  We suggest to combine the Anthropic Principle with the Many-Worlds
Interpretation of Quantum Theory. Realizing the multiplicity of worlds it
provides an opportunity of explanation of some important events which are
assumed to be extremely improbable. The Mesoscopic Anthropic Principle
suggested here is aimed to explain appearance of such events which are
necessary for emergence of Life and Mind. It is complementary to the
Cosmological Anthropic Principle explaining the fine tuning of fundamental
constants. We briefly discuss various possible applications of the Mesoscopic
Anthropic Principle including the Solar Eclipses and assembling of complex
molecules. Besides, we address the problem of Time's Arrow in the framework of
the Many-Worlds Interpretation. We suggest the recipe for disentangling of
quantities defined by fundamental physical laws and by an anthropic selection.
The main emphasis is made on the problem of the biological evolution.
