Inauthenticity and the Null Hypothesis

Some of my more astute students point out that problems that ignore everyday forces are unrealistic. This is true, in the sense that projectiles will face air resistance, rolling objects will experience friction etc. However, this is not to say that performing calculations using such unrealistic conditions is without merit.

Firstly, it provides the opportunity to practice calculation and build algebraic skills. Secondly, it provides a baseline, or null hypothesis.

It is often difficult to measure influences of obscure forces on a system directly. We can, however, devise a model to predict an outcome without such influences. By comparing authentic observations to this theoretical model, the deviation from the predicted outcome due to the extraneous influences can be observed. Thus, calculating the theoretical value without extraneous influences – resistance or friction etc. – can be an immensely useful tool for figuring out the effects of those influences.

This holds for any science, not just physics. Rate limitations in chemistry, galaxy rotation rates in astronomy, population dynamics in ecology, and genetic diversity all have specific models as a baseline. Any mathematical model in science can be used in this way. The Hardy Weinberg equation, in particular, is used specifically as a null hypothesis to determine the deviation of allele frequencies from predicted in order to identify factors influencing population genetics.

If you have students who frequently point out the inauthenticity of textbook questions, then you are on the right track – they are thinking. Bonus. If not, then introduce them slowly to the real world. Have them practice the theoretical problems and do some real-world experiments. Rather than sweep the discrepancies under the carpet, emphasize them. Have students look for trends, make estimates and models to try to predict the real world outcome.

Getting students in the habit of looking for the discrepancies between theoretical and observed can really get them thinking about the big picture, but in order to do this, the theoretical values must be known. So even though the outcome of such questions may seem inauthentic, if your students ask when in real life they would ignore these influences, you have an answer for them.

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