A great quote by Douglas Hofstadter that I think is pertinent to the debate I’ve been having with Kaz Maslanka and Bob Grumman over my use of analogy in my “mathematical poetry”:
“Analogical thought is dependent on high-level perception in a very direct way. When people make analogies, they are perceiving some aspects of the structures of two situations — the essences of those situations, in some sense — as identical. These structures, of course, are a product of the process of high-level perception.”
From the essay The Pedagogical and Epistemological Uses of Analogy in Poetry and Mathematics by Marcia Birken and Anne C. Coon (and which cites work by fellow mathematical poet JoAnne Growney).
For the debate, see the comments attached to my essays, “On Mathematical Poetry.”