  The article is devoted to a problem of elaboration of the real-time
interactive videosystems for accelerated nonverbal cognitive computer and
telecommunications. The proposed approach is based on the using of droems
(dynamically reconstructed objects of experimental mathematics) and
interpretational figures as pointers to them. Four paragraphs of the article
are devoted to (1) an exposition of basic notions of the interpretational
geometry, (2) the operator methods in the theory of interactive dynamical
videosystems, (3) the general concept of organization of the integrated
interactive real-time videocognitive systems, (4) the droems and processes of
their dynamical reconstruction, where the general notions are illustrated by a
concrete example related to the infinite dimensional geometry. The exposition
is presumably heuristic and conceptual (the first and the third paragraphs)
though some particular aspects such as content of the second and the fourth
paragraphs, which allow deeper formalization and detailing in present, are
exposed on the mathematical level of rigor.
