Creating problems and tasks as an initiative complication of the world

Abstract

Complexity-generating human activities, in which people create complexity in an initiative way, are considered. Creativity of artists, writers, scientists and practitioners is often related to design of new kinds and levels of complexity. Amongst all diversity of complexity-generating activities, those ones which are related to problem generating (design, posing) are analyzed in more details. Posing math problems at different levels by different persons is considered: from posing problems by prominent mathematicians and by posers of problems for math Olympiads to initiative posing problems by school students for themselves. Some results of I. Kontorovich' project «The art of problem posing» including introduction of concept of nesting ideas (idea-generation ideas) are described. An example of A. Poddiakov's posing a new chess problem is presented. The initial (idea-generating) idea was to study possibility/impossibility to design chess players' positions (positions of White and Black) in intransitive («rock-paper-scissors») relations, or in other words, design of intransitively winning chess players' positions. It is shown how abstract chess and checkers world was made more complex in this aspect by several people's efforts. In conclusion the following statement is introduced: initiative complexity-generating activities are fundamental constituents of development of culture and many individuals' personal and cognitive development.