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All methods for modelling reality rely on a basic idea, that the information in your model represents some aspect of reality, and your model should reflect the constraints that apply to it. This is called the knowledge representation hypothesis. They also rely on the idea that you can model the important parts of the system with something simpler than the system itself. This is the idea of algorithmic compression.
When using any form of modelling, you will go through a cycle of steps which will gradually bring your model sufficiently close to the parts of reality that you are trying to model so that you get useful answers to the questions that you ask it.
The modelling cycle is as follows:
1. Specify the real problem. This involves knowing why you want to make the model.
2. Set up the model. This involves listing all of the assumptions involved in building the model, which is done by the following method:
2.1 Choose the relevant variables.
2.2 Make the simplest realistic assumptions.
2.3 Specify the limitations of the model.
3. Formulate the mathematical problem.
4. Solve the mathematical problem
5. Interpret the solution.
6. Compare with reality.
7. Use the results.
8. Go around again until you have a good enough agreement with reality to be useful.
Science is the search for relationships between variables, and the methods of modelling are fundamental to science. Some good examples of non-mathematical modelling involve the use of stories as history, and as you will see, the methods are very similar when using any type of modelling.
One method of documenting a model that is worth looking at is Data Flow Diagrams.
Here are some other facts that need fitting in, and which apply mainly to mathematical modelling, but which I have not yet had time to figure out how to do it.
By looking at different measures of the same variable, you can seperate the components.
The similarity between two different measures gives a sensitivity to the variable.
The difference between two different measures gives a sensitivity to other components of the variables measured.
If you use an automatic recorder with a good clock with your sensor then you open up new posibilities.
If you use two readings at the same place but different times, you get the variability with time of the variable.
If you use two readings at different places but the same time, you get the variability with space of the variable.
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