I cannot make sense of your notion of visibility. Are you suggesting that there is a surface that may not be measured?
All of pure mathematics is "abstract." It is mathematical physics that, ultimately, may not be. For example, Einstein argued that the notion of spacetime is abstract (in my terms ist is not a "necessary distinction" but a "way of speaking"). In my work I have replaced this notion with energy/mass, arguing from a quantum pov that all particle necessarily have mass and allowing light to form the basis also of gravitation.
Other abstractions, are useful, but not all human inventions appear useful, and it is this utility that distinguishes between them. See the work of Charles Peirce, for example.
