skeeto wrote:The units don't actually cancel because it's confusing a common name for different things. Specifically, "miles per gallon". The bottom unit is not units of volume! If you write it out, it becomes "miles per gallon of gasoline", where "gallon of gasoline" is a unit of energy
Of course, making mistakes is the point of the comic.
I disagree. From my perspective the joke is funny in two ways. From my physics background, we were often taught to use dimensional analysis a s a last resort of solving a problem and as a check in the answer. The idea is that if the dimensions were correct, we would be off, at most, by some factor. The second joke is that this is equal to pie within a experimental error. In class, anything less than 10% was experimental error, and often acceptable. The comic brings back many good time.
As far as units not canceling, they do. The assertion that one buys a certain amount of energy is false. There is an average energy stored in refined petroleum product, but we do not buy on that basis, any more than we buy milk on the basis guaranteed calories. We buy a gallon, which is volume. One might be upset if the volume of a gallon of milk were materially different from the volume of a gallon of water.
The third joke is that for most of science, there are only three units: meter for distance, kilograms for mass and seconds for time. In this way, energy over pressure is a volume, while fuel consumption(already identified as inverse area) over distance is inverse volume. Of course none of this makes sense as it true it is taken out of context, but the final joke is when teaching this stuff most students will ignore context in favor of successful manipulation.