Defining the field as "numbers in space" shouldn't detract from the idea that it has physical reality. “It occupies space. It contains energy. Its presence eliminates a true vacuum.”[2] The field creates a "condition in space"[3] such that when we put a particle in it, the particle "feels" a force.

If an electrical charge is moved, the effects on another charge do not appear instantaneously. The first charge feels a reaction force, picking up momentum, but the second charge feels nothing until the influence, traveling at the speed of light, reaches it and gives it the momentum. Where is the momentum before the second charge moves? By the law of conservation of momentum it must be somewhere. Physicists have found it of "great utility for the analysis of forces"[3] to think of it as being in the field.