Sequence theory

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Sequence theory is the study of conceptual sequences, representing unfolding steps of a sequence like a recipe or an algorithm. A successful sequence is one which is backtrack-free.

Contents 1 History 2 Explanation 3 Successful sequences 4 Generative sequences 5 Examples 6 See also 7 Other sequence theories 8 References 9 External links

[edit] History

Sequence theory is related to various fields within mathematics and philosophy. One of the foremost proponents is Christopher Alexander who has studied the field of pattern languages and sequence theory resulting in numerous published works and books. He calls a generative sequence conceptually equal to a second generation pattern language.

[edit] Explanation

A successful sequence is a sequence which allows unfolding, and works as expected. Within a conceptual context or problem domain, the power set of sequences (i.e possible sequences) is much larger than the number of successful sequences. This ordinal is relative to the complexity of the task or 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 percentage considering the large number of 50! - which is almost unimaginable large. Trying to find all successful sequences would seriously question one's self-efficacy.

[edit] Successful sequences

Defining precisely in terms of mathematics which sequences are successful is not yet known to be possible. Using heuristics the sequences can be identified by using the following algorithm:

Observing the invocational unfolding of steps from a sequence to a conceptual context , one can detect if the process generated by the unfolding contradicts itself at any time. If backtracking is 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 method e.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 property of 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 efficacy of the sequence when the number of steps is moderately large, but consider statistics.

Looking for more than one successful sequence questions decision theory and rational ignorance for costs.

[edit] 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 a metalanguage of sorts. This becomes clearer considering pattern language as the instructional steps in a recipe or an algorithm, while the generative sequence is the process of producing such a successful sequence.

[edit] Examples

A successful generative sequence is e.g the Wikipedia, allowing Internet users to find and augment information or knowledge.

Business models and software patterns are other examples, as well as being part of a pattern language for the specific problem domain.

[edit] See also

pattern language best practice design pattern problem solving decision theory heuristics complexity

order theory sequence (mathematics) number theory generator iteration (similar to unfolding) recursion

infinity huge cardinal unfoldable cardinal

domain theory informatics formal languages generative grammars generative linguistics

Note the general applicability of sequence theory to many varying tasks.

[edit] Other sequence theories

• Variational sequence theory which is a field within differential geometry and topology - see also 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 in kinship structure of kinship systems and family types or clustering in social structures.

• Exit order sequence theory of face milling and formation mechanisms.

• Similar sequence theory of children's development.

[edit] References

[edit] External links

• Recipes and unfolding on patternlanguage.com - founded by Christopher Alexander et al.
• Informal introduction to sequence theory and unfolding on patternlanguage.com .
• What makes a good pattern language?, 2002, Ali Arsanjani on analysis of pattern languages.