Mathematical Model

In design&sbquo "model" not only refers to the concept of standard and example&sbquo it also means an existing sample or ideal copy of design. The reason I am including "mathematical model" as design terminology is to broach the theme of whether mathematical thinking&sbquo methods&sbquo and logic are really effective in design. I believe there are at least three aspects to thinking in design: 1) The conceptual stage n which the concept is formed&sbquo 2) the expressive stage in which the result of design is presented through modeling and&sbquo 3) evaluation of the result. These three aspects can be contraposed to the structuring of mathematical models&sbquo and similar aspects that correspond to these are seen in mathematical model. The following applies to mathematical models. 1) Establishing the model: corresponding to the phenomenon or issue in question&sbquo establish a standardized formula (with a certain set of assumptions) for a primitive concept that cannot be defined mathematically. This is exactly equivalent to hypothesizing concept as a design theme. 2) Analyzing the model: relevancy to the process and context of essential problem solving is abandoned for the time being by inferring a logical conclusion from a mathematical axiomatic system. This is equivalent to placing importance on the design expression and considering only the logic inferred from the relationship between concept and expression as expressive intent. 3) Applying the model: set up a parameter for applying the abstract concept to a concrete&sbquo factual prediction based on experience&sbquo and verify it. This is consistent with predicting&sbquo verifying and assessing the actual environment in which the model (which is a result of design) would exist&sbquo and using it as a logical endorsement in appealing to the value of design. As can be seen from the above contraposition and correspondence&sbquo the application of mathematical models in design is an effective method. It will be vital to associate design with such mathematical models as probability&sbquo graph theory&sbquo fuzzy theory&sbquo game theory&sbquo topology and catastrophe theory. This is in order to derive a method that will define design evaluations (made through our sensibilities) and the logic (engineered through our sensibilities) used in the design processes&sbquo and to establish such logic.

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