The trouble with models

29 03 2010

Naomi Campbell escorted by policeForget Naomi Campbell and her hissy fits. We’re talking about mathematical and logical models. If experimental results are the bricks in the cathedral of science, then models are the mortar. Simultaneously cementing facts into a framework of predictions, this is where success and failure come face to face in the scientific method.

What is a scientific model? At it’s simplest, a model is an abstraction of Watson and Crick with DNA modelreality. The best models take the single most important elements of reality and build a logical framework around them. For example, the elegant model of the DNA structure proposed by Watson, Crick, Franklin and others (see photo). By definition, a model is always less than, simpler than and different from what it represents.

That may sound bad, but it’s actually really good.

The power of models lies in simplification. Whether a model is a conceptual diagram, a logical/decision based flow diagram, or a system of equations it contains only the key elements of the reality we are trying to model. Scientists cannot hope to model everything in a physical system.

Unfortunately, the differences between various types of models isn’t immediately clear. Conceptual models (think of subject bubbles or concepts connected together with lines) are great for understanding the components of system, but it’s difficult to make predictions from them. They’re useful for understanding cycles and how things can be linked. They can also be an important step in developing mathematical models.

Logical or flow diagram models (e.g., “yes / no” flow charts) are a bit better in this regard, they help specify precisely how different components affect one another.

Mathematical models (typical complex sets of many equations) tend to be the most powerful when it comes to predictions, but this power is accompanied by concerns of accuracy. The more specific a model gets, the less general its applicability. The model to the right describes how a particle moves in a force field.

But the predictive power of models is what sets apart science from stamp-collecting. Without prediction science is about cataloging facts. An interesting exercise, but one that does not change the future.

Since modeling is so important in the scientific method, it should come as no surprise this is where critics attack first.

NASA GISS Model EUnder the weight of the importance of global warming, the phrase “climate model” has been abused by journalists to the point where it is almost a metaphor for “poor science”. Encapsulating all the elements of Earth’s climate and ecosystem interactions is logically impossible. So the criticism “they’re just models” is completely unfounded.

Even pillars of physics such as Newton’s Law of Gravitation, or Quantum electrodynamics are “just models”. They may be very accurate predictors of behaviour for some systems, but each breaks down known ways. Every model has limitations.

So the real question that should be asked about models, is not how well do they describe something, but rather, how important are the things that have been left out?

This is when things get tricky. In models that simulate physical systems using sets of equations there is always a length or time scale below which you don’t know what happens. There is always physics, chemistry or biology on these scales. So if these processes that you can’t follow directly in your model influence it, what can you do?

You have to include them as best you can. If that sounds imprecise, there’s good reason. Sometimes, you can do this really easily. For example all the collisions of atoms of air with the walls in a room can be modelled as one big push on that wall, i.e. atmospheric pressure. We don’t resolve the atoms when we simulate gas in a room because we don’t need to.

Other times, it can be quite difficult. For example, clouds form the atmosphere around very small particles in the atmosphere, “aerosols”. The exact type and distribution aerosols can lead to different clouds, and modelling this is one of the key uncertainties in current climate models.

Does this mean that climate models are somehow “broken”? Not all. The underlying physics behind the greenhouse effect is well known, and simple atmospheric models have demonstrated the increased temperature as a result of increasing CO2 since the 1950s.

This highlights one of the key problems with models – unrealistic expectations. The scientists who work on models will always admit there are limits to what a model can encapsulate. That is the scientific thing to do. But that does not mean they are irreparably flawed.

In the poetic words of the physicist Niels Bohr “Prediction is very difficult. Especially about the future.”

Next time: Math, computing and the environment.



2 responses

29 03 2010
Nathan Ackroyd

I like that we use models; Students don’t like it so much. They want the “right” answer, as if I have one. In organic chemistry we’re very concerned about bonding. Sometimes I have to stop and point out when we’re switching models and say “OK, we were thinking of electrons like particles and now we need to switch over and view them as waves. They aren’t particles anymore…. OK, for this view, the electrons need to go back to being particles.” It drives them nuts.

Then, they accidentally stumble on something that could happen in a mechanism and wonder why I didn’t tell them that in the first place…

29 03 2010

To be honest, models of quantum systems are about as hard as it can get! We have very little intuition for them — I’m not surprised it drives your students nuts! 🙂
Our “common sense” is driven by interaction with the world on about a 1mm to 20 km scale. That means we struggle with both the really small (i.e. quantum) and really large (infinite universe, expansion of space) ideas.

However, it sounds like you are doing a good job if they figure possibilities that you haven’t mentioned!

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