One of the joys of having written a set of wargame rules is,
of course, the opportunity for people to criticise them (I may be being a tiny
bit sarcastic, here). Recently, the order mechanics of Polemos: SPQR were
praised by someone, who then went on to say that the combat mechanics were far
too complex because they had 20 factors which needed to be added up.

Now, there are several responses, more or less grumpy, which
I could make to those sorts of comments, along the lines of ‘you might think
this is complex, but look at those rules over there’, or possibly some
insulting reference to the fact that adding and subtracting numbers is not
actually complex per se, and I’m sure that given some thought I could come up
with other, more or less crushing, responses.

On the other hand, I’m not sure that any of these sorts of
responses would help and, after all, my critic did describe the order and
movement rule as elegant (although, of course, someone else described them as a
ponderous game mechanic – I guess you cannot please all the people all the
time).

I have written before about the problems of complexity in
battles, and I think it is generally agreed that a battle is a complex thing
which cannot be handed by probabilistic mathematics, and least within any
reasonable time frame. So I will focus on the other factor that is mentioned in
this context, that of elegance.

Now, in my chequered past, I was a physicist and, as such,
encountered, as regular readers of this blog are probably painfully aware of by
now, mathematical models. The interesting thing about these things, in the
context here, is that some models were described as elegant, and even as a
struggling student with a reasonably low mathematical ability, I could see that
some were, indeed, aesthetically pleasing.

The most obvious place where this occurs in modern physics
is in the theories of quantum mechanics (QM). It is not a widely known fact
that there are three basic approaches to QM. These are the Schrodinger
equation, Heisenberg’s uncertainty principle and Dirac’s spinor.

I will not go into detail, but I will say this. Of the
three, I used Schrodinger’s equation most, because it gave tractable answers
that could be compared with observations (which I what I did as an active
researcher). However, the most elegant of the theories was that of Dirac. I
recall sitting in a tutorial while my tutor expounded Dirac’s theory and came
up, inevitably with a 4 vector (a single column of items, with four entries).
The top two ever electrons, and the question was ‘what are the bottom two?’.

The answer, of course, was “anti-electrons”, and that piece
of work both predicted anti-matter and won Dirac a Nobel prize. But how did
anyone know at the time it was right? Why would anyone go and look for
anti-matter, which is a pretty counter-intuitive sort of thing?

The answer, of course, is in the elegance of the theory.
Nothing is forced; anti-matter arises quite naturally in the mathematics. Dirac
knew it was correct because it was an elegant theory.

Now, of course, we have to let complexity have a bit of a
play. In some senses, particle physics is easy, because the objects at its
heart are simple. Bosons, electrons, leptons and so on are, at core, fairly
simple, (so far as we know) unstructured objects. They are tractable by
mathematics, conceptulisable (if not imaginable) by our minds, and, of course
can be observed (or strictly speaking, their effects can be observed) in the
world.

On the other hand, someone once said ‘Understanding atomic
physics is child’s play compared with understanding child’s play’. Human behaviour,
even in relatively benign environments, is not simple, and cannot be predicted
by mathematics, no matter how elegant.

That being the case, how can a set of wargame rules ever be
described as elegant? Not only are we dealing with humans on mass, under very
stressful circumstances, but we cannot even start a mathematical model of the
environment. There are too many factors to take into account.

Let me take an example, that of DBA. There are 17 basic
troop types, with a factor against foot and one against mounted. There are 6
tactical factors. However, by my counting, there are 78 different combat
outcomes. This is generally accepted to be a fairly elegant example of a set of
wargame rules, but it has to be accepted that the complexity is hidden in the
combat outcomes; as I recall, these are the bits that people find most
confusing.

Secondly, let me have a look at PM: SPQR. There are 11 troop
types, each with 4 factors, and 22 tactical factors (not all of which apply, of
course). However, there are 5 outcomes to combat.

If you add on to this analysis the fact that PM: SPQR has
provision for different grades of troops (so is more like DBM than DBA in this
respect), then, I submit, that it is no more complex than DBA. The difference,
of course, is where the complexity is hidden.

Now, I am not claiming that PM: SPQR is the simplest, most
elegant system that is possible. I do think that some aspects could be tidies
up, but I do claim that, by comparison with a widely used fast play rule set,
it is no more complex. After all, the close combat factors are clearly set out
in two tables, and a little experience means that you can glance at the table
top situation and work out the factors very quickly. In DBA, I’ve never managed
that, I always have to read the outcomes (it helps, I discovered, if you read
them out loud).

So where are we left?

I think the answer is that a battle is inherently complex,
and that complexity has to be represented somewhere. In SPQR it is in the
initial factors, in DBA it is in the combat outcomes. There just does not seem
to be an elegant solution to this, so, to return to my QM analogy, we will just
have to stick with Schrodinger, as Dirac seems to be beyond our reach.