and Nonconscious Processing€¦ · t t 0 0 Problem Solving Nonconscious Processing (Spatiotemporal...
Transcript of and Nonconscious Processing€¦ · t t 0 0 Problem Solving Nonconscious Processing (Spatiotemporal...
Towards a Quantitative Framework for Sudden‐Insight Problem Solvingfor Sudden Insight Problem Solving
and Nonconscious Processing
Jerome Swartz, Robert DeBellis, Aileen Chou
Insights Into Insight 2008Insights Into Insight 2008La Jolla, CA
AcknowledgementsAcknowledgements
• Scott MakeigScott Makeig
• Nava Rubin
hik i h• Eugene Izhikevich
• Frank Hoppensteadt
• Jonathan Victor
• John RinzelJohn Rinzel
• Hirsh Cohen
many others…
GenesisGenesis
• Invention
• Creativity• Creativity
• Puzzles
• Math Problems
• Abstract Reasoningg
The Rose in the Garden“May Garden View” I
(e.g., e large) (e.g., e ‐> 0)
“May Garden View” II “May Garden View” III(e.g., e medium)
The Rose in the Garden
Mother’s
Day!
(?) (~) (!)(?) (~) (!)
The Rose in the Garden“May Garden View” I
(e.g., e large) (e.g., e ‐> 0)
“May Garden View” II “May Garden View” III(e.g., e medium)
The Rose in the Garden
Mother’s
Day!
(?) (~) (!)(?) (~) (!)
The Rose in the Garden“May Garden View” I
(e.g., e large) (e.g., e ‐> 0)
“May Garden View” II “May Garden View” III(e.g., e medium)
The Rose in the Garden
Mother’s
Day!
(?) (~) (!)(?) (~) (!)
“Standard‐cut vegetable (7)”
“Standard‐cut vegetable (7)”
++
“Standard‐cut vegetable (7)”
+
Parsnip
+
‘Aha!’Aha!
“…the clearest defining characteristic of insight problem solving is the subjectiveinsight problem solving is the subjective ‘‘Aha!’’ or ‘‘Eureka!’’ experience that follows insight solutions ”insight solutions…
‐‐ Neural Activity When People Solve Verbal Problems with Insight
Mark Jung‐Beeman, Edward M. Bowden, Jason Haberman, Jennifer L. Frymiare, Stella Arambel‐Liu, Richard Greenblatt, Paul J. Reber, John Kounios
PLoS Biology, 4/04
Problem SolvingProblem Solving
• DifficultyDifficulty
• Representation
C l i• Complexity
• Insight vs. Gradual
• LTM/priming
• ‘Aha!’ (vs Duh!)Aha! (vs. Duh!)
‘Aha!’ A prioriAha! A priori• Impasse
• All‐or‐none solution, but…not necessarily correct
• Emotional response• Emotional response
• Accumulation process (time), multiple areas (space)
• Motivation and/or incentive
• Noise dependence
• Invariance• Invariance
Generalized NCP/ ‘Aha!‐pop’ Conceptual Model(Flow Diagram)
‘Aha!‐pop’
CATV
TemporalResonance
Selective Triggering
tt0
V0
Problem Solving
Nonconscious Processing
(Spatiotemporal Confluence)DA, 5‐HT, NE
Human Senses & Anatomical Pathways
‘Aha!‐pop’
RP1 MotorAction
External W
orld
“activity function”
PFC
MTL/aSTGb.g.
ACC∫ dt Accumulate & Build ofEvidence
Neuronal RecruitmentLIP
Distraction/Noise (Information Spam)
E
Cortical and Subcortical Regions
NCP
Generalized NCP/ ‘Aha!‐pop’ Conceptual Model(Flow Diagram)
‘Aha!‐pop’
CATV
TemporalResonance
Selective Triggering
tt0
V0
Problem solving
Nonconscious Processing
(Spatiotemporal Confluence)DA, 5‐HT, NE
Human senses & Anatomical pathways
‘Aha!‐pop’
RP1 MotorAction
xternal w
orld
“activity function”
PFC
MTL/aSTGb.g.
