Consider centered data X(1),...,X(n) from a stationary time series with some autocovariance function, c(.). A natural, consistent, estimator for the spectral density, the transform of c(.), is the fast fourier transform (FFT), for which convenient software is available. In many contextx, e.g. response times in cognition experiments, the power spectrum computed from data by FFT is observed to be approximately 1/f over a fairly broad range of frequencies, this range being, of course, bounded away from 0. In this talk we propose that the ubiquity of 1/f power spectra follows from a general principle, and that a few "innocent" hypotheses suffice to imply that a power spectrum will be near 1/f.