Comment by seanhunter

Not a physicist, but in classical mechanics stiffness is just the proportionality of some restorative force (ie the extent to which something tries to bounce back when you push it). It definitely would be overkill to make it an axiom.

So say you have a spring if you compress it, it pushes because it wants to go back to its natural length and likewise if you stretch it there is a restorative force in the opposite direction. The constant of proportionality of that force (in N/m) is the stiffness of the spring, and the force from the spring[1] is something like F=-k x with x being the position measured from the natural length of the spring and k being the stiffness. So not knowing anything about electromagnetism I read this and thought about fields having a similar property like when you have two magnets and you push like poles towards each other, the magnetic field creates a restorative force pushing them apart and the constant is presumably the stiffness of the field.

But obviously I’m missing a piece somewhere because as you can see the force of a spring is proportional to distance whereas here we’re talking about something which is short-range compared to gravity and gravity falls off with the square of distance so it has to decay more rapidly than that.

Edit to add: in TFA, the author defines stiffness as follows:

   For a field, what I mean by “stiffness” is crudely this: if a field is stiff, then making its value non-zero requires more energy than if the field is not stiff.

So this coincides with the idea of restorative force of something like a spring and is presumably why he's using this word.

[1] Hooke’s law says the force is actually H = k (x-l)ŝ where k is stiffness, l is the natural length of the spring and ŝ is a unit vector that points from the end you’re talking about back towards the centre of the spring.