George Box (1919-2013) is certainly on record as having wielded this sage insight more than once, almost fifty years ago. The blow to the gut is usually followed by a hair tussling “but some are useful”. Inspired by Tony Starfield, I feel inclined to rather say that all model worlds are valid, though not all are very useful.

The ‘original’ phrasing by Box has the negative feel of an ‘ah gotcha!’ moment: we lured you in with the promise of enlightenment at the end of the complex plane, but hey – all models are wrong! Had you going there for a moment, eh? You really saw the purity and truth of mathematics for a moment there, then oops. But cheer up, all is not lost – among all these wrong models, like among fools, some have their uses.

Is this some dark insiders joke? Are ‘modellers’ winking at the open secret that their so called expertise is some vacuous drivel? Apparently not. Apparently, it’s all about owning your limitations, and making them your strength. Through modelling, we get to wield our ignorance like armour against making false statements – and we manipulate the non-false statements into insights. Or something like that. All very ‘advanced’, cough cough.

Tony Starfield has inspired a nomenclature, of sorts, or at least a well-defined framework for referring to, and hence distinguishing 1) ‘the real world’ with all its depths and unknowns; 2) some ‘model world’ where a) we set the rules, and therefore know what they are, and b) we have the power to arbitrarily command the model world to appear into any particular state, defined by ‘initial conditions’ for configuration and motion; and 3) model equations which purport to describe some aspect of a model world.

The point of talking this way is very specifically to create a clear distinction between 1) A rich realm where we create rules and situations just as we see fit, and anyone can play, and find insights for themselves and others; and 2) Very specific mathematical analysis or computation, which is a real kind of engineering that requires specific skills.

Plus the real world of course. This ‘three realms’ view of Starfield has many uses. I’m reminded of ‘dimensional analysis’ which is often neglected in many contexts where it could be used to trigger or bolster insights. Both this ‘model world’ thing and dimensional analysis can look like small ideas – dainty steps, afraid of being wrong, saying very little. In fact, both can be endlessly used to better organise our thinking.

So, if you thought maths is cool, and you were braced for a bit of a laugh at how maths geeks sometimes get to thinking that they’re all that and more, and if you then made it this far, the real joke is that all your favourite crazy ‘what if’ worlds are not defined by their failure to be reality, but by being exactly what you say they are. The more you make them up and play, the more opportunities you have to learn things. So play!

Model worlds are everywhere, though they are usually not explicitly acknowledged, and they are not always, nor specifically need to be, amenable to being explored by the light of formal mathematics. Whether you are cooking or cleaning up, calculating payments which are claimed to be due, or trying to become acquainted with someone you have just met – not just our pedantic plodding thoughts, but also our intuition about how things will shake out – all this mental activity is supported by our vast capacity to create infinitely varied ‘model worlds’, to subject them to detailed experiments, and to distil out real insights.

The joke, then,  is that there is no joke ‘on you’. We can have a good laugh as we note that all our model worlds are valid and worthy of some engagement. And we move on. We can build so many model worlds, start them, stop them, watch them; count or measure things, under varying conditions. The next model world is always worth building, and after that the next.

All model worlds are right!