A spacetime region of size about 10-33 cm, where the gravitation interaction becomes strong and which corresponds to the very beginning of the Big Bang theory, is discussed. It is argued for incognizablility of laws that govern phenomena proceeding in this region. It is assumed that basic changes in the entropy, which determine the direction of the time arrow, occur in the same region; therefore, their nature will never be established either. It is conjectured that brain cells are controlled by a quantum computer featuring a large (or even an indefinitely) large number of degenerate states. An external observation removes this degeneracy, rendering impossible the cognition of the consciousness mechanism.