Continuing the discussion Categorizing with metaphor, analogy, generalization, and abstraction my next question is how two concepts metaphor/analogy equivalent to symmetry(change without change) .If yes how? Give me some examples
The concept of symmetry as "change without change" is already a "poetic" way to describe the fundamental concept of symmetry, which encompasses various forms like Reflectional Symmetry, Rotational Symmetry, Translational Symmetry, Scale Symmetry, and more. In other words, symmetry involves the constancy of fundamental qualities within an object or pattern despite undergoing different transformations. Therefore, if two analogous concepts fulfill the following conditions: 1) the definition of a transformation can be established, and 2) the results of these transformations are identical to each other, then symmetry can be defined. Merely applying "change without change" for discussing these matters lacks the necessary rigor.
Your insight that analogy aligns with generalization might be useful here. When there are two analogous concepts, A and B, their relationship represents a generalization—that is, two abstracted outcomes established over similar specific instances. Consequently, we can potentially "construct" a ratio function for the extracted predicate here and attempt to uncover another symmetry. However, I am doubtful whether this can be applied to any pair of arbitrary analogous concepts with a fixed transformation. Therefore, I perceive the responder's answer as negative.