Do not confuse the map with the territory.
[Below is what I wrote in April 2011. I've now created a new website, www.problemsfirst.com, which is where my modelling research is being put]Models are representations of reality, they are not reality itself. They are useful for understanding and for analysis. They can also be used to document existing situations as well as to define future, proposed situations. Mathematics and Physics are just our best attempts at modelling reality..
All models have context and limitations, the danger is in not understanding the limitations or when the model is being taken out of its context.
Modelling is at the heart of problem solving, however the model you make can limit your understanding of the problem and your ability to develop an optimal solution.
There are a number of modelling approaches that can be used when problem solving, depending on the nature of the problem. Modelling approaches include:
Architecture as used in the IT/Business Sytsems world
Information Systems Architecture
Soft Systems Methodology (SSM)
System Dynamics (SD)
Viable Systems Modelling (VSM)
Black box modelling
It is very important to make sure that the modelling approach suits two things:
When entities are poorly defined and relationships uncertain and "fuzzy", then "soft" modelling becomes more appropriate. Soft modelling is more qualitative than quantitative and often involves graphical analysis more than mathematics.
Mathematics is the language which describes the physical world. It is at its most accurate when the entities and relationships are well defined. When Mathematical techniques are used when the entities and relationships are not well defined, there is a risk that the mathematical modelling will provide an understanding comparable with that achieved in the well defined area.
All descriptions of the real world are models. Descriptions include our perceptions of the real world. A description can never be the real thing. Everything we know about the real world is via one or more models.