A contraction is said to be coalescent if it satisfies the following property: when the tracks of any two points meet, at time t, they remain together thereafter. We will see examples of compact contractible spaces which do not have any coalescent contractions; this absence of coalescence is linked to the existence of contractible non collapsible spaces. The lecture may serve as an introduction to the many exquisite and intriguing features of space contraction. References: Sections 1-3 (pages 1-15) from Shrinking Complexity : Some Heuristics for Contractible Spaces, Eduardo Francisco Rêgo (CMUP preprint 2005-43)