There was a time when the optimal exercise speed was however fast you had to run to get away from a saber-tooth tiger. Even today, in much of the developing world, people exercise through activities such as farming and fetching water that are necessary for survival.
However, in the developed Western world, where exercise tends to be an extracurricular activity, there is apparently tremendous interest in just how fast you should move in order to improve your health. Consider, for example, the many posts on The New York Times’ Well blog on the topic (walking versus running, the “right dose of exercise,” “walk hard, walk easy”), all of which focus on the relative benefits of walking versus jogging versus running.
So is it better to walk? To walk fast? To run slow? To run fast? On its face, this question is poorly posed, since it says nothing about our goals or our constraints. Am I aiming to lose weight? To live longer? To win road races? Am I willing to exercise for three hours a day? Twenty minutes? Almost never? Clearly, these considerations matter when trying to determine the optimal speed. Here is how I would think about asking the question instead: What is the easiest way to reduce my chance of death?