Towards a quantitative framework for sudden-insight problem solving ...

Towards a quantitative framework for sudden-insight problem solving and the feeling of ‘Aha!’ Jerome Swartz1, Robert DeBellis1, Aileen Chou1, Ryan Low2, Scott Makeig2

Piecewise Continuous Approximation

Relationship with Readiness Potential Φ5

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P(t)

External World

MTL/ aSTG b.g.

L P I F ACC PC

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Selective Triggering RP1 ‘Aha!pop’

Cortical and Subcortical Regions

γ = α ; ε = 0 (linear ramp-to-threshold) ‘Aha!-pop’

Distraction/Noise (Information Spam)

TEMPLATE DESIGN © 2008

www.PosterPresentations.com

 εt (εt)2  Aαβ t cos αt 1− + − ... β−α 6  2 

γ= α + ε; ε small (threshold crossing)

Dipole source localization suggests involvement of temporal areas (also see Kounios et al., 2008 and Jung-Beeman et al., 2004.

‘Aha!’ Timeout!

4 Hz mode

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γ = α + ε; ε large (no threshold crossing) 0

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Aha!-pop’ 1/2ε

CAT

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Information relevant to problem solving may originate from either the external world or within the brain. The use of such particularly relevant stimuli can be achieved both consciously and/or nonconsciously. It is the selective triggering of well-formed stimuli with the system kernel which leads to a resonance that rapidly brings the solution from “tip-of-tongue” to “top-of-mind”.

A phrase completion paradigm was used to study ‘Aha!’/insight problem solving using hi-res EEG.

 εt  Aαβ Va (t) ≈ t cos αt 1−   2 €β − α

€ Motor Action

t0

1/ε

CAT

CAT

2/ε

EMG signal

Neuronal Recruitment ∫ dt Accumulate & Build of Evidence

awareness of movement

Problem Solving “activity function”

Human Senses & Anatomical Pathways

Aαβ t cos αt β −α

The real part of the inverse transform of the above equation is then of the form 0

t

awareness of intent to move

Nonconscious Processing (NCP) (Spatiotemporal Confluence)

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Dangerrelated

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hours

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2 D puzzles 'Sleep(xword /jigsaw) on-it' 'tip-of-tongue' / Math/physics problems 'top-of-mind' 1D word puzzles/ Group Problem Visual anagrams Solving priming (Brainstorming) (jokes/cartoons) Sudoku Pattern Recognition

"1+1=2" (simple arithmetic) Face processing

8

years

Archimedes’ Eureka! Poincaré 's Conjecture

9

decades

Log10 T (Tsec= Time-to-Sol’n)

Einstein’s Relativity Existence Theorems

Degree of Consciousness

Conclusion

Aαβ + ... s+γ

Va (t) ≈

-2

10 ms

Snake/ spider (reflex)

 1 1  ε ε H 0 (s) = € ≈ + − ... 1− (s + α)(s + α + ε ) (s + α )2  (s + α) (s + α)2 

Temporal V0 Resonance

t

dc=0 -3

Experimental Findings

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‘Aha!-pop’

~85 ms*

*Haggard & Libet, 2001

‘Aha ! - pop'

T-problem sets:

The near-resonant “fuzzy-pole” expansion for β or γ = α + ε (ε small), yields a transfer function kernel

€  εt (εt)2  h(t) ≈ t cos αt1− + − ... , so that 6  2 

~200 ms*

~1000+ ms*

dc=½

1ms

For γ =α (double pole), the Ae-γτ RHS forcing function yields a steady state solution with a Real part:

Va (t) =

awareness of solution

1 d2  1 1  d +  +  +1 αβ dt 2  α β  dt

Increased lateral coupling (νL) tends to increase coherence in the theta band. Furthermore, a brief sinusoidal pulse at a resonant frequency in one population leads to increased coherence between other populations in the network.

d Va dV + (α + β ) a + αβVa = Aαβe −γt + ... dt 2 dt

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resonance

DA, 5-HT, NE

(track 2)

Spectral coherence between leads

Coupling: νL= 0.1; P(t): 4Hz pulse

Dα =

(s + α )(s + β )Va (s) =

700-900ms*

dc=1

The Laplace-transformed equation is

Conceptual Schematic CAT

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Conscious and Nonconscious Processing of Solved Problems w/r Time-to-Solution (T)

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Motor Cx

dc (c/c+n)

In time domain, we reduce the Robinson ODE to

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t RP1 onset (unconscious)

Task-stimulated Readiness Potential ≡ RP1 (Anticipation of Movement)

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NCP

Button Press

Coupling: νL = 0.1

Dα Va (t) = ∑ N ab sabφ b (t − τ ab )

Consider the anecdote of a cryptic crossword puzzle. Prior to working on the puzzle, the correct answer to a clue (“Standard cut vegetable (7)”) was observed in a market and forgotten. Several weeks later and after unsuccessful attempts, the correct answer (“parsnip”) was revealed in a flash of insight.

