Isomorphisms

From Gödel, Escher, Bach, by Douglas Hofstadter:
In the Introduction, the word “isomorphism” was defined as an information-preserving transformation. We can now go into that notion a little more deeply, and see it from another perspective. The word “isomorphism” applies when two complex structures can be mapped onto each other, in such a way that to each part of one structure there is a corresponding part in the other structure, where “corresponding” means that the two parts play similar roles in their respective structures.

A final word on the perception of isomorphisms: since they come in many shapes and sizes, figuratively speaking, it is not always totally clear when you really have found an isomorphism. Thus, “isomorphism” is a word with all the usual vagueness of words–which is a defect but an advantage as well.

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