In this paper we analyze in detail the central role of number '137', the so-called Fine Structure Constant in the collaboration of Pauli and Jung. First, we present the fascination or the obsession of Pauli for the interpretation of number '137'. Second, we treat the spontaneous messages originating from unconscious concerning number '137' in the well-known dreams of Pauli. We restrict our investigations to the dreams containing the especially important formulae of Fine Structure Constant (4π³ + π² + π), and also that containing the so-called background models of mathematical control systems. Third, we shortly mention four of the numerous synchronicities arising during the Pauli-Jung collaboration. © 2008 IEEE.