Discovering Hidden Invariance

Chapters 4 and 5 both present different aspects of relationships between invariance and change. Whereas in Chapter 4 we initiated some change for the express purpose of ensuring the preservation of some value or property, in Chapter 5 we present some problems in which the change takes place by itself – “without our intervention” – meaning that the invariance (either a preserved value or some preserved property) is concealed during some transformation. Through the discovery of this existing, yet hidden, invariance, we are provided with a way of dealing with the change that paves the way to solving the problem.