Infinite words on a finite non-empty alphabet have been investigated in various respects. We will consider here two important strategies in approaching such words; one of them proceeds from particular to general, while the other proceeds from general to particular. As we shall see, the respective hierarchies don’t interfer. There is between them an empty space waiting for investigation. 1.) C. S. Calude, K. Salomaa, S. Yu (eds.). Advances and Trends in Automata and Formal Languages. A Collection of Papers in Honour of the 60th Birthday of Helmut Jürgensen.