Why a Diagram is (Sometimes) worth Ten Thousand Words

Why a Diagram is (Sometimes) worth Ten Thousand Words 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. • 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 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. 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. 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 Data Structure • They are node-link structures that include schemas employing attribute-value pairs • Also called list structures 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. 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. 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. 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”. 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. 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. 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. Computational power of inference rules • Powerful inference rules will contain information that is specific to a particular task domain 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. The geometry problem(contd.) • Large search costs for matching conditions. • Large recognition costs for recognition of conditions for an inference rule. 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”. 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. 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.