Herein we introduce a technique for determining the fractal dimension of time series obtained from complex systems, in particular brain-wave data in which the fractal dimension is arguably a measure of awareness and learning. The technique is based on determining the probability distribution for the degree of irregularity in random time series and has been shown to be superior in terms of efficiency and reliability to more commonly used methods that rely on the correlation function. We speculate that the scaling behavior of the probability measure is an indicator of an allometric relation between learning and brain-wave activity.