Random thoughts as I run

If you've read yesterday's post, you'll know that I was in the mood for a good run yesterday. It would sound good to tell you that I do my best thinking as I run, but in honesty, the opposite is probably true. At least it was relaxing, in a tiring, sweaty, choking-on-my-own-airway-secretions sort of way. For you, my readers', edification, I've assembled a rather haphazard collection of thoughts from the run.

• It piqued my curiosity that I tend to pass many people going the opposite direction, and I pass several walkers going the same direction as me, but the former is always much more than the latter. Theorem: If I run 8 mph one direction and I assume that people are stationary and peppered evenly along the length of the trail, then for a given distance, say two miles (= 15 minutes of running), I pass X number of people. There are X people headed in a certain direction evenly spread along two miles of the trail. However, if you assume this conveyor belt of people moves toward me at their walking pace of 4 mph, then I would pass 1.5X number of people.
• Corollary: If I run the same 8mph for two miles (15 minutes of running) but I consider the people walking in the same direction, then it's as if I'm only running 4 miles per hour. In that same stretch, I would only pass 0.5X number of people. The obvious conclusion is that I will pass three times as many people walking opposite me as the number I pass walking in the same direction as I run.
• Corollary number 2: If we add the total number of those I pass (going with and against me) then we get 2X. Ironically, or shall I say mystically, this is the same number I would pass if everyone else were frozen in time. In two miles, I would pass X people facing me, and X with their backs toward me.
• Foundational Postulate: It is not necessary to factor in the number of people who pass me. This would be like teaching elementary school children about the square root of a negative number. Imaginary numbers needlessly complicate the main point.