Duality revolution: Discovery of new types and mechanisms of duality that are revolutionizing science and technology as well as our ability to solve problems

Duality is everywhere. It is one of the fundamental building blocks of the world. The book examines the phenomena of duality in mathematics, physics, chemistry, biology, technology, creative thinking, problem solving, etc.Among other things, it presents a new theory of creativity that is based on the discovery that thinking is a process of constant transition from one perspective on the object of thought to a dual perspective. Such transitions are called dual transitions in the book. Our thinking is a chain of dual transitions.To increase your creativity, you need to master as many dual transitions as possible. The book provides a list of dual transitions useful in problem solving. The emphasis is laid on inventive problem solving.In inventing, the transition from one way of doing things to a dual way requires knowledge of dual physical effects and chemical reactions. The book presents, for the first time, a catalog of such effects and reactions.Sometimes a problem cannot be solved in the form in which it is formulated, and it has to be changed into a dual problem. The book provides methods for such problem transformations.Very often at the core of a problem lies a contradiction. It has been found that contradictions can be resolved by separating contradictory requirements between the "dual sides" of an object. The book provides an exhaustive list of methods to accomplish such separation. Each method is illustrated with several examples of inventions in which it has been used.The book also presents the theory of dual technological systems and their evolution and shows how to use it when solving inventive problems.Surprising as it may appear, but developing the theory of thinking and attempts to formalize it, led to an insight into what mathematics is. It is the science about equal dualities. The latter means that axioms and theorems of mathematics can be reformulated to state the equivalence of dual expressions. This is demonstrated in the book on the example of the axioms of Euclidean geometry and some theorems of elementary mathematics.And the last but not the least the book is the first encyclopedia of dualities useful in inventive problem solving and forecasting technological evolution. Read more