The other day I was trying to help my students understand why the Cartesian coordinate system is so useful in specifying the location of a point in two-dimensional space. I began by asking them to imagine being stranded in a desert containing flat sand for miles in any direction, with no distinguishable landmarks against which one might orient oneself. I then asked them how they would signal their position by radio to a would-be rescuer. I was hoping to use that scenario to build to one in which there is just one distinguishable landmark, say a cactus plant. This would improve the situation slightly, as you could say approximately how far you were from that central point, but of course you still don’t have everything you need, as you could be at any point on the circle with a radius of your distance from the cactus. The next step would be to introduce two landmarks, and the possibility of orienting oneself with respect to two highways that intersect at right angles with each other.
Much to my chagrin, however, as soon as I proposed the desert scenario, my students began to tear it apart: how could there be no landmarks? If you had a radio, couldn’t the rescuers use its signal to pinpoint your location? If there is a single landmark, why not just go to it? I suggested that perhaps you’re immobilized due to some injury, but then they asked how you could operate the radio if you were so severely injured, and how you ended up there in the first place
I trust the moral of the story is clear: thought experiments that rely on slightly ludicrous scenarios to make their point run the risk of being hijacked by students intent on distracting the class and getting it off course. High school students are still at the age where they have trouble suspending their disbelief in order to achieve a greater understanding. Adults understand that thought experiments are deliberately simplified and/or ludicrous scenarios designed to illustrate a point, or to aid comprehension. But students’ imaginations are still untamed: they will take anything you say and run with it, without regard for the constraints that make the statement or scenario didactically useful.
The Thought Experiment in Action
Thought experiments are still incredibly valuable. The elucidation of some of the most successful theories of all time depended on this type of experimentation. Special relativity was born when Einstein began to wonder what a light wave would look like if you rode alongside it at the same speed. The theory of general relativity was conceived when Einstein realized that if you were in an elevator in free fall, you would not feel your own weight. But thought experiments must be carefully chosen, and students must be trained to approach them in the right way: not trying to poke holes in them, but going along with the constraints to try to figure out possible solutions.