Why a Diagram is Sometimes worth Ten Thousand Words

1
Why a Diagram is (Sometimes) worth Ten Thousand
Words
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Information on the authors

• Jill H. Larkin
• Former Faculty at the department of Psychology at
  CMU (cannot find her listed any more)
• Harvard Alumni 1965.
• Herbert A. Simon(1916-2001)
• Late Professor at CMU.
• Nobel prize winner in Economics in 1978 with his
  decision making theory.
• One of the founders of AI and the idea that
  computers can be made to mirror human thinking.
• Research mainly in modeling and simulation of
  human cognition.

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What this paper is about

• This paper aims to compare and contrast the
  computational efficiency of two representations
  for solving problems
• The two representations are
• Sentential
• Similar to propositions in a text
• Diagrammatic
• Indexed by locations in a plane

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Sentential and Diagrammatic representations

• In a sentential representation, each expression
  is in a formal language and derives directly from
  the corresponding statement in the natural
  language.
• In an diagrammatic representation, each
  expression has a similarly appropriate one to one
  correspondence to the components of the diagram
  describing the problem.
• Each expression stores information about a locus
  and adjacent loci.

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Informational and Computational Efficiency

• They are distinct (Simon 1978)
• Information Equivalence of representations
• If all information in one is also inferable from
  other
• Computational equivalence of representation
• They need to have information equivalence
• Any inference that can be drawn from one can be
  drawn from the other.

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What are representations

• They are a combination of data structures and
  programs operating on them to produce new
  inferences
• Computational Efficiency of a representation
  depends on 3 factors
• Data structure
• Program
• Attention Management

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Data Structure

• They are node-link structures that include
  schemas employing attribute-value pairs
• Also called list structures

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Programs

• Program operating on data structure produces
  three kinds of processes
• Search
• Operates on the data structures to locate
  elements satisfying one or more production
  conditions.
• Recognition
• Matches conditional elements of a production to
  data elements located through the search.
• Inference
• Executes the associated action to add new
  inferred elements to the data structure.

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Search

• In a sentential data structure, search times vary
  greatly by the size of the data structure.
• In a diagrammatic data structure, search is
  mostly confined with a limited location(which had
  been satisfied by the inference rule)
• Hence a diagrammatic data structure is much more
  search efficient.

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Recognition

• Strongly affected by explicit and implicit
  information.
• The more explicit the information can be made,
  the better the recognition.
• Diagram based representations can hold much
  explicit information as compared to sentential
  based representations.
• This is why sentential-based inference requires
  substantial computation as compared to diagram
  based inference.

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Recognition(contd.)

• Recognition is dependent on how well the
  representation corresponds to existing
  productions.
• If the current representation of a situation does
  not match existing productions well, then the
  cost of recognition increases because we are
  unable to retrieve it from long term memory due
  to the unfamiliarity.

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Inference

• Differential effects of the two types of
  representation on inference is much weaker (in
  comparison to search and recognition).
• Inference is largely independent of the
  representation if the information content of the
  inference rules are same.
• But inference rules can be made stronger or
  weaker, independent of the representation and
  this would affect inference costs.

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Demonstrating the difference the Pulley problem

• Sentential representation
• Verbal description in natural language
• Produce data structure from the description.
• Program based on physics concepts acts on the
  data structure to solve the problem.
• This program is composed of the inference rules
  that will act on the data structure to solve the
  problem.
• Psychological complexity due to repeated need for
  cross referencing values and original elements
  (sentences) from the data structure.
• Total search elements 138
• Change of attention becomes a big problem due to
  the cross referencing and hence costs are high
  for the 138 element search.

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The pulley problem(contd.)

• Diagrammatic
• Translate sentential data structure into diagram
• Use the same program based on physics concepts.
• Labels in sentinel data structure replaced by
  locations.
• Change of attention is much easy here, as it is
  always confined only to an adjacent location.
• Hence much more computationally efficient.

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Computational power of inference rules

• Powerful inference rules will contain information
  that is specific to a particular task domain

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The geometry example

• Sentinel representation
• Verbal description
• Formalized into data structure and production
  rules
• Developed perceptually enhanced data structure
  from the original one by the help of perceptual
  production rules.
• Four inference rules applied to the enhanced data
  structure to solve.

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The geometry problem(contd.)

• Large search costs for matching conditions.
• Large recognition costs for recognition of
  conditions for an inference rule.

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The geometry problem(contd.)

• Diagrammatic representation
• Perceptual enhancements done very cheaply as
  compared to sentinel representation(just the
  drawing and viewing of the diagram)
• Hence recognition is much easier as it is
  automatic and easy(as opposed to being extensive
  for sentinel representation)
• Search is also much more efficient due to the
  localization of information.

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Summarizing the difference

• Diagrams are more efficient.
• Diagrammatic representations produce perceptual
  enhancements with little effort.
• A diagram produces all elements for free.
• Labels for object not required in diagrammatic
  representations. This was a considerable saving.
• However, including more powerful rules would
  increase the efficiency of both sentinel and
  diagrammatic representations.

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Conclusion

• Other examples (e.g. graphs in Economics and free
  body diagrams in Physics) show ready perceptual
  enhancement.
• Diagrams enable people to detect localized cues
  and hence enables problem solving.
• Authors say that mental imagery might also
  exhibit same properties of localization of
  information.
• This comparison of paper versus memory imagery is
  difficult and has not been empirically tested
  yet, but can be an important direction of future
  research.