  We discuss the algorithmic information approach to the analysis of the
observational data on the Universe. Kolmogorov complexity is proposed as a
descriptor of the Cosmic Microwave Background (CMB) radiation maps. An
algorithm of computation of the complexity is described, applied, first, to toy
models and then, to the data of the Boomerang experiment. The sky maps obtained
via the summing of two independent Boomerang channels reveal threshold
independent behavior of the mean ellipticity of the anisotropies, thus
indicating correlations present in the sky signal and possibly carrying crucial
information on the curvature and the non-Friedmannian, i.e. accelerated
expansion of the Universe. Similar effect has been detected for COBE-DMR 4 year
maps. Finally, as another application of these concepts, we consider the
possible link between the CMB properties, curvature of the Universe and arrows
of time.
