Iron Filings and Magnetic "Lines of Force"

The classic experiment of sprinkling iron filings onto a piece of white paper that covers a strong magnet reveals "Lines".

"Magnetic Lines of Force."

But iron filings in a magnetic field will self-assemble into "Lines" due to their own ferromagnetic * mutual attraction when within a magnetic field. That they're free to move about enables this self-assembly.

(* Likely not a prerequisite. Other materials that are not ferromagnetic might display similar emergent properties.)

The evident "Lines" are clearly an emergent property of the iron filings in a magnetic field, not a reflection of some deeper Line-like discrete structure of magnetic fields.

But the term Magnetic "Lines" of Force has embedded itself, arguably taking on more meaning than it deserves. I've seen it too many times to count.

Magnetic fields in free space will typically have a continuous ("smooth") nature, not discrete "Lines".

Iron filings do not reveal "Lines", they create them.

When I've seen this experiment, clearly showing "Lines", with the teacher explaining about "Magnetic Lines of Force", my immediate reaction is to ask, 

"Why are there six or seven Lines? Where did that number come from? Why not one, or 400?"