Power Spectrum Running

As discussed last millennium here (cf. NoiseAndPredictability (1999-09-14), LongTails (2000-02-14), etc.) power spectra are a valuable way to analyze events and understand patterns or the lack thereof. Completely random, uncorrelated activities produce a flat power spectrum, also known as "white noise". Completely regular, periodic activities make a sharply spiked power spectrum with all the energy at a single frequency. A random-walk staggering drift gives a power spectrum dominated by low frequencies — 1/f2 mathematically.

Also as mentioned many times here (cf. JogLogFog (2002-06-09), etc.) variety and consistency are both essential components of training to run long and/or fast. Do the same thing every day? Boredom sets in while improvement ceases. Try to ramp up distance too abruptly or run too hard without preparation? Injury and failure will likely result. (The humorous "Up Your Mileage" prescription is not actually wise in real life.)

So apply the concept of the power spectrum to the running logbook? The same mileage every day (or every week) is too regular and makes for a huge bump in the spectrum. Wildly varying day-to-day mileage is too chaotic. Perhaps the optimum is something in between, like a 1/f distribution?

Project: analyze the power spectrum of my running logbook over the past several years, see what kind of frequency distribution it exhibits, and explore whether a "spectral advisor" could suggest what distances to run in order to make the spectrum better.

^z - 2012-09-09