Alexander Grigoriev (Russia)

The guess of how it is possible for itself begins with a heuristic question, aggravated to a contradiction, indicating its possible solution, revealing at the limit of its capabilities a problem that can be formulated, but impossible to solve within these limits. "And how to open such a question that only you can raise for the first time and help others in this?" Is a question that presumes not only the potential infinity of the many possibilities of individual progress irreducible to each other, but also the continuity of this set (only in this case the "principle of the fragility of good" does not apply when changing one type of progress to another). The hypothesis that seven simultaneous nonlinear methods of interaction of two opposites is necessary and sufficient to enable a countable infinite set of progress types irreducible to each other is substantiated through the mathematical optimization problem, which is isomorphic to it, known in the theory of singularities of differentiable mappings, in which, starting with of seven parameters, an infinite number of irreducible enumerated types of singularities of variables arises, and explains some anomalous with respect to the law of unity and struggle of opposites and its multipolar form, facts and theoretical provisions of the humanities and natural sciences. But, starting from the 11th parameter, in the optimization problem, a continuous set of irreducible types of singularities arises. In this case, the individuality of each does not risk being left without the possibility of his creative unique self-realization. The author of this development hypothesis made five pedagogical inventions marked with diplomas of the All-Russian competition of pedagogical inventions and innovative educational technologies "Modern School".