I think that Mathematics gets boring when it tries to prove itself.
Off the bat -- the difference between analogous and digital is only a question of resolution, so - now you can choose the spectacles you want to wear.
Analogy or analogous thinking (as opposed to analog thinking) is actually more a way of looking at things rather than a thinking process. Visually speaking, it is the overlaying of two, or more, matrices each one depicting a logic pathway, or OP_n at some potential ^x, and then looking at where, how and how much they overlap or are similar.
See also the blog and article on AI and teaching computers to laugh.
That which we call humor is our capacity to recognize that there are several ways to reach the same point.Although A in 1 may look similar to or seem to be the same as A in 1.,
by overlaying the logics
we can see that the same point has been reached by different ways.
See also my definition of paradox.