The book is the presentation of the conception in progress. An important contribution to its development was made by my friend Andrzej Bielecki, a mathematician, physicist, and computer scientist. A popular discussion about relations between mathematics and the models of consciousness began our scientific collaboration several years ago. The mathematical description of the model presented in a book may be, on the one hand, considered as a specific kind of verification of its internal consistency, and on the other hand opening of the perspectives of application of this model in artificial intelligence studies. Until know we wrote and published several papers and we are continuing the collaboration.