ACC
Neuronal RecruitmentLIP
∫ dt Accumulate & Build ofEvidence
Distraction/Noise (Information Spam)
E
Cortical and subcortical regions
Choosing a Modelg• Mean‐field• Specifically models EEG/ECoGSpecifically models EEG/ECoG• ‘Realistic’• Extensible• Linearity still meaningful• Predictor
Mean Field ApproachesBiological ComputationalBiological Computational
In vivo
Tsodyks, et al. 1998
In silica
Wong and Wang, 2006
Robinson’s Cortico‐Thalamocortical ModelRobinson s Cortico Thalamocortical Model
• Specifically models EEG/ECoG• Delay‐Dependent (DDE) and linearized
PDE ODE• 18 physiologically‐based, experimentally‐verified
parametersparameters• Parametric decoupling of compartments• Extensible – more complicated configurations
may be constructed across distinct brain regions• Captures many EEG‐specific features in linear
dynamics (Breakspear, DeBellis)
A linear resonator model is the simplest instantiation for astimulus‐triggered rise‐to‐threshold
17
Robinson Model of Neural Population Dynamics(Historical development via Wilson & Cowan, Freeman,
Amari, Haken, Nunez, and Wright & Liley)
Nonlinear form (Robinson et al., 1997)
( ) ( ') ( ') 'a aV t L t t P t dt∞
−∞
= −∫ ( )uu eeuL βα
αβαβ −− −−
=)(
max( ( ) )( )
1V x
QQ xe
θσ
− −=+
( ) ( )a ab bb
P t v tφ= ∑
( )2
2 22 2
1 2 1 ( , ) ( , )a a aa a
r t Q V tt t
φγ γ
⎛ ⎞∂ ∂+ + − ∇ =⎜ ⎟∂ ∂⎝ ⎠
r r
Space‐clamped, Linearized form (Robinson et al., 2005)
( ) ( )D V t N tφ∑21 1 1 1d dD ⎛ ⎞
⎜ ⎟
18
( , ) ( , )a ab ab b abb
D V t N s tα φ τ= −∑r r 2 1Ddt dtα αβ α β
⎛ ⎞= + + +⎜ ⎟
⎝ ⎠
Thresholds and BifurcationsThresholds and Bifurcations
Fuzzy Pole MathFuzzy Pole Math( , ) ( , )a ab ab b ab
b
D V t N s tα φ τ= −∑r r2
2
1 1 1 1d dDdt dtα αβ α β
⎛ ⎞= + + +⎜ ⎟
⎝ ⎠
Fuzzy Pole MathFuzzy Pole Math( , ) ( , )a ab ab b ab
b
D V t N s tα φ τ= −∑r r2
2
1 1 1 1d dDdt dtα αβ α β
⎛ ⎞= + + +⎜ ⎟
⎝ ⎠
( )2
2 ...ta aa
d V dV V A edt dt
γα β αβ αβ −+ + + = +
In time domain, we reduce the Robinson ODE to
Fuzzy Pole MathFuzzy Pole Math( , ) ( , )a ab ab b ab
b
D V t N s tα φ τ= −∑r r2
2
1 1 1 1d dDdt dtα αβ α β
⎛ ⎞= + + +⎜ ⎟
⎝ ⎠
( )2
2 ...ta aa
d V dV V A edt dt
γα β αβ αβ −+ + + = +
In time domain, we reduce the Robinson ODE to
( )( ) ( ) ...( )aAs s V ss
αβα βγ
+ + = ++
The Laplace‐transformed equation is
Fuzzy Pole MathFuzzy Pole Math( , ) ( , )a ab ab b ab
b
D V t N s tα φ τ= −∑r r2
2
1 1 1 1d dDdt dtα αβ α β
⎛ ⎞= + + +⎜ ⎟
⎝ ⎠
( )2
2 ...ta aa
d V dV V A edt dt
γα β αβ αβ −+ + + = +
In time domain, we reduce the Robinson ODE to
( )( ) ( ) ...( )aAs s V ss
αβα βγ
+ + = ++
The Laplace‐transformed equation is
For γ =α (double pole), the Ae‐γt RHS forcing function yields a steady state solution with a Real part:
( ) cosaAV t t tαβ α
β α=
−
Fuzzy Pole MathFuzzy Pole Math( , ) ( , )a ab ab b ab
b
D V t N s tα φ τ= −∑r r2
2
1 1 1 1d dDdt dtα αβ α β
⎛ ⎞= + + +⎜ ⎟
⎝ ⎠
( )2
2 ...ta aa
d V dV V A edt dt
γα β αβ αβ −+ + + = +
In time domain, we reduce the Robinson ODE to
( )( ) ( ) ...( )aAs s V ss
αβα βγ
+ + = ++
The Laplace‐transformed equation is
For γ =α (double pole), the Ae‐γt RHS forcing function yields a steady state solution with a Real part:
( ) cosaAV t t tαβ α
β α=
−
The near‐resonant “fuzzy‐pole” expansion for β or γ = α + ε (ε small), yields a transfer function kernel
