A new theoretical and methodological approach of the processing of information is presented. On line modifications in the structure of information, such as stretched, broken, re- unified, or stuck pieces of information can be characterized from linguistic markers. For that two kinds of detachability from the situation are analyzed in a cognitive interpretation of Culioli's enunciative model. On one hand, the detachability linked to starting terms has for criterion the anaphora. It marks the categorization of external aggregates of information, their internalization, re-inscribing them at a subjective level, and their externalization, re-inscribing them in the spatio temporal environment. On the other hand, the detachability linked to modal terms marks a strategic reorganization of information. Both kinds of detachability are modelled by Culioli's diagram involving different levels between parameters S (subjective space) and T (temporal space). The passages from one of these levels to another follow specific routes with loops and strange loops. This paper analyzes the modification of information at the highest subjective level in the verbal protocol of a 10-year- old solving the Tower of Hanoi puzzle for the first time. The generalization to other tasks and to interaction between intelligent agents results from the interactive characteristics of linguistic markers.