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We present some puzzling evidence about galaxies, such as their apparent motionless localization with respect to the cosmological rest frame, quantization of redshifts and the "fingers of God" phenomenon. We propose that these facts can be understood within the classical self-consistent multidimensional field theory with a dilation. In particular, some peculiar features of emission lines from active galactic nuclei can be explained in a natural way by assuming that dilantonic configurations are placed in central parts of AGNs. Moreover, dilatonic balls in the centres of galaxies may be responsible for recently discovered kinematical effects usually attributable to hypothetical massive central black hole. We suspect that the large-scale structure in the universe could be built upon dilantonic condensates. The presence of gauge fields around dilatonic configurations could make the resulting pattern static. Properties of intrinsic redshift in dilantonic theory (steepness of z(r) near centres of condensation and its domination over Doppler shifts) also make this model attractive from the point of view of the discordant redshift problem.

A search for quantization of redshifts was performed for objects belonging to the Iwanowska lines connected with our Galaxy and M31. A distinct periodisation effect was found. No exact quantization effect was detected. The accuracy of observational data was not sufficient for more precise analysis. No correlation between values of redshift or morphological types of objects and locations on lines was visible.

Any cosmological consideration must be based on one or more cosmological principles. Six of them are described namely: The Ancient Hindu, the Ancient Greek, the Genuine Copernican, the Generalized Copernican, the Perfect and the Anthropic Ones. Some cosmological principles have common properties, some are contradictory; some are logically independent, some dependent. Cosmological principles influence not only interpretation of results but they influence the results of cosmology as such. A consciousness of problems connected with cosmological principles is necessary when getting in touch with cosmology.