A discursive look at Napoleonic & ECW wargaming, plus a load of old Hooptedoodle on this & that

Wednesday, 4 May 2011

Compromise in Wargames - Adventures in Space, Time and Probability

This post is the preface to what, with a bit of luck, should turn out be a trilogy.

I did consider doing another off-topic post - I am about to defragment the hard drives on my main computer, so I could talk you through that, or I could describe some problems I've been having with my truck, which might be more exciting. On balance, I thought it was probably time to do something a bit more relevant to wargames, so I'm going to attempt to organise some rambling thoughts into proper, joined-up ideas. If they end up still looking like rambling thoughts then you may imagine their state when they started out.

In recent weeks there have been some good-going comments here on the subject of realism in wargames, and I thought that might still be worth some more attention. So I had a go at standing back a little and focusing on what the problems are, and how we got here. It seems to be much easier to detect that something is wrong than to identify just what it is, or why.

For as long as I can remember, I have been fascinated by the challenge of playing and devising games (especially sports games) which simulate reality - originally with matchboxes and dice and bits of string, later with mathematical models running on computers. The most obvious, most definite thing I have learned is that there are very clear limits to how closely you can make a game reflect the real world - you always end up making compromises. One of the challenges is to identify where the compromises are necessary - your game, after all, has to be capable of being played, yet the experience is going to be impaired - the game may even be pointless - if the results are blatantly silly. I also learned that the more you change the scale of the thing, the more carefully you have to look at this area.

This scaling problem crops up in all sorts of places. I remember, when I was about 7, watching some epic British film about a disaster at sea, and realising that something wasn't quite right. In the action scenes, a brilliantly executed miniature ship would be wreathed in fake mist and cleverly lit, and in a still photo it would have looked brilliant, but in a movie it didn't work. It was something about the appearance and the behaviour of the water - any fool could tell that this was a toy boat in someone's bathtub, even though we might be pushed to explain just what was wrong. The problem, of course, is that mucking around with the scale of something, reducing it to a miniature version of itself, for example, introduces some nippy little paradoxes. If you reduce the size, you may have to do some other things as well - in the case of the sinking ship, slowing the film down might have helped the little waves look more convincing. As soon as you start reproducing space and time (and a cinema film gets you into time issues), modelling and simulation have to be thought through. I admit I may have been a rather odd child.

Later on - I'm 12 and I'm back at the movies. I took some comfort from the fact that the monster spider in some horror show of the day was impossible. OK - the story was clearly fantasy anyway - even to a child - but I knew that mathematically the thing couldn't exist. The back-projected, blown-up footage of a normal-sized spider which obviously terrified the cast would not be able to move if it were real. This is school maths, it may even be primary school maths nowadays, and I apologise for setting out what is well known and otherwise obvious: if you multiply the linear dimensions of a spider by a factor of, say, a hundred, so that a 1-inch spider is now 8-feet-something across (which is, I admit, a horrifying idea), then - if everything remains in exact proportion - its weight will go up by a factor of one million, but the structural strength of its legs (for example) will go up by only ten thousand times, since this must be related to the cross-sectional area of the components in its legs. So the load on its legs, proportionally, will be a hundred times as great as the original. Its legs could not bear its weight. OK - this does not mean that you cannot have a spider which is 8 feet across (in theory), but it does mean that such a spider would not look like a big version of a small one. This is why elephants do not look like ants.

If you are nervously looking for a means of escape as you wait for a point of some sort to emerge from this - here is the point: changing the scale of something will change its properties and its behaviour unless you do some other stuff as well. I'd like to have a look at a number of aspects of this in the context of wargames - Space (size, ground scale), Time (converting a continuous action into a series of jerky moves - maybe even alternate moves) and Probability (the use of numerical data to produce a "realistic" game). These things are not entirely independent, but it suits me to divide the subject into parts, so I'll address it under these three headings.

Accordingly, the first instalment will be about Space...


  1. This reminds me of a project we once did for a civil engineering class I once took (long time ago ...) about fluid simulations. In order to study the effects of the tides on a port estuary, the whole port (including channels, rivers, etc.) was built to scale. So, distance was scales, and time as well to run 10 years worth of real time into a simulation of let's say an hour.

    As students, we expected the professor would just open the valve, let the water in, and we would all see what was going to happen. But no water came out, but some other fluid I can't remember. It turned out that, in order to scale the whole simulation down, we also needed to change the viscosity of the fluid - specifically to dampen the effect of waves ( so it relates to your boat example as well ...).

    Although I don't remember the exact differential equations that explained it all, it's one aspect I always remembered about running scaled down simulations: unexpected properties have to be changed as well, in order to maintain the predictability of the whole simulation.

  2. But wait, haven't you forgot that whatever weird event caused the spider to expand also changed the molecular structure of its muscles and tendons etc making them 100 times stronger than...... yeah perhaps not.

    I'm looking forward to the rest of this.

  3. Sounds interesting looking forward to your ideas .

  4. Changing time--I was four, sneaking a peek after my bedtime, when my uncle was watching the movie THEM, with the Giant Ants--and it scared the bejeesus out of me to see those jaws.

    Only in 8th grade was I able to consider 'them' scientifically, after that. Still like ants.

  5. What Phil says is the result of the "Buckingham theorem" or "pi-theorem". It basically says that if you have a mathematical model, all the dimensional quantities must be rendered adimensional by scaling them with respect to characteristic Length, Masse, Time or some combination of them.
    This allow to remove from the model the scale effects. Moreover it tells you that if you scale a quantity in your problem (say length 1:10) you must scale also the other quantities, the ratio between the length scaling and their sacling given by the problem equations (which indeed express the relation between quantities in the mathematical model you have to describe a phenomena).
    This is the reason why you can't have two-floor high ants and why you use gels in place of water in hydraulic experiments.
    In our wargaming world this means that to scale lenght, times and number of models independently introduces a distortion with respect "reality". What we need is a model of "reality" to use the "B. theorem", and this is the classical "can of worms".

    All the best

  6. Thanks for comments, gentlemen. Fabrizio - thanks for this - I am not familiar with Buckingham's Theorem, but have done dimensional analysis using (I think) Rayleigh's equations, which was a great technique for building formulae when you didn't know them!

    No-one can say this blog is lacking in educational value - well, maybe.

    Ross - I'm glad you were not around at the time to destroy my spider theory - I'd have been even more terrified!


  7. Since in wargaming many effects are dependent on time, which we assumes scales linearly w.r.t. distance etc., applying Buckingham's theorem to wargaming models is probably overkill? But it would be a nice exercise ...