(PFC  Motor Cortex)

t=T0

Logical Gap

Amplitude (µV)

“Fuzzy” Pole Resonance €

Priming or Insight?

BA10

t=0

-5

(space-clamped, linearized form)

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temporal

(track 1)

Dα Va (t) = ∑ N ab sabφ b (t − τ ab )

C

NC

A Spectrum of ‘Aha!s’

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Jung-Beeman, M. et al., 2004 Neural Activity When People Solve Verbal Problems with Insight PLoS Biology

Parsnip

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Conscious Access Threshold

…spatiotemporal “confluence”/coordination NCP/CP Neuromodulation Neuronal Recruitment Temporal Accumulation Functional Clustering

No coupling

αβ Va (t) = ∫ L(t − t')Pa (t')dt' L(u) = ( e −αu − e −βu) β−α −∞ Q max Pa (t) = ∑ν abφ b (t) Q(x) = −(V (x )−θ ) b 1+ e σ €  1 ∂2 2 ∂  +1− ra2 ∇ 2 φ a (r,t) = Q(Va (r,t))  2 2+  γ a ∂t γ a ∂t  €

€

“…the clearest defining characteristic of insight problem solving is the subjective ‘Aha!’ or ‘Eureka!’ experience that follows insight solutions…”

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problem solving NC

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NC

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Stickgold, R., 2008 Insights into Insights UCSD/ Rancho Santa Fe

“Standard-cut vegetable (7)”

(Combination of NC ) (& C preprocessing)

(full, nonlinear)

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Aha!-Pop

E0

(stimulus-driven brain activity)

Thought Fragments coalescing

Conscious

Conscious

Internal/ External Trigger

Robinson’s ‘continuum’ model of population dynamics

“The sudden appearance in conscious awareness of a really big new and useful relationship among previously known information.”

Pre-

Unconscious Frontal Lobe (PFC/ACC) circuits

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‘Top of Mind’ transition ‘Tip of tongue’

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Time Courses of Insight Problem Solving & Button Press Dynamics (Conceptual Model) … Relating ‘NCP/Aha!-pop’ with Readiness Potential & Reports of Awareness (Fragmented Thoughts ) (Sudden Insight) (Awareness)

νL

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Φ4 νL

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Φ3 νL

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Mathematical Model

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What is ‘Aha!’?

Φ2 νL

Problem Solving

We hypothesize that a spatiotemporal resonance of cortical potentials generated by interacting neural populations supports a rapid rise of activity toward a threshold of conscious access (Del Cul et al., 2007), the crossing of which signifies the availability of an insight solution. We attempted to model the mechanism for achieving an ‘Aha!’ via resonance using P.A. Robinson’s “continuum” model for EEG as a simple, archetype of distributed population behaviors which directly link neurophysiology to behavior (Robinson et al., 2005). Supporting preliminary data from high-resolution EEG in a semantic, phrase completion task suggests that activity in the theta and alpha bands reflects activity corresponding to suddeninsight solutions and consistent with the theoretical work.

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Necessary Conditions Rapid all-or-none solution – feeling of immediacy and fully formed solution, although not necessarily correct Emotional response/appreciation – neuromodulators help determine the strength of the post-event ‘Aha!’ “feeling” Impasse – a ‘logical gap’ exists at the final stage of solution processing…how close is the answer in emerging from ‘tip-of-tongue’ to ‘top-of-mind’? Accumulation process (over time), multiple areas (across space) – confluence of working memory and problem solving circuits (PFC, LIP, basal ganglia, ACC, aSTG/MTL, etc…) Motivation and/or incentive – neuromodulation (e.g., DA, 5-HT) from start-tofinish of problem solving process Noise dependence – minimal distraction or noise Invariance – neural dynamics conserved across insights (mini- to macro-‘Aha!’) Triggered by ‘well-formed’ stimulus – an endogenous or exogenous trigger stimulates a rapid rise-to-threshold with sufficient energy to drive the consequent ‘Aha!-pop’

Problem solving via Sudden-Insight has several qualities, notably the feeling of ‘Aha!’ and the seemingly instantaneous occurrence of fully formed solutions, which distinguish it from more incremental, methodological approaches. This corresponds to neural activity and dynamics with properties different than other types of problem solving, as shown by recent studies using fMRI and EEG (Kounios et al., 2008; Sandkühler and Bhattacharya, 2008; Low and Makeig, 2008). However, attempts to describe or predict high-level cognitive behaviors such as ‘Aha!’ problem solving with quantitative models have been lacking.

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Introduction

1The Swartz Foundation, Stony Brook, NY 11790, Center for Computational Neuroscience, University of California San Diego, La Jolla, CA 92093

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2Swartz

10 Hz mode -

1/ε

2/ε

Depending on the magnitude of ε, the activity of a population rises toward and, in some cases (ε