A scalar field is usually defined as a function which assigns a number to every point in space. But aren't all equations assigning a number to every point in space? For example, take z = x^2. If I plot it in a 2D graph, I get a line. But if I plot it in a 3D graph, I get a surface. So there I have it, I can safely say this equations defines a scalar field in 2D space. The point I'm trying to make is this. Every function of one and two variables can be treated as a function of three variables, where the third variable doesn't have any importance. Every curve can be extended into the third dimension to form a surface. So every function is assigning a number to every point in space, and this is a scalar field. Am I right?