Models and reality


Yesterday, the topic for O-Chem was resonance structures and quantum*. One of the points I tried to get across to the class was about the appropriate selection and use of models.
Models are what we use to represent nature – perhaps the entire world, if you’re feeling solipsistic- and we try to build our models to get usefully close to “reality” as tested by experiment.
I want my students to realize that there are different levels of modeling, and that they should use the one that is simplest without being too simple. And most important, if a model is too simple, they should recognize that the appropriate choice is to pick a better model.

If a model’s explanation agrees with experiment, great. Maybe the model is a good representation of reality. Or maybe it’s just coincidence, and you might soon find that other experiments don’t fit your model. Then, if you’re a good scientist, you either revise your model to accommodate the new results, or you might have to chuck the model entirely and come up with a new one. Thomas S. Kuhn’s “The Structure of Scientific Revolutions“, which every science major should read in college, goes through that process with several examples.

Many cases of scientific error come about because a researcher is overly attached to his or her pet theory, a model of how nature works that makes some predictions. The model works well enough during early work to show some promising results. But as the experiments become more detailed, sometimes the predictions of the model don’t match the data. If the researcher is overly invested (psychologically, professionally, or financially), s/he may, instead of discarding or further refining the model, revise the experiment until it shows something closer to the “expected” results. Generally this begins as an innocent assumption: “I don’t know why the mice died. I’ll try again and this time make sure to watch them closer.” In bad cases, the behavior evolves to changing it he parameters of the experiment so that it can no longer produce results inconsistent with the model, at the expense of failing to actually test the theory in the first place. And, ultimately, sometimes this does degenerate into outright fraud.

Submitted for your consideration today: a lot of the problems in the world come from people using models in inappropriate situations.

  • A model of human behavior that works fairly well with Americans or Western Europeans might be disastrous when attempting to work with other cultures.
  • A model of the relationship between humanity and the natural world that was suitable for a low-population, high-resource country (17th-19th century America) no longer works well when resources are scarcer and demand for them is great.
  • A model of economic behavior that applies at one set of conditions fails in a different set of conditions.
  • A model of interpersonal generosity and mutual support that works well in small tribes/towns might not apply as well in a huge city. (And vice versa.)

All of those are instances of models where the model has validity in some instances, but fails when it is applied to other conditions. A more dangerous occurrence is when the model is knowingly false but is promulgated in order to serve an agenda. Climate-change denialism might fit that. The Laffer Curve in tax theory is self-evident at the extremes but not supported by data in the areas where policy is made.

And when people respond with hostility to challenges to their models, the results can range from argument to warfare.

What models do we cling to that need to be adjusted or replaced?

*For the non-chemists out there, apologies for forthcoming confusion. For the chemists, sorry for the oversimplification and probably the inaccuracies. The following is an overview of the models under consideration.

The concept of “resonance structures” is a pre-quantum way of explaining how two seemingly different arrangements (called Lewis structures) of electrons in a molecule can coexist. In the simplest model of bonding, atoms form molecules by sharing their electrons two at a time. But sometimes there can be more than one reasonable way of distributing those electron pairs. Experiment often shows that the molecule is best described as an average of these possible distributions.

So in O-chem, resonance structures are a pretty useful tool for describing molecules and their behavior. For example, we can explain why a particular reaction gives two products but not a third, using this concept. So even though it is a pretty simple model, it allows us to make reasonably good predictions most of the time.

General chem courses typically then add in the “extended π system” model, claiming that a resonance hybrid (average structure) can be viewed as one big bond extending over all atoms involved. Better in some ways because at least it uses orbitals.

Now introduce quantum and the LCAO-MO model. (Viewed from a safe distance, it’s fairly harmless.) LCAO-MO tells us that we can replace the resonance structure model with a set of larger molecular orbitals that are built by using the atomic orbitals available from the bonding atoms. For the simple resonance structures in the acetate ion, there are three contributing p atomic orbitals and thus three molecular orbitals can be generated. There are enough electrons available to full two of them, and the resulting picture agrees with the resonance model and explains why there is only a charge on the oxygen atoms, not the carbonyl carbon.

One thought on “Models and reality

  1. Another good example is the kind of limiting law such as the ideal gas law – almost perfectly accurate at low p and high T, less and less so as volume and speeds decrease, but still useful as a starting approximation. As for climate and earthquake models – don’t start.
    D

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