The amount of information available in spectro-polarimetric data is
estimated. To this end, the intrinsic dimensionality of the data is inferred
with the aid of a recently derived estimator based on nearest-neighbor
considerations and obtained applying the principle of maximum likelihood. We
show in detail that the estimator correctly captures the intrinsic dimension of
artificial datasets with known dimension. The effect of noise in the estimated
dimension is analyzed thoroughly and we conclude that it introduces a positive
bias that needs to be accounted for. Real simultaneous spectro-polarimetric
observations in the visible 630 nm and the near-infrared 1.5 microns spectral
regions are also investigated in detail, showing that the near-infrared dataset
provides more information of the physical conditions in the solar atmosphere
than the visible dataset. Finally, we demonstrate that the amount of
information present in an observed dataset is a monotonically increasing
function of the number of available spectral lines.