Analogical Problem Solving With Visual Models

Davies, J., Nersessian, N. J., & Goel, A. K. http://www.cc.gatech.edu/~jimmyd/research/visual-analogy/ May 2001

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Analogical Problem Solving With Visual Models

Jim Davies, Nancy J. Nersessian, Ashok K. Goel {jimmyd, nancyn, goel}@cc.gatech.edu

Program in Cognitive ScienceGeorgia Institute of Technology

Davies, J., Nersessian, N. J., & Goel, A. K. http://www.cc.gatech.edu/~jimmyd/research/visual-analogy/ May 2001

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Outline• Background: where these ideas are

coming from• Our computational account of

visual analogy• Examples: radiation problem and

Maxwell’s case study

Davies, J., Nersessian, N. J., & Goel, A. K. http://www.cc.gatech.edu/~jimmyd/research/visual-analogy/ May 2001

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Motivation

• People use analogy and visual reasoning when problem solving – In Scientific theory creation

• Nersessian’s cognitive-historical analysis of Maxwell

– Psychological studies support this

Davies, J., Nersessian, N. J., & Goel, A. K. http://www.cc.gatech.edu/~jimmyd/research/visual-analogy/ May 2001

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This Work• This work builds a new, cognitively

informed, computational theory of visual analogy for problem solving, one form of which is scientific discovery.

• We hypothesize that representing problems as visual abstractions facilitates the analogical process in problem solving.

Davies, J., Nersessian, N. J., & Goel, A. K. http://www.cc.gatech.edu/~jimmyd/research/visual-analogy/ May 2001

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Visual Analogy

• Visual analogy is analogy with visual elements

Davies, J., Nersessian, N. J., & Goel, A. K. http://www.cc.gatech.edu/~jimmyd/research/visual-analogy/ May 2001

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Bitmap Images

• Neuron432: on• Neuron479: off• Neuron200: off• Neuron136: off• Neuron326: on• Neuron344: on

Davies, J., Nersessian, N. J., & Goel, A. K. http://www.cc.gatech.edu/~jimmyd/research/visual-analogy/ May 2001

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Symbolic ImagesSymbolic Image

contains contains

square

contains

circle triangle

inside right-of

Davies, J., Nersessian, N. J., & Goel, A. K. http://www.cc.gatech.edu/~jimmyd/research/visual-analogy/ May 2001

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Symbols Are Mapped

Davies, J., Nersessian, N. J., & Goel, A. K. http://www.cc.gatech.edu/~jimmyd/research/visual-analogy/ May 2001

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Goel’s Computational Work• Structure-Behavior-Function: Goel et al.

1997• IDEAL: Bhatta & Goel 1997

– Generic Teleological Mechanisms• ToRQUE: Griffith, Nersessian, Goel 2000.

– Generic Structural Transformations

Davies, J., Nersessian, N. J., & Goel, A. K. http://www.cc.gatech.edu/~jimmyd/research/visual-analogy/ May 2001

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Primitive Visualization Language (Privlan)

• Primitive visual transformations (privits)

• Primitive visual elements (privels)• Symbolic images (simages)

Davies, J., Nersessian, N. J., & Goel, A. K. http://www.cc.gatech.edu/~jimmyd/research/visual-analogy/ May 2001

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Privits: Primitive Visual Transformations

• Decompose (object, number)• Move (object, new-location)

Davies, J., Nersessian, N. J., & Goel, A. K. http://www.cc.gatech.edu/~jimmyd/research/visual-analogy/ May 2001

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Privels: Primitive Visual Elements

• Line (thickness, start point, end point)

• Generic-Visual-Element (size, location)

Davies, J., Nersessian, N. J., & Goel, A. K. http://www.cc.gatech.edu/~jimmyd/research/visual-analogy/ May 2001

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System: Galatea

Davies, J., Nersessian, N. J., & Goel, A. K. http://www.cc.gatech.edu/~jimmyd/research/visual-analogy/ May 2001

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Davies, J., Nersessian, N. J., & Goel, A. K. http://www.cc.gatech.edu/~jimmyd/research/visual-analogy/ May 2001

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Maxwell’s Model Development

Davies, J., Nersessian, N. J., & Goel, A. K. http://www.cc.gatech.edu/~jimmyd/research/visual-analogy/ May 2001

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Generic Abstraction

Davies, J., Nersessian, N. J., & Goel, A. K. http://www.cc.gatech.edu/~jimmyd/research/visual-analogy/ May 2001

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Davies, J., Nersessian, N. J., & Goel, A. K. http://www.cc.gatech.edu/~jimmyd/research/visual-analogy/ May 2001

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Primitive Visualization Language (Privlan)

• Primitive visual transformations (privits)– Add-component, decompose, move

• Primitive visual elements (privels)– Circle, line, generic-visual-element

• Symbolic images (simages)

Davies, J., Nersessian, N. J., & Goel, A. K. http://www.cc.gatech.edu/~jimmyd/research/visual-analogy/ May 2001

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Conclusions• Galatea has been applied to two examples,

supporting our computational theory of visual analogy and Privlan.

• This implementation has provided support for visual interpretations of the Duncker case and Nersessian’s interpretation of the Maxwell case.

• We conjecture that visual representations and generic abstractions are useful for a wide variety of problem-solving instances, including scientific discovery.

Davies, J., Nersessian, N. J., & Goel, A. K. http://www.cc.gatech.edu/~jimmyd/research/visual-analogy/ May 2001

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Thank You

• http://www.cc.gatech.edu/~jimmyd/research /visual-analogy/