A model is an abstraction ... for a purpose.
There is an intimate relationship between a model and its abstraction.
I think it was Andrew Koenig who said
Abstraction is selective ignorance.
The word 'ignorance' might mislead you here. It doesn't mean ignorance in the sense of an ignorant person - a person who should know something important but doesn't. It means ignorance in the sense of not being aware of something unimportant. The word 'selective' relates to the word 'purpose'. A clear purpose helps you decide what's important and what's not. Things that aren't important can then be omitted. Modelling is primarily an act of omission. The less clarity of purpose in your mind, the less omission is likely to take place, the more the model will try to say, without clarity.
The London underground tube map as a nice example of modelling. The usefulness of the tube map is directly related to the massive amount of omission in it (or should that be not in it?)
- it's not scaled - 5cm on the map does not relate to 5 miles on the ground.
- it's not proportional - stations 8cm apart on the map are not twice as far apart (on the ground) as stations 4cm on the map.
- it's not relative - stations north/south of each other on the map are not necessarily north/south of each other on the ground.
- it doesn't tell you street names.
- it doesn't tell you where the bus stops are.
- the turns in the River Thames are not all 90 degrees or 45 degrees.
- the little nicks on one side of the line don't tell you if the platform will be on the left or right.
Things that a model does say should be said consistently. For example, the station names are all written horizontally, in the same font and style. If some were horizontal, some vertical, some slanted, some in black, some in blue, some large, some small, we might start wonder if the differences were significant. The model would be leading us astray. If the tube map was trying to be geographically accurate some parts of the map would get very squashed. The squashed stations might get a smaller font. And some might be angled into the only available space.
There is also at least one act of addition in the tube map. The lines have different colours. The circle line is yellow for example. Kevlin promises me that the steel tracks on the circle line are not yellow! But then again, perhaps the colour refers to the trains running on the track. Are the trains on the circle line noticeably yellow? If so, which had the yellowness first, the tube lines on the map or the actual trains? Or, over time, have they influenced each other?
It's easy to ignore just how much effort went into figuring out what to remove from the tube map. Wikipedia has a nice entry on how the tube map has changed over time. I remember once reading how Harry Beck spent years working on an early version of the tube map which his supervisor rejected because it needed to contain less.
A powerful abstraction helps you create a model of clarity, but the clarity can easily seduce you - you're not aware of all that has been omitted, and the effort needed to omit it. When you look at the tube map you just see the tube map.