If a system is to be stable the number of states of its control mechanism must be greater than or equal to the number of states in the system being controlled.
In trying to understand what is happening around us we are faced with a fundamental problem. In approaching any situation, the system trying to understand it, does not attempt to gather all information. Instead it selects certain facts and searchers for others.
This selection of some items and ignoring of others is a process of abstraction.
It is the abstracting form a real or if you will empirical situation the things seemingly most important to deal with.
In this process of abstraction and model building we deliberately select a few items, ignore may others, and then place the items chosen in a particular relationship to one another.
In doing so we are intentionally ignoring facts or relationships that can influence the type of situation under study.
The problem it to select the most meaningful elements and relationships and dropout the rest.
Those who use abstraction skillfully know well that they neither have all the facts nor have considered all the relationships bearing on the outcome of what they are analysing.
We do not use the abstractions from one situation in another setting without carefully examining the fit. Neither do we expect a model to handle all aspects of a situation.
We shall be dealing with many abstractions and models, not with the intention of exactly mirroring the real world but with the objective of clarifying our perception of its most essential features.
Abstractions and models are mechanisms for economizing both time and effort, but like any tool they must be used within their limits.
Model your goals
Taking the abstracted elements, a character with the flat tire begins to connect them into a pattern.
Better yet, he weaves them into a model of the confronting situation, which we can use both to understand his plight and figure out what to do about it.
The parts of this model would probably include, among other things, the flat tire, the image of the spare in the trunk, the telephone, the service station, a forthcoming business meting, etc.
A second model would contain the telephone, the service station, and the repairman there.
Finally, he concludes that he will call a cab and leave his wife to deal with the flat tire as best as she can.
These are extraordinarily elementary models, but they serve a very practical purpose.
With them the main character in our illustration can see the likely consequences of various courses of action.
We can find out these things by doing them directly by actually handling the tire and observing that we get dirty, or by calling the repairmen and waiting for him and learning that it takes too long.
In the age of big data; information models are good.
- For any given size of data, the bigger the model, the better it generalizes, provided you regularize well.
- This is obviously true if your model is an ensemble of smaller models.
- Adding extra models to the ensemble always helps.
- It is a good idea to try to make the data look small by using a big model.
By using the model, however, we can make some reasonable predictions about what will occur and thereby accept or reject the choices open to us.
Several references have been made with the intent of this guide to provide conceptual tools for analysis. As with any other tool models, abstractions and generalizations are useful only when within their limitations.