Entry
Problem solving: Overview: Why could knowledge of problem solving techniques be important?
Aug 11th, 2007 07:18
Knud van Eeden, Joe Pike,
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--- Knud van Eeden --- 09 October 2020 - 00:27 am --------------------
Problem solving: Overview: Why could knowledge of problem solving
techniques be important?
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Disciplines like mathematics, physics, chemics, computer science, ...
could from some point of view be seen as bags of tools and the final
historical collection of it to help you solve specific problems.
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Problem solving looks at the general patterns and methods to solve
this problems
in this areas.
So from some point of view this disciplines like mathematics, physics,
chemics,
computer science, ... are but special cases of problem solving.
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So having knowledge of the techniques and methods to solve problems
should in general be important.
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If you should collect all problem patterns, and their different methods
to solve problems, and formalize it further, you could call this the
'theory of problem solving'.
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The laboratory study of problem solving has been supplemented by field
studies of professionals solving real-world problems--for example,
physicians making diagnoses and chess grandmasters analyzing game
positions, and, as noted earlier, even business corporations making
investment decisions. Currently, historical records, including
laboratory notebooks of scientists, are also being used to study
problem-solving processes in scientific discovery. Although such
records are far less "dense" than laboratory protocols, they sometimes
permit the course of discovery to be traced in considerable detail.
Laboratory notebooks of scientists as distinguished as Charles Darwin,
Michael Faraday, Antoine-Laurent Lavoisier, and Hans Krebs have been
used successfully in such research.
From empirical studies, a description can now be given of the
problem-solving process that holds for a rather wide range of
activities. First, problem solving generally proceeds by selective
search through large sets of possibilities, using rules of thumb
(heuristics) to guide the search. Because the possibilities in
realistic problem situations are generally multitudinous,
trial-and-error search would simply not work; the search must be highly
selective. Chess grandmasters seldom examine more than a hundred of the
vast number of possible scenarios that confront them, and similar small
numbers of searches are observed in other kinds of problem-solving
search.
One of the procedures often used to guide search is "hill climbing,"
using some measure of approach to the goal to determine where it is
most profitable to look next. Another, and more powerful, common
procedure is means-ends analysis. In means-ends analysis, the problem
solver compares the present situation with the goal, detects a
difference between them, and then searches memory for actions that are
likely to reduce the difference. Thus, if the difference is a
fifty-mile distance from the goal, the problem solver will retrieve
from memory knowledge about autos, carts, bicycles, and other means of
transport; walking and flying will probably be discarded as
inappropriate for that distance.
The third thing that has been learned about problem solving--especially
when the solver is an expert--is that it relies on large amounts of
information that are stored in memory and that are retrievable whenever
the solver recognizes cues signaling its relevance. Thus, the expert
knowledge of a diagnostician is evoked by the symptoms presented by the
patient; this knowledge leads to the recollection of what additional
information is needed to discriminate among alternative diseases and,
finally, to the diagnosis.
In a few cases, it has been possible to estimate how many patterns an
expert must be able to recognize in order to gain access to the
relevant knowledge stored in memory. A chess master must be able to
recognize about 50,000 different configurations of chess pieces that
occur frequently in the course of chess games. A medical diagnostician
must be able to recognize tens of thousands of configurations of
symptoms; a botanist or zoologist specializing in taxonomy, tens or
hundreds of thousands of features of specimens that define their
species. For comparison, college graduates typically have vocabularies
in their native languages of 50,000 to 200,000 words. (However, these
numbers are very small in comparison with the real-world situations the
expert faces: there are perhaps 10120 branches in the game tree of
chess, a game played with only six kinds of pieces on an 8 x 8 board.)
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[Internet: source: Herbert Simon - http://dieoff.org/page163.htm]
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