FindingKillerWords: PatternLanguage

"About Patterns and pattern languages" (for mathematicians):

A pattern language is a consistent set of patterns. In the making a pattern language starts as an informal collection.
A pattern is a 2-tuple (pattern name, pattern description) that describes an optional transformation of a system. One can think of this as a constituent of meaning or a module of knowledge. Often a pattern is a solution to a problem. Often a pattern corresponds to a physical object.
The description of a pattern may include the use of other pattern names. There is no guarantee that the graph of usage of pattern names is connected or acyclic.
The state of the system is evaluated or monitored by some means to allow for the concept of improvement of the system. Unfolding, or designing a system means to improve the system relative to that measure.
A sequence of transformations describes the process and so the unfolding of the system. This is considered a creative process, or a design process. The system is thought to unfold step-by-step, transformation by transformation.
The process of unfolding is understandable and rational but it doesn't need to be strictly causal, deterministic or predictable. Some typical examples are the game of chess, or the building of architecture. With masters you get great results, but typically this is an open, unpredictable, individual process. Seeking a solution or proof of specific quality, there may be more than one way to do it.
A pattern language is consistent when:
- its patterns refer to the same system or design situation
- when the given set of patterns is sufficiently complete for a large variety of design processes.
- when the natural language used for the pattern descriptions is consistent in its words and concepts.
- when the pattern description is formally complete. The formal requirements depend on the system and the field of application. (this is often structured like a database record containing 5-10 specific fields)
There are guiding heuristics that have been found by comparing systems of architecture and nature:
- regarding the abstract geometrical structures of systems. They are called structure properties. (15, given elsewhere)
- regarding the process. They can be called process principles. (about 10, given elsewhere)
The overall system of concepts can be called "pattern theory". Pattern theory can be considered universal in a tautological sense: any meaning can be brought into pattern form, any system can be seen as abstract structure, abstract process and abstract development using the pattern formalism.

Additional considerations and information:

The originator of pattern theory (though not in this formal sense, although he doesn't use the term) is the architect-mathematician-philosopher Christopher Alexander. He wrote the influential and name-giving book "A Pattern Language", and a dozen other books in this field, primarily from the perspective of architecture. He is the prime source for insight and inspiration.

Pattern theory can be seen as an abstract system theory, specialized on non-deterministic systems: of life, of games, of design situations, of complex systems like ecologies or societies, of pedagogical and therapeutical scenarios.

There are potential conflicts zones (1) towards artists (it removes some myths around the creative process, makes it more rational), (2) towards architects (it changes their role toward more transparency and participation) and (3) in a competitive situation towards some sciences (that try to use deterministic theories for non-deterministic systems with disappointing results).

A pattern language is a tool for analysis and reuse, typically in a collaborative setting. It is "by construction" open for extension. One can always add new patterns (solutions, transformations) to a pattern language without breaking it. Patterns present themselves as options to the designer, he has to choose based on his judgement, he can always ignore a pattern. It is in his interest to make the best possible decisions, if he has to live with the results.

The term "pattern theory" comes from the German book "Mustertheorie" (translated title: "pattern theory"). It seems the logical naming to an immense theoretical field, that has certain problems to put its findings into language (Alexander labels his central quality "quality without a name", he labels his 4-volume closing book-series "the nature of order", both labels seem to lack intuitive meaning).

The relationship of (Christopher Alexander, architecture, us) is isomorphic to (Charles Darwin, biology, us). Christopher Alexander is a cognitive genius that gave a tremendous present to mankind.