- Sequence theory
Sequence theory is related to various fields within
mathematicsand philosophy.One of the foremost proponents is Christopher Alexanderwho has studied the field of pattern languages and sequence theory resulting in numerous published works and books. He calls a generative sequenceconceptually equal to a second generation pattern language.
A successful sequence is a sequence which allows
unfolding, and works as expected. Within a conceptual context or problem domain, the power setof sequences (i.e possible sequences) is much larger than the number of successful sequences. This ordinal is relative to the complexityof the taskor problem. The possible sequences of a fixed number of steps is equal to the factorial"n!" if the sequence consists of "n" steps.
* Example::if there were 50 steps involved in a sequence, the different ordering of these steps equals 50! which is an enormously large number of tasks. If only a few thousand of these orderings are successful, they make a very small
percentageconsidering the large number of 50! - which is almost unimaginably large. Trying to find "all successful sequences" would seriously question one's self-efficacy.
Defining precisely in terms of
mathematicswhich sequences are successful is not yet known to be possible.Using heuristicsthe sequences can be identified by using the following algorithm:
invocational unfoldingof steps from a sequence to a conceptual context, one can detect "if" the processgenerated by the unfolding contradicts itself at any time. If backtrackingis needed, at any time, thus forcing the undoing of a previously unfolded or invoked step, the sequence is "not" successful.
::Essentially, a backtracking-free sequence is considered successful.
This algorithm resembles the
trial-and-error methode.g. when experimenting on test cases, and makes it possible to weed out or correct unsuccessful sequences into at least one successful sequence.
Such a sequence also has the objective
propertyof being stable, and once identified this property persists for all contexts. This is a type of extensional definition. Finding one such sequence says little about the efficacyof the sequence when the number of steps is moderately large, but consider statistics.
Looking for more than one successful sequence questions
decision theoryand rational ignorancefor costs.
unfolding generative sequenceis social language itself. It is being used to generate the successful sequences. This reminds us of the role of a metalanguageof sorts.This becomes clearer considering pattern languageas the instructional steps in a recipe or an algorithm, while the generative sequenceis the process of producing such a successful sequence.
generative sequenceis e.g. the Wikipedia, allowing Internetusers to find and augment informationor knowledge. Business models and software patterns are other examples, as well as being part of a pattern languagefor the specific problem domain.
iteration(similar to unfolding)
* generative grammars
generative linguistics"Note the general applicability of sequence theory to many varying tasks."
Other sequence theories
*"Variational sequence theory" which is a field within "
differential geometry and topology" - see also [http://www.emis.de/proceedings/CDGD2000/pdf/K_Krupka.pdf Recent results in variational sequence theory, 2000, D. Krupka and J. Musilova] .
*Geological sequence theory concerning
tectonics, geomorphologyand more - see also "Ancient Environments and the Interpretation of Geologic History, 3rd ed., L. S. Fichter and D. J. Poche, ISBN 0-13-088880-X" .
Main sequence theoryof social change in kinshipstructure of kinship systemsand family typesor clusteringin social structures.
Exit order sequence theoryof face millingand formation mechanisms.
Similar sequence theoryof children's development.
* [http://www.patternlanguage.com/leveltwo/recipes.htm Recipes and unfolding] on patternlanguage.com - founded by
Christopher Alexanderet al.
* [http://www.patternlanguage.com/leveltwo/recipesframe.htm?/leveltwo/../sequencetheory/sequenceopener.htm Informal introduction to sequence theory and unfolding] on patternlanguage.com .
* [http://www.arsanjani.org/pl/Pattern%20Languages%20List.htm What makes a good pattern language?, 2002, Ali Arsanjani] on analysis of pattern languages.
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