JoshuaZ comments on Inverse Speed - Less Wrong
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Comments (56)
For some reason no one does the obvious cancellation to end up in m^2. This even has an intuitive meaning, it's the cross-section that a line of fuel would need so that as you travelled along it you'd be "picking it up" at the same rate you were burning it.
That's not nearly as helpful for most people. They don't think in terms like that as having an intuitive meaning simply because cars don't work that way. When people think of problems of this sort they frequently use other data about the reference classes to help them. If you alter the behavior of the reference class they will generate confusion. For example, that's why so many people have trouble with "If some doctors are men, and some men are tall, does it follow that some doctors are tall?" but don't have trouble with "If some US Presidents were Republican and some Republicans were women, does it follow that some US Presidents were women?" Don't underestimate how much people use the actual behavior of a class to guide them rather than just the section of it that you have abstracted.