 These suggestions solve some, but not all problems. While many of these mappings are not symmetrical, they are all still reflexive. But even if these formal issues could be resolved in one way or another, a view based on structural mappings would still face other serious problems. For ease of presentation we discuss these problems in the context of the isomorphism view; mutatis mutandis other formal mappings suffer from the same difficulties. Like similarity, isomorphism is too inclusive: not all things that are isomorphic represent each other. In the case of similarity this case was brought home by Putnam’s thought experiment with the ant crawling on the beach; in the case of isomorphism a look at the history of science will do the job. Many mathematical structures were discovered and discussed long before they were used in science. Non-Euclidean geometries were studied by mathematicians long before Einstein used them in the context of spacetime theories, and Hilbert spaces were studied by mathematicians prior to their use in quantum theory. If representation was nothing over and above isomorphism, then we would have to conclude that Riemann discovered general relativity or that that Hilbert invented quantum mechanics. This does not seem correct, so it doesn’t seem like isomorphism on its own establishes scientific representation (Frigg 2002: 10).