How to translate math equations back to emotions?

Mathematics is the art of giving the same name to different things

Henri Poincaré, in The future of Mathematics, 1908

Poetry is the art of giving different names to the same thing

Unknown poet, in response to Poincaré

This post is basically the article Making concrete analogies and big pictures, with just different title. For Vietnamese readers, you can read my example of how I “translate” the connection projective geometry, representation theory, and harmonic analysis in my Vietnamese blog. Its explanation is provided at the end of the article above.