Duality Revolution

Book excerpt: There are many books on duality. All of them fall into the following hackneyed categories: putting various spins on the classical dualities of good and evil, right and wrong, light and dark, mind and body, male and female, etc.: dualities as limitations and how to overcome them, or how to not limit oneself to one side; duality as illusion and how to free oneself from it; duality between women and men and how to reconcile it; etc. poetic and odd dualities such as the duality of the third dimension; haphazard dualities such as duality of risk and pain, moon and sun, wall and ceiling or any two other haphazardly chosen objects; treatises on the dual nature of something, e.g. the dual nature of matter, or the dual nature of mind, or the dual nature of soul, or the dual nature of space, etc. and, finally, scientific textbooks and monographs on duality principles in mathematics and physics. This book breaks a new ground and presents dualities discovered in the course of the research on how people think, solve problems and invent. The research began within the framework of TRIZ (the Russian acronym for the Theory of Inventor's Problems Solving) but went beyond it. It all started with the discovery of duality patterns in the TRIZ methods of invention. Attempts to formalize them led to the discovery of mathematical operators with properties that no other mathematical operator has. This led to the hypothesis that until now mathematics was the science about equal dualities. Accordingly, a program was launched to transform mathematics so that the axioms and theorems would assert the equivalence of dualities. Then dual transitions were discovered in the mechanisms of thinking and evolution. All this was put to use in devising new methods and algorithms of invention. The duality revolution has begun and continue to spread across domains revolutionizing them. This is what this book is about.