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