The human brain is the only biological information system in the universe as we know it, that can willfully create “off-line” (i.e., without external information input in real time) images of non-existing things or never-experienced happenings, predict the long-term future of events, and make long-term plans (pet-owners: sorry, but this is an experimentally proven fact!). Physics is the art of crafting quantitative models, which are approximations of the reality “out there”, based on purely mental images—whether you are working with particle interactions in an abstract 11-dimensional space in M-string theory, or with the reconnection process in 3D magnetospheric physics. So, in the latter, “physical understanding” will depend on how well you can picture in your brain a model of what is going on “out there” in the magnetosphere. In elementary mechanics we create models with material points (as a purely mathematical concept which does not bear physical reality) as a useful mental image; in magnetospheric physics we tend to use magnetic field lines (which also are purely mathematical concepts, devoid of any physical reality).
Without in any way stepping into the hallowed halls of philosophy, I will discuss the “fake physical reality” of magnetic field lines (for instance: why don’t we ever play mentally with their orphaned relatives, the electric field lines??), and confront this with the “true physical reality” of (i) local electric currents (convection, equivalent and conduction); (ii) the distant sources of the magnetic field (mostly given currents); (iii) the distant and local sources of the electric field (mostly given distant time-dependent currents, and local polarization, respectively); and (iv) the effects of fast (v=c) vs. slow (v~VAlfvén) electromagnetic information propagation. My final Halloween Statement will be: If you have no clear picture in your mind of all the current and charge distributions and their time variations involved in what you are modeling numerically, you have not yet understood the physical processes involved. You merely may have solved an interesting but only mathematical problem.