Viewing the multi-channel EEG as a sequence of momentary field maps corresponds to the concept of a trajectory in K-dimensional state space (K = number of channels). This approach permits a quantitative, single value measure of complexity of the brain state trajectory, the global correlation dimension that describes the ensemble characteristics of all recorded channels. In 5 normal volunteers, 4 records of 16-channel resting EEG were obtained during each of 4 randomized sessions (double blind design) after a single dose of placebo or 2.9 g or 4.8 g or 9.6 g piracetam. The global correlation dimension of a 40 sec epoch from each record was estimated, using 50 computational runs with 8192 point pairs. The results were combined for the two intermediate doses and averaged over repeated records. The dimensionality decreased from placebo (median = 5.89) to low dose (median = 5.72) to high dose (median = 5.59), significant in a Friedman ANOVA at P < 0.02, with significant differences between placebo vs. high and low vs. high dose. Thus, the subtle change of brain global functional state after a single dose of piracetam is reflected by the non-linear measure of global dimensional complexity of the multi-channel EEG.