  We study the Crofton's formula in the Lorentzian AdS$_3$ and find that the
area of a generic space-like two dimensional surface is given by the flux of
space-like geodesics. The "complexity=volume" conjecture then implies a new
holographic representation of the complexity in terms of the number of
geodesics. Finally, we explore the possible explanation of this result from the
standpoint of information theory.
