For some years there has been a controversy about whether brain state variables such as EEG or neuronal spike trains exhibit chaotic behaviour. Wright & Liley claim that the local dynamics measured by spike trains or local field potentials exhibit chaotic behaviour, but global measures like EEG should be governed by linear dynamics. We propose a different scheme. Based on simulation studies and various experiments, we suggest that the pointwise dimension of EEG time series may provide some valuable information about (...) underlying neuronal generators. (shrink)