Abstracting Models

I am on record here as claiming that a wargame is a set of interacting models, and I think that this description has some truth to it. We have, after all, a load of scale models in the toy soldiers and terrain. We also have a set of wargame rules of some description or another which, I suggest, are another set of interacting models – models for movement, combat, morale, command and control and so on. These, of course, control the ‘on table’ activities of the scale models.

I think I observed a long time ago that, in fact, on the table, there are multiple scales. We might use, say, 15 mm toy soldiers and 10 mm buildings, while the ground scale might be one inch to a hundred yards (I am making these up). We cope with these scale changes with little apparent cognitive effort, except occasionally arguing that this unit is, or is not, in range because it looks right. I often find myself explaining to some of my students that visualisation makes both understanding and explaining something complex much easier, and I suspect the same might be the case in a wargame.

I have just been reading an article by Nancy Cartwright, who is an empirical philosopher of science whose main claim to fame seems to be a book called ‘How the Laws of Physics Lie’, which, however, I have not read.  The article is

Cartwright, N., 'Do the Laws of Physics State the Facts?', in Curd, M., Cover, J. A. and Pincock, C. (eds.), Philosophy of Science: The Central Issues (New York: W. E. Norton, 2013), 871 - 882.

I tend to think of Curd et al as the ‘Big Blue Book of Philosophy of Science’, and it is an interesting, if weighty, read. Cartwright’s article is reprinted in a section on ‘Laws of Nature’, and basically argues that laws of physics cannot state facts, because, for example, the gravitational law is never a pure law; there are always other bits added in to the real situation. The explanation of a phenomenon is by composition. Thus, in, say, atomic physics, we have a central Coulomb potential which gives an energy level, which is then split by angular momentum. These levels may then be split again by spin-orbit interaction. From our original single level, in the case of the carbon atom and its ground state (Cartwright’s example), we now have five fine structure levels.

Cartwright’s point, it seems to me, is that in real life we never have a single ground level energy state in carbon. It just does not exist. What we do have are five fine structure levels. The ‘laws’ of physics by which we account for them are not ‘real’, in the sense that they cannot be applied directly.

This is, of course, perfectly true, but coming at the issue from a modelling perspective might help a little. Models (such as the Coulomb law) are abstract. They are tools to help us think about the thing modelled. They extract the things we think are important and ignore the things which we believe are minor or irrelevant. This does not mean, incidentally, that the abstracted model is less rich than the original, it is just more tractable.

In physics, we make a model of the central force approximation to the carbon atom. We note with satisfaction that it reflects the gross structure of carbon. This is a first level approximation, and we realise that we can do a bit better, so we add in considerations of angular momentum and obtain three levels. This too reflects the real world, except that we observe (perhaps with a better instrument) the finer structure, which (as it happens) we can also account for. The laws of physics are not lying, particularly. We are simply employing different levels of approximation to obtain different results. Our model, for some purposes, could stop at the first level of approximation. We know there is fine structure, but we might also know that it gets washed out by environmental effects, such as the atom being in a plasma.

OK, you might say, looking at me as if I am turning into a mad professor, what has this to do with wargaming?

The point is surely similar. In a historical account of a battle, we have only the reactions of the participants to go by. ‘Monke’s foot surrendered’ is an outcome, but an outcome of what? We might not know the circumstances of the combat, the reasons why Monke’s men had decided to throw in the towel. We know, because we know a bit about battles generally, that usually factors such as being surrounded, running out of ammunition, not being committed to the cause and so on can result in the outcome we know about. And we can model these factors.

The point here is that we do model the factors, and we split them up into different parts which interact to form the whole. We model morale, and combat outcomes and so on. We add these up, moving the troops on the table to reflect them. We might note from the situation that Monke’s men are surrounded. A quick count up of the factors (part of the model) and a roll of the dice and the historical circumstances of the surrender are achieved. The models combine, in the same way, that gravitational and Coulomb forces can combine, to give an outcome. The abstraction of the models enables the obtaining of the final result.

Of course, in a wargame, there is also a narrative. Stuff happens because other stuff happened first. Monke’s men are surrounded because they crossed the river before the rest of the army was ready, for example. This is not as obviously the case in a carbon atom, as it just ‘is’ what it is. However, the models we apply give us the means by which we can talk about the various levels of structure in the atom, as the wargame rules and models give us a means to discuss the surrender of Monke’s foot.