ABSTRACT
This chapter introduces the inverse approach to using algebraic inequalities for generating knowledge about real physical systems. The approach is based on meaningful interpretation of the variables entering the inequalities and the different parts of the inequalities. By interpreting an algebraic inequality that can be obtained from the Cauchy–Schwarz inequality, it is established that irrespective of the uncertainties related to the stiffness values of n springs (elastic elements), the equivalent stiffness of the springs connected in series is always at least n2 times smaller than the equivalent stiffness of the same springs connected in parallel. Similar relationships are valid for the electrical resistance of elements connected in parallel and series, the thermal resistance of elements connected in parallel and series and for capacitors connected in series and parallel. With these results, the chapter demonstrates that properties related to different domains can be inferred from the interpretation of the same inequality.
The meaningful interpretation of two new algebraic inequalities is used to extract useful knowledge and construct the most reliable parallel–series system. Finally, the meaningful interpretation of an inequality referred to as ‘the inequality of negatively correlated events’ is used to identify the system with superior reliability.
