Verfiying Wargame Models

I think I have written sufficient so far so as to suggest, quite strongly that a wargame is a collection of models which all, more or less, fit together to produce something approximating to a real, historical, human situation, a battle. Now, of course, we are aware of the limitations associated with the modelling of a battle. While the models, for example, might acknowledge the flow of human emotions that exist within a battle, through the morale rules, they do not attempt to actually portray these directly, but merely to suggest them through abstract and collectively applied rules.

Modern day models are found, most frequently, in the sciences, and so it might be a useful tack to try to identify the sorts of things models are used for, and the sorts of limitations we find with them. Here, however, is the first of the warnings which must be placed in front of this exercise. Science is often flagged as being the exemplar of truth in our current culture and society. Whole fields of human activity, such as sociology and economics, attempt to grab the ‘science’ label, to give a fig leaf of respectability to what is, in the case of economics, at least, usually a waffle of unverifiable opinion. Anyone who disagrees can point to three examples of independent economic forecasts which have been right in the last ten years or so.

Caveat at the ready, the way science proceeds is to take a set of observations and attempt to understand them. However, as with a historical battle, the real physical world is a complex sort of place and does not easily lend itself to being understood in any reasonable, intelligible and predictable manner. I do not mean here, of course, the normal world humanity moves in, although that is a lot more complex and difficult than we usually give it credit for. What I do mean is, in physics, the scale of the very small or the very large, the very fast or the very slow. As a colleague of mine once remarked ‘If in quantum mechanics you get a counter-intuitive answer, it is probably right.’

However, as scientists we still want to understand and predict the sorts of things that might happen. Thus, we need to construct a model and the model we construct has to have, broadly speaking, two criteria. Firstly, it must be intelligible. A model which is not intelligible is not going to help. Secondly, the model must bear some resemblance to reality, hopefully in ways we can at least be aware of or, better, be able to define.

As an example, consider spectral line broadening in the solar spectrum. We know that the normal spectral lines of hydrogen are to be found – the Ryman, Balmer series, and so on. But we also find that they are broadened out, are wider than we would expect from the Bohr model of the atom (which has them as spikes) or from the Doppler effect. So we try to model, mathematically, what is going on.

To this end we can write down the Schrödinger equation for an atom in a fluctuating electric field, for that is what the environment of an atom in the sun is. And we can also write down an equation for the distribution of energy of the electrons passing by which set up part of the electric field, and another for the much slower moving ions which add extra electric field. But there we stop.

There is a joke in the physics community: in classical mechanics you cannot solve the three body problem, in quantum mechanics you cannot solve the two body problem, in quantum field theory you cannot solve the one body problem and in quantum chromodynamics you cannot solve the vacuum. And we have hit precisely the second issue here; we cannot solve Schrodinger’s equation for the situation we have at hand.

The way this problem is tackled is to make approximations. We can approximate the ion electric field as something that is static, while we calculate the effects of the electrons, and then we can calculate the averaged values of the ion fields over all the possible configurations of ions and then we can (effectively) add the two lots up. Admittedly, this is a lot more complex than it sounds (a proper explanation takes a decent sized text book) but it can be done.

However, we now need to verify our models, and so it is back to the experimental apparatus to check that our calculations, with our approximations, are correct, and, if they are not correct, by how much and in what way they are incorrect. For example, even by my simple explanation above, you might have thought ‘what if the ions are not that static?’ and, indeed, that is a good point, which has to be addressed by an extension to the model called ion dynamics. The point is that the whole model complex has to be verified by contact with the real world and, occasionally, the fit is not that good and further work is entailed.

So, the analogy with a wargame should be obvious. A set of wargame rules and other models should be capable of being verified against real world activity. A French column advancing against a British battalion in line should, on the whole, be forced to stop and be driven off by a bayonet charge. If it is not, then perhaps the model needs tweaking.

Of course, in the real world both the scientific process and the wargaming one I have described is unattainable. Experimental difficulties abound, as do questions of the interpretation of historical events. But the process, while hard, is not impossible; however, the temptation is to take short cuts.

Finally, a scientific model usually asks further questions. I hinted at one above – what if the ions are not static? What happens in this case, or at that limit which we excluded from our model because we could not incorporate it? Most wargame rules that I have seen in use, however, are treated as some sort of holy grail, some untouchable mechanism. I know there are notable counter examples, but do you think that on the whole we treat rules with too much respect?