All models are wrong

What is a model?

If everything around us – all of the physicals things from the very small to the very large, all of their properties, and all of the interactions between them – are reality, then anything which categorizes, describes, interprets, represents or conveys information about that reality, is a model.

Here’s a few examples of what I would consider a model:

  • mathematical equations representing physical relationships (such as Einstein’s famous E = mc²)
  • the entire body of scientific knowledge (both the descriptive theory and empirical evidence)
  • my Great Aunt’s recipe for the perfect chocolate cake
  • engineering drawings and architectural plans
  • natural language
  • our own memories and sensory perceptions.

 

How are they useful?

Models allow us to abstract away the complexity of physical reality, making it simpler and easier to understand or to discuss with others. Perhaps the most important aspects of models however, is that they allow us to make useful predictions about the future, from experience with the past.

I like to think of science as being the development or amalgamation of models and evaluation of their usefulness (in making predictions). Engineering could then perhaps be defined as the application of models to make predictions, with the hopeful outcome being a new design which will perform as intended. This requires models which make useful predictions.

Indeed, engineering is built on models; rules of thumb, mathematical equations, computer algorithms, scientific theorems; even the collective experience and wisdom of past and present practitioners.

What do you mean abstract away complexity?

I thought you’d never ask! Everything in the Universe is in some way connected. Nothing exists completely in isolation. When I say abstraction, I mean that we make assumptions and ignore the vast majority of reality, and focus on only what we need to consider to make useful predictions.

This concept is best illustrated with an example:

This morning, my 4 year old son asked how a toaster works. My response was, in a nutshell, that electricity goes into the toaster, which makes the elements get hot (at which point I showed him the glowing filaments in the toaster), which in turn heats up the bread, causing chemical reactions that turn the bread brown and crunchy – toast. That description was clearly not the entire reality of a toaster, but rather a model of how it functions.

Now, I could easily have just told him that you put the toast in, it toasts, and then it pops out. That would have been a more simple, yet perfectly valid model of a toaster. It’s useful, but it’s not very informative, and I always try to mention all of the key steps when I explain things to him, even though I know he won’t understand all of what I said.

If I had started talking about electric theory, thermodynamics and human taste perception, in addition to being completely out of my depth, I would have completely failed at communicating anything useful to him at all. In contrast, this more complex model might be useful to someone designing a toaster.

Another example, more relevant to us here, is pressure and temperature. There is a tendency to think of them as specific physical properties. But a more detailed model (kinetic theory) describes pressure (in a gas or liquid) as the result of molecules colliding with whatever is experiencing the pressure – an average of collision force over an area. Likewise, temperature is an average of the molecular kinetic energy – related to their velocity and mass. There is even a mathematical model to express this – derived from the Boltzmann Distribution.

So, what’s your point?

The important point is that no model represent an objective “truth” about reality, but rather an incomplete approximate description. They rely on simplifying assumptions to reduce the complexity (and computational cost) of making predictions. This incompleteness limits generalization; the ability to apply the model to a wide range of conditions and still make useful predictions.

In his book Empirical Model Building and Response Surfaces statistician George E.P. Box stated:

Essentially, all models are wrong, but some are useful.

While probably not entirely consistent with George’s intended message, my interpretation of these words has developed into a philosophy of sorts, relevant to both my professional and personal life, as a reminder not to get too attached to any particular way of looking at the world around me.

It is as relevant to the established wisdom of the specialty coffee industry, as to my articles here. It’s all (in some sense) wrong, but that doesn’t really matter so long as it’s useful.

Further reading

I’ve hopefully covered enough here, but for anyone who’s keen to explore the concept of models further, then I highly recommend Scott Page’s excellent Model Thinking course on Coursera.