I've Been Thinking

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  • 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
    Enterprise Architecture
    Information Systems Architecture

    Systems Thinking
    Soft Systems Methodology (SSM)
    System Dynamics (SD)
    Viable Systems Modelling (VSM)

    Mathematical Modelling
    Black box modelling

    It is very important to make sure that the modelling approach suits two things:
    • What is being modelled
    • The purpose of the model.
    The most important issues in modelling are:
    1. The nature of the entities. This issue is concerned with the preciceness of the definition and meaning of the entities. In physics, for example, it is possible to define physical variables to a very high degree of accuracy. In other areas the entities are very much less well defined. In Information Systems, for example, a person's name is actually very difficult to define precisely. A person can have multiple names, their name can change over time, their name can be the same as someone else's. In economics, entities such as value and Gross Domestic Product are open to dispute and argument. The big danger comes when entities that seem to be the same are compared or aggregated.
    2. The relationships between the entities. Relationships between entities are not always clear. Sometimes there are hidden relationships between entities that destroy assumed independence. Relationships can change depending on the particular magnitude of entities (often dues to the non-linear nature of the real world) and on the phase relationship between entity values as they change over time.
    When the entities are well defined and the relationships are clear and known, then "hard" modelling is both possible and appropriate. Hard, here refers to the certainy and/or unchanging nature of the entities and relationships. Mathematical physics is a form of hard modelling. Stochastic processes, which involve randomness, can also be modelled using "hard" techniques because randomness does not impact the defininitions of the entities or relationships.

    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.

    Bernard Robertson-Dunn
    February 2014