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state for very long, spontaneously and irregularly jumping from one unstable dynamical state to another (1997). This suggests that meaningful tension between experimental sample lengths long enough to minimize statistical error and short enough to be stationary may be, for the biological sciences, more apparent than relevant.

The studies reviewed below exploit measures arising from the view that the noisy statistics of nonstationarity in biological processes are not a sign of measurement error, but rather evidence consonant with the statistical physics of nonequilibrium states and phase transitions (Stanley, 1971; Stauffer, 1985; Yeomans, 1993). Very high amplitude fluctuations and multiple, up to infinite, correlation lengths are characteristic of the normal, on-going biological dynamical behaviors, which are apparently without characteristic amplitude and time scales. From this point of view, if most or all information is widely distributed in the brain (e.g., serial order of visual tasks involving motor cortical neurons, Carpenter et al, 1999) ) then the “binding problem” (see above) could also be solved by multiple, up to infinite spatial and temporal correlation lengths in place of the current theories of monofrequency resonances (Singer, 1993). Hierarchical neurodynamical mechanisms communicating across many mechanistic temporal and spatial scales, brain information transport analogous to the energy cascade of hydrodynamic turbulent velocities (Tennekes and Lumley, 1972), would be likely in the parametric vicinity of incipient bifurcations and phase transitions.

Three closely related techniques for quantifying the systematic changes in average fluctuation amplitudes with n (scale, sample length) involve a “power law,” linear slope relationship between the logarithm of an index of variability and the logarithm of sample segment sizes. These easy, yet powerful methods were brought to experimentalists’ attention by Benoit Mandelbrot (Montroll and Badger, 1974; Mandelbrot, 1983; Fedor, 1988; Bassingthwaighte et al, 1994; Liebovitch, 1998). To estimate the exponent in Hurst rescaled range analysis, we compute the standard deviation and the range of the deviation of the running sum from the mean on sequential subsamples of increasing size. The Hurst power law exponent is the slope of the straight line formed by graphing the logarithm of the subsample length

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