... and, extending that (I had to hop onto the bike to go off to teach class), oscillations around a mean presume that there is a structural dynamic creating a central tendency with a fluctuation around that. If what is creating the movement is what is identified above as fluctuations around the mean, then the mean is an epiphenomena of the wave, rather than the wave being oscillations around the mean.

I've been accused of being a Marxist, yet while Harpo's my favourite, it's Groucho I'm always quoting. Odd, that.