- Sequence theory
**Sequence theory**is the study ofconcept ualsequence s, representingunfolding steps of asequence like arecipe or analgorithm . A successful sequence is one which is backtrack-free.**History**Sequence theory is related to various fields within

mathematics andphilosophy .One of the foremost proponents isChristopher Alexander who has studied the field ofpattern language s and sequence theory resulting in numerous published works and books. He calls agenerative sequence conceptually equal to a second generationpattern language .**Explanation**A successful sequence is a sequence which allows

unfolding , and works as expected. Within aconcept ual context orproblem domain , thepower set of sequences (i.e possiblesequence s) is much larger than the number of successful sequences. This ordinal is relative to thecomplexity of thetask orproblem . The possible sequences of a fixed number of steps is equal to thefactorial "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

percentage considering the large number of 50! - which is almost unimaginably large. Trying to find "all successful sequences" would seriously question one'sself-efficacy .**uccessful sequences**Defining precisely in terms of

mathematics which sequences are successful is not yet known to be possible.Usingheuristics the sequences can be identified by using the followingalgorithm :::

**Observing the**invocation alunfolding of steps from a sequence to aconcept ual context, one can detect "if" theprocess generated by the unfolding contradicts itself at any time. Ifbacktracking is needed, at any time, thus forcing theundo ing 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 method e.g. when experimenting ontest case s, and makes it possible to weed out or correct unsuccessful sequences into at least one successful sequence.Such a sequence also has the objective

property of beingstable , and once identified this property persists for all contexts. This is a type ofextensional definition . Finding one such sequence says little about theefficacy of the sequence when the number of steps is moderately large, but considerstatistics .Looking for more than one successful sequence questions

decision theory andrational ignorance forcost s.**Generative sequences**One morphologically

unfolding generative sequence is social language itself. It is being used to generate the successful sequences. This reminds us of the role of ametalanguage of sorts.This becomes clearer consideringpattern language as theinstruction al steps in a recipe or an algorithm, while thegenerative sequence is the process of producing such a successful sequence.**Examples**A successful

generative sequence is e.g. theWikipedia , allowingInternet users to find and augmentinformation orknowledge .Business model s andsoftware pattern s are other examples, as well as being part of apattern language for the specificproblem domain .**ee also***

pattern language

*best practice

*design pattern

*problem solving

*decision theory

*heuristic s

*complexity

*order theory

*sequence (mathematics )

*number theory

* generator

*iteration (similar tounfolding )

*recursion

*infinity

*huge cardinal

*unfoldable cardinal

*domain theory

*informatics

*formal language s

* 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 ,geomorphology and 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 theory of social change inkinship structure ofkinship systems andfamily types orclustering insocial structure s.*

Exit order sequence theory offace milling andformation mechanisms .*

Similar sequence theory of children's development.**References****External links*** [

*http://www.patternlanguage.com/leveltwo/recipes.htm Recipes and unfolding*] on patternlanguage.com - founded byChristopher Alexander et 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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