Simone Weil reminded us that Greek science begins with Thales’ formulation of the concept of similarity between triangles. And she wrote that “here science would seem to be only a more attentive perception.” But science changes: following Simone Weil, Greek science was about numbers, figures and machines, whereas now science seems to consist only of pure relations (Sur la science). But we are interested exactly in this greater attentiveness, i.e. in actions of paying closer attention to something: from the ancient Greeks to Douglas Hofstadter’s cognition-core hypothesis, and beyond. Constructing ever more accurate, ever subtler analogies is still a method of refining our knowledge. Hence we propose an introduction to this approach to analogy and its applications, which encompasses its history but also new perspectives. We present selected and basic issues related to various concepts of analogy. We put a strong focus on their special and delightful flexibility: using analogies not only opens new areas and values within the metaphysical universe, but also teaches us attention in Simone Weil’s sense, and humility in a dialogical meeting with the Other.