It's only a model: knowing your limitations

Science is all about making & testing models to describe the real world, and it's always important to remember that the map is not the territory.

The word "science" in the meaning we know it is relatively new. It originated in the 19th Century to encompass the old term "natural philosopher". Isaac Newton was a natural philosopher1, as was Robert Hooke and Benjamin Franklin2.

I'm uncertain why the term changed, but I do know that this is a good thing, since modern-day science carries no truck with philosophy. Beyond a superficial level, science does not explain, it describes. It does this by the use of models. The Theory of Gravitation is a model, as is General Relativity and Electromagnetism. These scientific theories are as profound a description as exists of reality, but they are still models of reality; they do not belong in the field of philosophy.

Philosophers of science do exist. I know this because my friend is one. We have many interesting conversations that always provoke thought and are an excellent way to expand your imagination3. On the day-to-day professional level though, these are almost entirely useless in my job.

Models are simplified approximations of reality that can be used to help describe it. They have no intrinsic value beyond this; approximations by their very nature, are never 'correct'.

"Essentially, all models are wrong, but some are useful" - George Box, statistician and pioneer of time-series analysis, 1987

So how do we know that a model is wrong but useful, and worth using?

It depends4. Any model that helps you understand your problem is useful - even if that model is wholly unsuitable for providing you with an answer.

The most important thing you can do with a model is not fall in love with it - models are a tool to aid understanding and possibly prediction, nothing more. Always be aware of a model's limitations and be wary of extending it's application beyond those lines. Even better, build a model so that it becomes explosively, obviously wrong, when pushed beyond those tolerances, discouraging creativity from those who like to substitute initiative for a complete lack of understanding.

When facing a new problem, I always start with a very simple model. I ignore all the little voices in the not-as-close-to-the-back-of-my-mind-as-I-would-like insistently saying "yes but, yes but, ...". I'm aware of how horrifyingly simplistic this approach may seem and I don't really care. Starting on solid ground makes it far easier and justifiable to add complexity and sophistication in later stages of analysis, the subtleties of a particular model always based on a strong bedrock.

In the immortal words of Patsy from Monty Python And The Quest For The Holy Grail:

... it's only a model.

  1. He was a lot of other things too.

  2. So was he.

  3. Because of him I have a new and profound respect for Bill and Ted's Excellent Adventure.

  4. In my experience, the glib answer - "it depends" - is actually a valid response to the vast majority of important scientific questions.

Mick Cooney

Mick is highly experienced in probabilistic programming, high performance computing and financial modelling for derivatives analysis and volatility trading.