I enjoyed reading this paper today by Ronald Giere called "Representing with Physical Models".
Its an interesting thought that one can consider a graph or other representation of data like a 3-d image as a model in a similar sense that one has legos for a model car, or lincoln logs for a model house.
In the process of working through some problem, I often want feedback at an early stage, and so I produce some kind of plot that may partially get at what I want to say, or where I want to go, and I show it to a supervisor, or someone else. Its always an interesting process to have someone else look at your plot and take it as it is. For me, it is a termporary representation of some data I've been playing around with, but for someone else, it becomes an object contained within itself. They look at its boundary, ask about its imperfections, and describe the picture that it paints.
In the article, Giere describes representation via theoretical, physical, and computational models. His example of a theoretical model is a harmonic oscillator, his physical model example is Watson and Crick's colored balls representing DNA, and for a computational model, it is a 3-D image picture of a protein based on theoretical calculations and some protein data. He wants to say that these are all basically doing the same thing. That together with a person to do the interpreting, each of these can be acted on in various ways to learn something about the real system.
I guess this makes some sense to me. The nice thing about a toy model of something is you can play with it, get some feeling for it. You know harmonic oscillators have a fixed frequency, you can picture them oscillating in your mind, and you can even imagine the force they push against you as you try to compress the spring. Similarly with the real balls representing DNA and the 3-D image, you can play with them and relate them to things you know in the world. So with a plot you produce. Its limits and its potentialities may come alive in the viewers mind. It doesn't tell all, but it gives something concrete to hang on to to start building a picture of a given something or other you're trying to understand.
In my last post I said that physics gives us a bunch of models which have been used to describe electron storage rings (the example I focus on because I work on this, and want to clarify certain messy aspects of it). I think maybe some of the difficulty in this field is that computational approaches were developed, but somehow the last step of using them to make models didn't happen so well. One has a picture of a map with a resonance, but there's no good software to really turn this into a model where one can play with it and get a feel for it. (I suppose frequency map analysis software may qualify in this sense. One gets colorful pictures in which the resonances show up in the tune diagrams.) The concepts are there, and the software has been written (e.g. FPP) but not many people know how to use it, or how it relates to the phenomena of storage ring maps. In this context, model has usually meant the elements going into the computer code, and I suppose that's the theoretical model. But with the incoming model being very complex (so its hard to play around with in one's mind), and the software not being easy to use and visualize and relate to familiar things, one is left without good conceptual tools to understand some of these phenomena.