The common thread will be to talk about the recurrence phenomena that occur across various time scales in climate dynamics, and how one can characterize them mathematically within a unified framework. A discussion about whether there is any fundamental limitation inherent to their prediction — beyond the sensitivity of initial data that nowadays is almost taught in kindergarten — and the study of their sensitivity to perturbations, anthropogenic or not. This talk will try to deconstruct several passionate intuitions about it, illustrating how modern mathematical tools can help us to build-up a cold-minded understanding, without removing the excitement.