluating spoken
sentences
Spoken-word recognition
Mindpixel
Chris McKinstry (1967-2006)
Mindpixel Examples
Does gravity suck?
0.38
Can a bottle of beer talk?
0.0
Do all humans have the
same level of
consciousness?
0.1
YES
NO
“Should you brush your teeth everyday?”
Probability: 1.0
YES
NO
“Is a thousand more than a billion?”
Probability: 0.0
YES
NO
“Does J come after K in the alphabet?”
Probability: 0.1
YES
NO
“Can a kangaroo walk backwards?”
Probability: 0.2
YES
NO
“Is the sky ever green?”
Probability: 0.3
YES
“Can fish swim backwards?”
Probability: 0.4
NO
YES
NO
“Are humans logical?”
Probability: 0.5
YES
NO
“Is murder sometimes justifiable?”
Probability: 0.6
YES
NO
“Is it difficult to get kids to cooperate?”
Probability: 0.7
YES
NO
“Is the daughter younger than the mother?”
Probability: 0.8
YES
NO
“Does water boil at a hundred degrees Celsius?”
Probability: 0.9
Y-coordinate
300
200
100
0
-200
Yes
No
-100
0
100
200
X-coordinate
McKinstry et al., 2008
Velocity (pixels/sec)
1000
950
900
850
800
1000
1100
1200
1300
1400
Time (ms)
Yes
No
McKinstry et al., 2008
Yes
No
McKinstry et al., 2008
color categorization (Huette & McMurray, 2010)
face perception (Freeman & Ambady, 2009)
visual attention (Song & Nakayama, 2009)
conceptual color priming (Finkbeiner, Song, Nakayama, & Carramazza, 2010)
spoken word recognition (Spivey, Grosjean, & Knoblich, 2005; Magnuson, 2005)
sentence processing (Farmer, Anderson, & Spivey, 2007)
verb-aspect comprehension (Anderson, Matlock, & Spivey, 2009)
linguistic negation (Dale & Duran, 2011)
perspective-taking (Greenwood et al., 2011; Duran et al., 2011)
semantic categorization (Dale, Kehoe, & Spivey, 2007)
category learning (Dale, Roche, Snyder, & McCall, 2008)
decision making (McKinstry, Dale, & Spivey, 2008)
task switching (Hindy & Spivey, 2008)
deception (Duran, Dale & McNamara, 2010)
social judgments (Wojnowicz, Ferguson, Dale, & Spivey, 2009)
Processes evidence in action...
• Action dynamics offer a window onto the timing of
mental processes, especially related to events that
unfold in time, such as the perception and higher-order
interpretation of spoken language.
• The measure often relies on forced-choice paradigms,
the exploration of “decision dynamics”...
cognaction.org/denis
Outline
• Rick: Brief introduction...
• Denis: Decisions, decisions, decisions
• Petri: Relevant concepts of nonlinear dynamics
• Denis: Mousetracker!
• Denis and Rick: Some other examples (MATLAB, R,
PsyScope, etc.)
• Petri: Dynamical systems analysis of trajectories
cognaction.org/denis
Outline
• Rick: Brief introduction...
• Denis: Decisions, decisions, decisions
• Petri: Relevant concepts of nonlinear dynamics
2.0
• Denis: Mousetracker!
• Denis and Rick: Some other examples (MATLAB, R,
PsyScope, etc.)
Decision Making
Killeen, 1992
0.0
0.5
shp
1.0
1.5
• Petri: Dynamical systems analysis of trajectories
PETER R. KILLEEN
454
GML$and$Reinforcer Dimensions
Any two-choice discrimination trial
In#these#circumstances,#a#concatenated#form#is#used#to#
movement in a
0 can be described as50
100
encompass#the#different#variables#influencing#choice.
bistable attractor landscape.
Index
1.0
0
c
cn
150
200
0
'_
cn
0
0
._
L.
0
c
.0
0
L.
VI
0
Baum & Rachlin (1969)
100
Fl
Fig. 12. Average data for 3 pigeons who received food with a probability of .50 after 30 s for a response to the FI
key, and with a probability of .005 after every second for a response to the VI key. Nonreinforced trials ended with
a blackout after 100 s. The vertical axis shows the probability of not making a response in any unit of time. A marble
loosed on this surface and constrained only by the march of time would roll first to the VI side, then into the potential
well of the FI, and then would be carried out by time back to the VI key. The data are from an unpublished study
by the author.
Probability of choosing
one
alternative
or
the
changes in the rate of switching from one tra-
Contingencies
•
Experiment 1 (1.4)
•
•
•
M(low) = 5 points
M(high) = 7 points
•
Experiment 3 (4)
•
•
M(low) = 5 points
M(high) = 20 points
Experiment 2 (2)
•
•
M(low) = 5 points
M(high) = 10 points
Acquisition
•
M(high)/M(low)
predicted acquisition
•
Greater M(high)/
M(low)
•
Faster
Trajectories - Condition
M1=M2 responses affected by overall
M(high)/M(low)
Low-low - longer latencies
Low-low - greater complexity (x
flips)
Low-low - greater curvature
High-High less curvature when M
(high)>>M(low)
Decision Making
Low
Low
Low
High
High
High
x1
x1
x1
x2
x2
x2
least curvature
longer latencies
greater complexity (x flips)
greater curvature
(as Mlow/Mhigh -> 0)
Mlow/Mhigh => x1/x2