Posing problems and tasks as initiative complication of the world

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.

1. Autonomova N. S. (1988). Reason. The mind. Rationality. M.: Science.

2. Vasyukova E. E. (2020). Heuristics of thinking. Psychology of Cognitive Processes, 9, 129–142. https://elibrary.ru/item.asp?id=45720797.

3. Zagorsky V. (2002). Intellectual Olympiads: where do «young talents» go? Russian magazine. August 1, 2002. http://old.russ.ru/ist_sovr/sumerki/20020801.html.

4. Knyazeva E. N. (2014). Enactivism: a new form of Constructivism in Epistemology. Moscow, St. Petersburg: Center for Humanitarian Initiatives; University Book.

5. Krutetsky V. A. (1988). Psychology of mathematical abilities of schoolchildren. M.: Publishing house «Institute of Practical Psychology».

6. Levidov M. Yu. (2008). Steinitz, Lasker. M.: Russian Chess house.

7. Leontiev D. A. (2018). Life on the waves of chaos: lessons of Prigozhin and Taleb. Mobilis in mobili: Personality in an era of change. Under the general editorship of A. G. Asmolov. M.: Ed. House of YASK. pp. 29–39. https://psy.

8. su/mod_files/additions_1/fle_file_additions_1_8075.pdf.

9. Petrovsky V. A. (2021). Man over the situation. M.: Meaning.

10. Poddiakov A. N. (2011). Changing ideas about the transitivity of superiority under the influence of familiarization with «non-transitive» objects. Modern experimental Psychology: In 2 vols. Vol. 2, pp. 193–205. Edited by V. A.

11. Barabanshchikov. M.: Publishing House «Institute of Psychology of the Russian Academy of Sciences». https://publications.hse.ru/pubs/share/folder/1w8ip8xnzj/74121687.pdf.

12. Poddiakov A. N. (2014). Complicology: the creation of developing, diagnosing and destructive difficulties. M.:

13. Publishing House of the Higher School of Economics. https://publications.hse.ru/mirror/pubs/share/folder/s2vrh8vuk1/direct/144995075.

14. Poddiakov A. N. (2016). The non-transitivity of superiority and its use for deception and training of thinking. Psychological and economic research. 3 (9), 43–50.

15. Poddiakov A. (2022). The principle of «rock, scissors, paper» in mechanical toys and its «kinship relations». Science and life. 4, 68–73. https://www.nkj.ru/archive/articles/43663.

16. Poddiakov A. N. (2019). The principle of non-transitivity of superiority in different paradigms. Questions of Psychology, 2, 3–16. https://www.researchgate.net/publication/335014658.

17. Popov G. (2021). Non-transitivity is a storehouse for chess composers. SuperProblem. June 6, 2021. http://superproblem.ru/doc/columns/expert/2021/Non-transitivity.pdf.

18. Rutersvard O. (1990). Impossible figures. M.: Stroyizdat.

19. Sirotkina I. (2020). Dance: the experience of understanding. Boslen.

20. Filatov A. (2017). Non-transitive positions in chess. Science and Life, 7, 117–120. https://www.nkj.ru/archive/articles/31727.

21. Brown S. I., Walter M. I. (2005). The art of problem posing. New Jersey, London: LEA.

22. Kontorovich I. (2016). Considerations of aptness in mathematical problem posing: Students, teachers and expert working on Billiard task. Far East journal of mathematical education, 16(3), 243–260. https://www.pphmj.

23. com/abstract/10028.htm.

24. Kontorovich I. (2020). Problem-posing triggers or where do mathematics competition problems come from? Educational studies in mathematics, 105, 389–406. https://link.springer.com/ article/10.1007/s10649-020-09964-1.

25. Schön D. A. (1983). The reflective practitioner. How professionals think in action. Basic Books, Inc.