The paper deals with the basic features of the so-called synchronistic stochastic (control) systems on the basis of the extended Kalmanian system and realization theory, using the synchronicity paradigm of Jung and Pauli. It is shown that the introduced additive geometric structure number (characterizing the representation structure of synchronistic stochastic systems) is theoretically equivalent to the fine structure constant (determining e.g. the fine structure of hydrogen spectra) redefined by the authors of this paper. Finally the redefined form of fine structure constant as additive structure number (mediator number or identificator number) and the amplified interpretation of structural patterns of some important objects of cultural history, as well as the hypothetically related natural and geometric structure numbers, are compared. © 2008 IEEE.