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There have been tantalizing indications from many quarters of physical cosmology that we are living in the multiverse - a huge set of cosmological domains ("universes"). What is the structure of this larger whole is an entirely open problem on the interface between physics and metaphysics. A goal of the present paper is to draw attention to the connection between this problem and an old and celebrated puzzle in mathematical physics. Among the unresolved problems David Hilbert posed in 1900 as a challenge for the dawning century, none is more philosophically controversial than the Sixth Problem, requiring the axiomatization of physical theories. In the new century and the new millennium, this problem has remained a challenge, usually swept under the rug as "not belonging to mathematics" (as if that impacts its epistemical status) or simply "unresolved". Recent radical ontological/cosmological hypothesis of Max Tegmark, identifying mathematical and physical structures, might shed some new light onto this allegedly antiquated subject: it might be the case that the problem has already been solved, insofar we have formalized mathematical structures! While this can be seen as "cutting the Gordian knot" rather than patiently resolving the issue, we suggest that there are several advantages to taking Tegmark's solution seriously, notably in the domain of (future) physics of the observer. [Project of the Serbian Ministry of Education, Science and Technological Development, Grant no. ON176021: Visible and Invisible Matter in Nearby Galaxies: Theory and Observations and Grant no. ON179048: The Theory and Practice of Science in Society: Multidisciplinary, Educational, and Intergenerational Perspectives]

We review Fermi's paradox (or the "Great Silence" problem), not only arguably the oldest and crucial problem for the Search for ExtraTerrestrial Intelligence (SETI), but also a conundrum of profound scientific, philosophical and cultural importance. By a simple analysis of observation selection effects, the correct resolution of Fermi's paradox is certain to tell us something about the future of humanity. Already a more than three quarters of a century old puzzle - and a quarter of century since the last major review paper in the field by G. David Brin - Fermi's paradox has generated many ingenious discussions and hypotheses. We analyze the often tacit methodological assumptions built into various answers to this puzzle and attempt a new classification of the numerous solutions proposed in an already huge literature on the subject. Finally, we consider the ramifications of various classes of hypotheses for the practical SETI projects. Somewhat paradoxically, it seems that the class of (neo)catastrophic hypotheses gives, on balance, the strongest justification for guarded optimism regarding our current and near-future SETI efforts., Comment: 39 pages, 3 figures, slightly expanded in comparison to the journal version

The number and distribution of habitable planets in the Milky Way is one of the foremost problems of contemporary astrobiological research. We investigate the effects of applying general neocatastrophic paradigm to the evolution of the Galactic Habitable Zone. In this paper, we investigate the limits of simple, 1-dimensional astrobiological models, and consider the role of regulation mechanisms in shapening the 'astrobiological landscape'. We show that the transition from predominantly gradualist to predominantly (neo)catastrophist history of our Galaxy leads to the build-up of large-scale correlations between habitable sites, offering possible keys to such important problems as Carter's 'anthropic' argument and Fermi's paradox. In addition, we consider the possibilities for extending the present class of models into spatially realistic 3-dimensional case via probabilistic cellular automata.

Several assumptions used in the recent review paper on the search for extraterrestrial intelligence (SETI) by Duric and Field (2003) are critically discussed. New astrobiological results-in particular those on the age distribution of terrestrial planets-enable relaxing of some of these assumptions, which gives further justification to optimism regarding SETI projects.

We investigate a quantitative consequence of the Acausal-Anthropic approach to solving the long-standing puzzle of the thermo dynamical arrow of time. Notably, the size of the required multiverse is estimated on the basis of the classical Boltzmann connection between entropy and probability, as well as the thermodynamic properties of black holes.

A kinematics of a z = 2.81 galaxy toward bright QSO 0528-250, as inferred from the absorption spectroscopy is discussed. There are sufficient arguments for a far-reaching conclusion that we are observing an older, uninvolved version of the local Galactic interstellar medium.

A puzzle of the low-redshift damped Ly? absorption system toward QSO 1854+116 is presented. Problems which conventional intepretation of damped Ly? systems encounters in this case are sketched and a possible explanation, based on transience of the phenomenon, is suggested. It is shown that the detailed H? tomography can observationally resolve the controversy in the very near future.

The metallicity structure of galactic haloes is one of the major unknowns in modern galactic astrophysics and observational cosmology. Hereby we outline a very simple method for obtaining at least a crude picture of gas abundances, based on recent important statistical determination of the relationship between neutral hydrogen absorbing column density and galaxy impact parameter. It is a fine illustration of the great theoretical and observational power of low-redshift Ly? absorption studies. Future detailed analyses of large samples of absorption-selected galaxies will certainly provide us with more data on the abundance structure of extended gaseous component of galaxies.