Droems: experimental mathematics, informatics and infinite dimensional geometry

TL;DR

This paper introduces droems, a concept in experimental mathematics and infinite dimensional geometry, to develop real-time interactive video systems for accelerated nonverbal cognitive communication, combining geometric and operator methods.

Contribution

It proposes a novel framework using droems and interpretational figures for organizing and reconstructing infinite dimensional geometric objects in interactive video systems.

Findings

Introduction of droems as dynamic reconstructed objects in experimental mathematics

Application of operator methods to interactive dynamical videosystems

Conceptual framework for integrated real-time videocognitive systems

Abstract

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.