> A thing cannot be isomorphic. It seems like it's pretty common to refer to something as Isomorphic X if it's an instance or implementation of X which relies

> A thing cannot be isomorphic. It seems like it's pretty common to refer to something as Isomorphic X if it's an instance or implementation of X which relies heavily on the concept Isomorphism. For example, in homomorphic encryption the homomorphism is really describing the relationship between the encrypted text and the clear text. Not the encryption itself, so really a pedantically correct name would be "encryption in which the clear text and encrypted text are homomorphic with respect to certain operations" but "homomorphic encryption" serves as shorthand for that. > Second, and more importantly, the client and the server do not share an isomorphism under this paradigm. An isomorphism describes two objects which have a mapping between them such that, for all intents and purposes, they are equivalent. “Equivalence” is a specific mathematical term distinct from equality: 5 and 7 are not equal, but under a function that outputs the same number for all odd inputs, 5 and 7 are equivalent. I disagree that they don't share an isomorphism and also disagree with your terms here. The standard definitions of isomorphism, at least the ones I found, do not seem to use the notion of equivalence, I'd be interested to see a link to one that does. Furthermore "equivalence" by itself isn't a specific mathematical term, again I'd be interested to see a link its definition but neither Mathworld or Wikipedia seem to have definitions. Equivalence Relation is defined but there are other uses of equivalence in math. > More precisely, you cannot tell two objects apart using only their properties Yes, and this seems to apply very well to the Client and Server because you can't tell them apart by running Go code on them since they both will give you the same answer. You can tell them apart by doing other things to them, but that's true of all isomorphisms. For example the groups ({0}, +) and ({1}, *). (0 under addition and 1 under multiplication.) Are clearly isomorphic since they're both just a group with their identity element. But you can also obviously tell them apart in other ways.