We distinguish diagrammatic from sentential paper-and-pencil representations
of information by developing alternative models of information-processing
systems that are informationally equivalent and that can be characterized
as sentential or diagrammatic. Sentential representations are sequential,
like the propositions in a text. Diagrammatic representations are
indexed by location in a plane. Diagrammatic representations also
typically display information that is only implicit in sentential
representations and that therefore has to be computed, sometimes
at great cost, to make it explicit for use. We then contrast the
computational efficiency of these representations for solving several
illustrative problems in mathematics and physics. When two representations
are informationally equivalent, their computational efficiency depends
on the information-processing operators that act on them. Two sets
of operators may differ in their capabilities for recognizing patterns,
in the inferences they can carry out directly, and in their control
strategies (in particular, the control of search). Diagrammatic and
sentential representations support operators that differ in all of
these respects. Operators working on one representation may recognize
features readily or make inferences directly that are difficult to
realize in the other representation. Most important, however, are
differences in the efficiency of search for information and in the
explicitness of information. In the representations we call diagrammatic,
information is organized by location, and often much of the information
needed to make an inference is present and explicit at a single location.
In addition, cues to the next logical step in the problem may be
present at an adjacent location. Therefore problem solving can proceed
through a smooth traversal of the diagram, and may require very little
search or computation of elements that had been implicit.
%0 Journal Article
%1 LaSi87a
%A Larkin, Jill H.
%A Simon, Herbert A.
%D 1987
%J Cognitive Science
%K DISS mf modelling toscan
%N 1
%P 65--100
%T Why a Diagram is (Sometimes) Worth Ten Thousand Words
%U http://www.sciencedirect.com/science/article/B6W48-4FW6JX3-4/2/9f39ec088401118e1fff1f847412dbe0
%V 11
%X We distinguish diagrammatic from sentential paper-and-pencil representations
of information by developing alternative models of information-processing
systems that are informationally equivalent and that can be characterized
as sentential or diagrammatic. Sentential representations are sequential,
like the propositions in a text. Diagrammatic representations are
indexed by location in a plane. Diagrammatic representations also
typically display information that is only implicit in sentential
representations and that therefore has to be computed, sometimes
at great cost, to make it explicit for use. We then contrast the
computational efficiency of these representations for solving several
illustrative problems in mathematics and physics. When two representations
are informationally equivalent, their computational efficiency depends
on the information-processing operators that act on them. Two sets
of operators may differ in their capabilities for recognizing patterns,
in the inferences they can carry out directly, and in their control
strategies (in particular, the control of search). Diagrammatic and
sentential representations support operators that differ in all of
these respects. Operators working on one representation may recognize
features readily or make inferences directly that are difficult to
realize in the other representation. Most important, however, are
differences in the efficiency of search for information and in the
explicitness of information. In the representations we call diagrammatic,
information is organized by location, and often much of the information
needed to make an inference is present and explicit at a single location.
In addition, cues to the next logical step in the problem may be
present at an adjacent location. Therefore problem solving can proceed
through a smooth traversal of the diagram, and may require very little
search or computation of elements that had been implicit.
@article{LaSi87a,
abstract = {We distinguish diagrammatic from sentential paper-and-pencil representations
of information by developing alternative models of information-processing
systems that are informationally equivalent and that can be characterized
as sentential or diagrammatic. Sentential representations are sequential,
like the propositions in a text. Diagrammatic representations are
indexed by location in a plane. Diagrammatic representations also
typically display information that is only implicit in sentential
representations and that therefore has to be computed, sometimes
at great cost, to make it explicit for use. We then contrast the
computational efficiency of these representations for solving several
illustrative problems in mathematics and physics. When two representations
are informationally equivalent, their computational efficiency depends
on the information-processing operators that act on them. Two sets
of operators may differ in their capabilities for recognizing patterns,
in the inferences they can carry out directly, and in their control
strategies (in particular, the control of search). Diagrammatic and
sentential representations support operators that differ in all of
these respects. Operators working on one representation may recognize
features readily or make inferences directly that are difficult to
realize in the other representation. Most important, however, are
differences in the efficiency of search for information and in the
explicitness of information. In the representations we call diagrammatic,
information is organized by location, and often much of the information
needed to make an inference is present and explicit at a single location.
In addition, cues to the next logical step in the problem may be
present at an adjacent location. Therefore problem solving can proceed
through a smooth traversal of the diagram, and may require very little
search or computation of elements that had been implicit.},
added-at = {2008-01-04T16:59:10.000+0100},
author = {Larkin, Jill H. and Simon, Herbert A.},
biburl = {https://www.bibsonomy.org/bibtex/25cf00b631719badf1339596af8dace44/michael},
citeulike-article-id = {382002},
description = {Citeulike 06/22/07},
interhash = {0cdf89e38b0bfc129df03d1f4d9999be},
intrahash = {5cf00b631719badf1339596af8dace44},
journal = {Cognitive Science},
keywords = {DISS mf modelling toscan},
number = 1,
pages = {65--100},
priority = {0},
timestamp = {2008-08-13T12:01:16.000+0200},
title = {Why a Diagram is (Sometimes) Worth Ten Thousand Words},
url = {http://www.sciencedirect.com/science/article/B6W48-4FW6JX3-4/2/9f39ec088401118e1fff1f847412dbe0},
volume = 11,
year = 1987
}