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Steven Novella - From "Mediocrity and Meritocracy"
... An amateur can make valuable contributions to science, and having a position of scientific authority is no guarantee of correctness. Some amateurs are inherently brilliant... . However, most people are mediocre at most things. Most amateur scientists are mediocre..., and this is often compounded by the fact that they do not have any formal training. This may leave them blissfully ignorant of exactly how mediocre they are as compared to professional scientists.

Lang's Calculus - Fiding v or f?
Can you find v if you know f, and vice versa, and how? If we know the velocity over the whole history of the car, we should be able to compute the total distance traveled. In other words, if the speedometer record is complete but the odometer is missing, its information could be recovered. One way to do it (without calculus) is to put in a new odometer and drive the car all over again at the right speeds. That seems like a hard way; calculus may be easier.