01( )
( )( )H s
s sα α ε=
+ + +
2
2 2
1 1 ...( ) ( ) ( )s s s
ε εα α α
⎡ ⎤≈ − + −⎢ ⎥+ + +⎣ ⎦
β γ (
Fuzzy Pole MathFuzzy Pole Math( , ) ( , )a ab ab b ab
b
D V t N s tα φ τ= −∑r r2
2
1 1 1 1d dDdt dtα αβ α β
⎛ ⎞= + + +⎜ ⎟
⎝ ⎠
( )2
2 ...ta aa
d V dV V A edt dt
γα β αβ αβ −+ + + = +
In time domain, we reduce the Robinson ODE to
( )( ) ( ) ...( )aAs s V ss
αβα βγ
+ + = ++
The Laplace‐transformed equation is
For γ =α (double pole), the Ae‐γt RHS forcing function yields a steady state solution with a Real part:
( ) cosaAV t t tαβ α
β α=
−
The near‐resonant “fuzzy‐pole” expansion for β or γ = α + ε (ε small), yields a transfer function kernel
01( )
( )( )H s
s sα α ε=
+ + +
2
2 2
1 1 ...( ) ( ) ( )s s s
ε εα α α
⎡ ⎤≈ − + −⎢ ⎥+ + +⎣ ⎦
The real part of the inverse transform of the above equation is then of the form
β γ (
0
2( )( ) cos 1 ...2 6t th t t t ε εα
⎛ ⎞≈ − + −⎜ ⎟
⎝ ⎠, so that
2( )( ) cos 1 ...2 6a
A t tV t t tαβ ε εαβ α
⎡ ⎤= − + −⎢ ⎥− ⎣ ⎦
Resonance and “Conscious Access”
( ) cos 12a
A tV t t tαβ εαβ α
⎡ ⎤≈ −⎢ ⎥− ⎣ ⎦
γ = α ; ε = 0(linear ramp‐to‐threshold)
γ= α + ε; ε small (threshold crossing)
γ = α + ε; ε large(no threshold crossing)
Aha!‐pop
CAT1/2ε CAT
/
CAT
‘Aha!’‐pop
V0V0 V0
1/ε 2/ε 1/ε 2/ε
1/2ε
t t tt0 t01/ε
26
Predictions from ModelPredictions from Model
• ‘Aha!’ generates EEG activity with envelopesAha! generates EEG activity with envelopes with linear‐exponential envelopes
• EEG gamma band peaks at t0
• Stimulus ‘closeness’ represented by ε parameterizes EEG response
• ‘Distraction/Noise’ attenuates response
Interleaving of Time CoursesInterleaving of Time Courses
Unconscious
Time Courses of Insight Problem Solving & Button Press Dynamics (Conceptual Model) … Relating ‘NCP/Aha!-pop’ with Readiness Potential & Reports of Awareness
Conscious(Awareness)(Fragmented Thoughts ) (Sudden Insight)
Pre-
‘Tip of tongue’
‘Top of Mind’
Unconscious Conscious
ConsciousAccessThreshold
E0
Frontal Lobe (PFC/ACC)circuits
old
Aha!-Pop
(stimulus-driven brain activity)Internal/ External Trigger
transitionPro
Conscious
temporal resonanc
Rise to
Thr
esho
ld
problem solving
( y)
awareness of soluti
ThoughtFragmentscoalescing BA10 (PFC Motor Cortex)
C
NCC
oblem Solving
(track 1)
(Combination of NC )(& C preprocessing)
NCC
…spatiotemporal “confluence”/coordination
ce
t=0
t
NCP/CPNeuromodulation
Neuronal RecruitmentTemporal AccumulationFunctional Clustering
t=T0
onNC
Logical Gap
MW
a
CNC
Motor Cx
Button Pr
(track 2
MW
EM
G signal
awareness of m
ovem
awareness of intent to
RP1 onset (unconscious)Amplitude (µV)
-5
Eagleman, 2004
*Haggard & Libet, 2001
Task-stimulated Readiness Potential ≡ RP1(Anticipation of Movement)
t
ress2)
~1000+ ms*
~200 ms* ~85 ms*
ment
move
700-900ms*
0
Camouflage RevealCamouflage Reveal
Phrase CompletionPhrase Completion
_ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _
_ N _ _ _ _ I _ _ _ _ O _ _ _ _ N_ _ _
_ N _ _ E _ I _ _ _ _ OU _ _ _ N _ _E time
_ N _ HE _ IP _ F _ OU _ _ ON_ _ E
ON THE TIP OF YOUR TONGUE
Next StepsNext Steps
NYU – camouflaged image psychophysics (withNYU camouflaged image psychophysics (with N. Rubin)
NYU – computational modeling (with F. H d d J Ri l)Hoppensteadt and J. Rinzel)
UCSD – EEG/ICA dynamics (with S. Makeig)
Thank you