My point exactly - fields are real, they are not merely mathematical models. (It's just that some words acquire a more precise meaning, being formalized as part of a model, and while it's true that models may contain an additional "scaffolding" that has no analogue in reality, field is not one of those.)
Field is mathematical abstraction, used in mathematical model, to represent a physical thing.
Physical things are real. Mathematical abstractions are not. OpenGL is not real too, but it looks very real and accurately predicts reality. In OpenGL, field is array, e.g. "float[][][] field;".
